A study of those factors that affect the propagation of sound energy in the sea and determine the subsurface path of a sound beam after it is transmitted from a transducer is essential to a full understanding of the sonar problem. Some of the factors that make up the transmission anomaly were discussed in chapter 1. The influence of temperature conditions in the upper layers was especially noted.

The variability in the transmission loss was first observed in actual echo-ranging operations at sea. In certain areas, the ranges achieved in the afternoons of clear, relatively calm days were found to be less than those obtained in the mornings. Temperature gradients change from season to season, from day to day, and even from hour to hour and place to place. Numerous explanations were advanced, but the true reason was discovered

  by the Woods Hole Oceanographic Institution as the result of experiments performed in cooperation with the Navy.

In many respects the ocean is very similar to the atmosphere, and thus there is a close analogy between oceanography, on the one hand, and meteorology and climatology on the other. One may speak of the subsurface weather and of its seasonal and diurnal changes, of the subsurface climate, and the annual and seasonal averages of the components of the weather.

The analogy between oceanography and meteorology holds true further in that one of the practical objectives of the oceanography of underwater sound is the forecasting of subsurface weather. The study of subsurface weather was neglected until its importance for underwater acoustics was recognized.

General Processes and Their Interaction
The outstanding characteristic of weather, both in the air and under the sea, is its changeability. This changeability is the outcome of a complex set of processes, which are continuously in action. Sometimes one of these processes may dominate all others; more often, several exert appreciable influences on the resultant.

There are at least 10 such processes that cause the temperature gradients in the upper layers of the ocean to change. They can be grouped conveniently into four general processes-(1) heating, (2) cooling, (3) mixing, and (4) flowing at a speed different from that of the underlying water. All four processes are closely interrelated but each has its own characteristic effect on the temperature

  gradients that are revealed by bathythermograms. Each process is caused by a variety of factors. All four, however, are affected by the condition of the atmosphere at the ocean surface. The immediate effect of each process is to alter the dynamic state of the surface layers.

Table 2 presents an outline of the general processes, with their causes and dynamic effects. A characteristic complication is illustrated by processes 2 and 3-cooling makes the surface layer unstable, and instability in turn causes mixing. In the same way, strong currents may cause turbulence, which again results in mixing. There are many other chains of cause and effect linking all the processes.


TABLE 2 -Outline of Processes Influencing Temperature
General process Cause Dynamic effect
Heating Sunshine and/or warm, moist air. Stability of surface layer.
Cooling Evaporation, back radiation, and/or cold, dry wind. Instability of surface layer.
Mixing Wind and waves, instability and/or turbulence. Neutral stability of surface layer.
Flowing Wind and waves, internal waves, and/or currents. Variable; turbulence if strong.


Bathythermograms show that the ocean is more or less stratified. Two points separated by several hundred yards but at the same depth beneath the surface have practically the same temperature. If the ocean were in equilibrium, this stratification would be complete. The warm, lighter water would be at the surface; the cooler, heavier water would be at the bottom; and the boundaries between strata would be horizontal surfaces. Such an equilibrium is disturbed by three of the four general processes. The observed stratification is thus the result of other processes tending to bring the ocean to equilibrium.


It is a general hydrodynamic principle that when a mass of fluid is in stable equilibrium under the force of gravity its density must everywhere increase in the downward direction and be constant in every horizontal plane. A commonplace illustration of this principle is furnished by a bottle containing oil and water.

The density of sea water is determined primarily by its temperature and salinity. The changes due to temperature are the largest, just as with the velocity of sound. However, salinity has a proportionately greater effect on the density of sea water than on the velocity of sound.

In the open ocean, where the salinity is practically constant, the lighter water almost always is the warmer water, and it is to be expected that the temperature either remains constant or decreases with increasing depth. Near the shore, salinity

  differences may sometimes dominate the density distribution so that a layer of cold dilute water may overlie warmer water of high salinity.


The concept of stability is a convenient one to apply. Stability depends on the rate at which density increases with depth. If the temperature in a layer decreases rapidly with depth, as in the thermocline, the layer has high stability, for the density increases rapidly. On the other hand, a layer in which the density decreases with depth is unstable and exists only transiently.

Mixing processes are retarded by high stability; thus wind of a given strength may easily mix a surface layer in which the temperature gradient is small and the stability is low. The same wind may have little mixing effect if the temperature gradients near the surface are large. The development of a sharp thermocline tends to retard mixing to greater depths.

A completely mixed isothermal layer has neutral stability. Cooling at the surface increases the density of the surface layer, Evaporation, because of the cooling and the increase in salinity that accompany it, also increases the density of the surface layer. Hence these processes tend to make the density of the surface water greater than that of water immediately below it and to produce a condition of instability. This unstable density distribution near the surface results in convective mixing.

The stability can be estimated from a bathythermogram if the salinity gradients are assumed to be negligible. Density decreases with increasing temperature and for most practical purposes the isotherms on the bathythermogram grid can be interpreted as lines of equal density. The slope of the temperature trace is therefore a measure of the rate of change of density with depth-that is, of stability. If this fact is kept in mind, the bathythermograph traces can be interpreted in terms of the four major processes.


Negative thermal gradients are very stable because there is little exchange of heat between neighboring layers unless they are mixed by some General Processes and Their Interaction


Depth vs. temperature charts for 6 months.
Figure 2-1 -Annual cycle of ocean temperature gradients.

stirring action. This fact is shown readily by laboratory experiments. If a tank is partly filled with warm water, and if water of room temperature is then run in through a hose lying on the bottom, the warm water floats on the colder. Thermometers placed in the two layers show that the cooler water is not heated by the overlying warm water.

This stability of layers when the temperature gradients are negative is in marked contrast to the instability of positive temperature gradients. In the experiment of warm and cold layers of water in a tank, the surface of the warm layer may be cooled by blowing a gentle stream of cold air over it. The cooling of the layer at the immediate surface causes it to become heavier than the water beneath it. Consequently it sinks and in so doing mixes with and cools the underlying water. Two thermometers at different depths in the warm layer show that cooling proceeds nearly simultaneously at all depths, without the development of large positive temperature gradients. The mixing that accompanies cooling is called convective overturn.



The progressive or intermittent effects of the four processes-heating, cooling, mixing, and flowing-lead to the complicated and variable conditions illustrated in figure 2-1. The manner in which any one of these processes operates individually to change the bathythermogram is shown in figure 2-2. The change in temperature distribution produced by solar heating is illustrated by curves 1, 2, and 3 in figure 2-2, A. Initial conditions, indicated by curve 1, are assumed to be isothermal. The absorption of heat, accompanied by some mixing, results in curve 2 and finally curve 3. Negative gradients extending from the surface downward are characteristic of recent heating. The negative gradients, and consequently the stability, become greater as the amount of mixing that occurs during the heating becomes smaller. Under these conditions, wind is the principal cause of mixing.


The cooling that takes place during the night and during the winter is essentially a reversal of the heating process. In curve 1 (figure 2-2, B),

  Four bathythermograms as described.
Figure 2-2 -Manner in which the general processes working individually change the bathythermogram. A, development of negative gradient by heating of surface layer; B, development of isothermal surface layer by cooling; C, development of isothermal surface layer by mixing; D, effect of current.

which is assumed to be the same as curve 3 in the preceding diagram, surface cooling with its accompanying convective overturn produces curve 2 and ultimately curve 3. If continued long enough, it would finally produce completely isothermal water. Although the cooling takes place at the surface, measurable positive gradients do not develop because of the mixing involved in the convective overturn. Winds hasten this mixing process, but convective overturn takes place even in very calm weather. Theoretically, the upward transfer of heat must be associated with slight positive gradients, but such gradients are so small that they usually escape detection.


The result of vigorous mixing by the wind, when there is no gain or loss of heat by the surface layer, is illustrated in figure 2-2, C. Note that in this example surface isothermal layers develop just as they did in figure 2-2, B, and the surface temperature decreases, but the temperature distribution immediately below the mixed layer is different. The wind mixes warm water with cooler water beneath it, increasing the temperature at intermediate depths, and thus produces a very sharp thermocline instead of retaining the initial gradients present when cooling is the primary cause of the mixing. Curve 1 in figure 2-2, C, is the same


as curve 1 in figure 2-2, B, but the result of wind mixing without cooling produces distributions quite different from those resulting from cooling alone. Obviously, conditions intermediate between those of figures 2-2, B, and 2-2, C, often develop, because cooling and wind mixing can occur simultaneously.


The effect of addition or removal of water by currents is illustrated in figure 2-2, D. Curves 1, 2, and 3 show the development of an isothermal layer; curves (1), (2), and (3), of a negative gradient. The transfer of water can be produced by various causes, such as winds. If warm surface water is carried over the top of cooler water, a progressive change in temperature distribution may occur, as illustrated by curves 1, 2, and 3. If warm surface water is removed, the reverse sequence, indicated by curves (1), (2), and (3), may develop. Note that the gradients remain unchanged and are merely lowered or raised. Internal waves,. which periodically raise and lower the thermocline, can cause similar effects in a very short time. These waves may be single or have a well-defined periodic character and are accompanied by single or periodic surges of current.


The four general processes all involve passage of time-that is, continued heating, cooling, wind mixing, or flowing produces progressive changes in the temperature distribution. In the sea the temperature distribution in a given locality is the result of interplay of all four processes. For a limited time, such as during one afternoon, one of them may dominate, so that the temperature conditions near the surface are the result of heating, cooling, wind mixing, or currents. The complicated distributions illustrated in figure 2-1 are usually the result of intermittent action of the four general processes.

Thermal Structure at Great Depths

All these processes except the flowing originate at the sea surface, and their effects are propagated to greater depths by convective overturn or mixing or both. These effects are rarely noticeable at

  depths greater than from 600 to 700 feet. Below these depths, stable stratification exists at all times, and the only changes are due to slow seasonal currents. This deep region is therefore characterized by the so-called permanent thermocline or negative temperature gradient.

The density of sea water increases with decreasing temperature down to the freezing point (about 28.5° F), which sets a lower limit for the temperature in the sea. Below 6,000 feet the temperatures everywhere are less than about 37.5° F and decrease with depth. They also decrease toward the south, where the coldest water is formed.1 The circulation of the deep, cold water is exceedingly slow, probably of the order of 1 foot per minute. For all practical purposes the conditions in the deep sea do not change with time; they do, however, vary slightly from one region to another. In any one locality below about 3,000 feet the temperature decreases slowly and the salinity is either constant or increases slightly with depth.

Annual Cycle

In middle and higher latitudes there is a marked annual cycle in temperature conditions. The cycle can be observed in figure 2-1, which is based on bathythermograms taken in the open ocean, in latitude 40° N in the North Pacific.

It is convenient first to consider conditions in March. The isothermal layer then is more than 450 feet thick, and is produced by cooling and by mixing induced by winter storms. In May some heating of the surface layers occurs, and mixing by winds produces an upper isothermal layer of a slightly higher temperature than the original; thus, there is a small thermocline at a depth of about 150 feet. The negative gradient at the surface probably represents heating during the day and is either obliterated by wind mixing or disappears during the night because of cooling and convective overturn.

Progressive heating continues through the summer months so that the temperature near the surface increases, as shown by the July and September bathythermograms; but wind maintains a mixed layer with a rather sharp thermocline, which increases in depth as the season progresses.

1 H. U. Sverdrup, M. W. Johnson, and Richard H. Fleming, The Oceans, New York, Prentice-Hall, 1942.

 Effect of wind on the average temperature gradient in the surface layer during various seasons.
Figure 2-3. - Effect of wind on the average temperature gradient in the surface layer during various seasons.

In the fall, cooling once more exceeds heating; the surface isothermal layer becomes cooler; and, with the added effect of strong winds, the thermocline goes deeper until in January it is below 400 feet. Cooling and mixing continue until about March.

In general the systematic seasonal changes are subject to modification by local weather conditions. The mixing of the surface layer by wind is especially important in this connection. In figure 2-3 the average temperature decrease in the top 30 feet is plotted for each season as a function of wind force. High winds can practically obliterate the seasonal trend.

Diurnal Cycle

The diurnal cycle in temperature conditions is in many ways a miniature replica of the annual cycle, but it must be remembered that progressive heating occurs during the spring and summer and that progressive cooling and mixing occur during the fall and winter. Consequently, the daily cycle sometimes is practically obliterated by the progress of the seasonal changes.

Four selected examples of diurnal changes are given in figure 2-4. The data are from the open ocean and are based on bathythermograms taken over periods of from 23 to 48 hours during the summer. Each set has been adjusted so that the temperature at a depth of 50 feet is used as the reference. The heating is indicated by shading.

The series shown in figure 2-4, A, was taken during a day when winds averaged force 3. Although heat was added to the water, the stirring

  action of the wind caused a mixed layer to persist near the surface throughout the day. The layer was so shallow, however, that poor sonar conditions prevailed during the afternoon. During the night, cooling and mixing resulted in isothermal conditions to a depth of 50 feet.

The series shown in figure 2-4, B, is an example of heating on a day with light winds when negative gradients extended to the surface during the late morning and afternoon. Beginning at 1800, a mixed layer was present and cooling continued during the night. An observation at 0600 the next morning showed a small positive gradient which had disappeared by 0800.

The series shown in figure 2-4, C, covers a period of approximately 48 hours with variable winds. No progressive heating is noticeable, and there is a return to isothermal conditions each night.

Diurnal cycle of ocean temperature gradients.
Figure 2-4 -Diurnal cycle of ocean temperature gradients. A, Persistent mixed surface layer; B, typical diurnal cycle with light winds; C, variable winds with changeable pattern; D, persistent negative gradients.


The series shown in figure 2-4, D, is an example of heating when a negative gradient existed early in the morning. The shallow isothermal surface layer had practically disappeared at noon; the gradient became progressively more pronounced during the day and persisted during the following night.

As in the annual cycle, high winds can obliterate the daily cycle in the upper 30 feet. This fact is shown in figure 2-5.

Effect of wind on the average temperature gradient
in a surface layer at various times of day.
Figure 2-5 -Effect of wind on the average temperature gradient in a surface layer at various times of day.

  Afternoon Effect

In general, strong negative surface gradients are most common in the afternoon and produce what is called the afternoon effect. The gradients reach a maximum about 1600 and a minimum about 0600. Because solar radiation is greatest in the summer, such gradients are more common during the summer than during the winter.

This simple explanation is essentially correct but fails to provide an explanation of the geographical distribution effect. Instead of being most frequent at the equator, where solar radiation is greatest, the afternoon effect is actually less frequent there than in high latitudes. Solar radiation is undoubtedly the primary cause of the negative surface gradients, but the magnitude of its effect is modified by the other three factors, especially wind mixing and evaporation.

Although in the open ocean, afternoon effect is most frequent in high latitudes, this principle does not necessarily apply inshore. The waters off southern California, for example, are noted for the prevalence of afternoon effect.

Analysis of the Four Processes
The preceding paragraphs have indicated the general types of temperature distribution encountered in the sea and the four major processes that affect the temperature conditions. The causes of temperature conditions will now be discussed.


The temperature structure of the ocean is determined primarily by its heat content, which is a constantly varying quantity. There is a continuous exchange of heat at the surface of the ocean. The ocean receives heat by absorption of the sun's radiation and by the condensation of water vapor in the air when the water is colder than the air. The ocean loses heat by radiation to the sky, by evaporation of water vapor when the water is warmer than the air, and possibly by conduction. Of the received heat, by far the largest quantity is due to incoming solar radiation. Over the ocean as a whole incoming solar radiation is balanced by the cooling resulting from reradiation and evaporation. The effects of other processes are comparatively negligible.

  Incoming Radiation

The incoming radiation includes the invisible infrared and ultraviolet as well as the visible light. Because it is received from the sun and the earth's atmosphere it obviously varies with latitude, time of the year, time of day, and atmospheric conditions-particularly the cloud cover. The total energy received during the year decreases with increasing latitude. In the lower latitudes of the tropical regions the seasonal variation is small, but with increasing latitude the difference between the amounts received during the summer and winter becomes very great. The effect of clouds is very pronounced-a heavy cover of cloud may reduce the incoming radiation to less than 25 percent of that received on a clear day.

Direct heating of the water by the sun is limited to relatively shallow depths (fig. 2-6). Only about 3 percent of the radiation penetrates below 300 feet and over 50 percent (all of the infrared) is absorbed in the first few inches. If there were no compensating heat losses and no mixing, fantastically high surface temperatures and extremely sharp negative gradients just below the


Spectrum of radiant energy at various depths in the ocean.
Figure 2-6. -Spectrum of radiant energy at various depths in the ocean. Insert: Percentage of incident radiation reaching various depths.
surface would occur. The penetration of light varies somewhat from place to place depending on the amount of suspended debris and organic pigments in the water. The foregoing discussion applies to the open ocean. Near shore and in areas of vigorous plant growth the water is practically opaque to all wavelengths.

Besides the direct solar radiation, the sea surface also receives some infrared from the air. Although the air is an appreciable source of heat, it is customary to subtract it from the corresponding infrared radiation emitted by the sea surface.

Effective Back Radiation

The excess of infrared emitted by the sea surface over that received from the air is called effective back radiation.2 Effective back radiation balances somewhat less than one-half of the incoming solar radiation, on the average. It decreases with increasing water temperature and with increasing humidity and cloud cover. With heavy, low-lying clouds present, the effective back radiation drops to less than 25 percent of that on a clear day, largely because the clouds are themselves sources of infrared and radiate heat into the ocean on their own account. Clouds prevent direct solar radiation from reaching the sea surface. Heat

2Oceanography for Meteorologists. New York, Prentice-Hall, 1942.
  losses from back radiation occur in the uppermost fraction of an inch of the water and are transmitted to greater depths by convective overturn and wind mixing.


Evaporation depends primarily on the temperatures of the water and the air, on the humidity, and on the wind strength. Evaporation can be understood best by considering the process as one of transfer of water vapor away from the surface. The greater the water-vapor gradient, the more rapid is the evaporation and hence the greater is the heat loss. Cold, dry air overlying warm water therefore favors rapid evaporation. High winds increase evaporation by removing the water vapor.

The relative importance of the heat losses through evaporation and back radiation can be seen from the average heat budget between 70° S and 70° N, as follows:

Total heat received 0. 221
Evaporation losses 0. 118
Effective back radiation 0. 090
Conduction to atmosphere 0. 013
Total heat lost 0. 221


Convective Overturn

Thus far only the cooling effect of evaporation has been considered. When surface water cools, its density increases and causes convective over-turn. Equally important is the increase in salinity resulting from evaporation; the increased density arising from this cause contributes greatly to overturn and to the development of isothermal surface layers. Thus, cooling by evaporation is even less likely to be accompanied by positive temperature gradients than is cooling by back radiation.

Conditions that tend to lessen the salinity of the surface layer would, of course, have the opposite effect and would tend to favor the development of positive gradients. Such a condition might result from precipitation. For the ocean as a whole, however, evaporation exceeds precipitation. This fact is illustrated in figure 2-7. Shaded areas show regions where precipitation exceeds evaporation. The symbol 0/00 represents parts per thousand. Note that regions of excess evaporation in low latitudes and mid-latitudes correspond to regions of relatively high surface salinity and deep thermoclines. Just north of the equator and in latitudes above 40°, where precipitation exceeds evaporation, the surface salinity is low.

Variation of average evaporation, precipitation,
and salinity with latitude.
Figure 2-7 -Variation of average evaporation, precipitation, and salinity with latitude.


Effect of wind on the temperature gradient in the
surface layer at various latitudes.
Figure 2-8.-Effect of wind on the temperature gradient in the surface layer at various latitudes.

The deficit in the water content of the ocean that is caused by the general excess of evaporation over precipitation is made up by run-off from land. Near land-especially near the mouths of rivers-surface salinities are lower than in the open ocean. This condition favors the development of positive temperature gradients, because it increases their stability.

Mechanical Mixing

Mechanical mixing is caused by wind and does not necessarily involve any gain or loss of heat. nevertheless, it may modify the temperature distribution. The effect of winds depends not only on their strength, but also on their duration and on the distance over which they have blown It is obvious that the first effect of the wind is confined to the immediate surface, but that the turbulence extends to greater depths after the wind has been blowing for some time. The original density distribution of the surface layer affects the rate at which the turbulence penetrates the layer. A very stable layer is less easily mixed.

Effect of Rotation of the Earth

The daily rotation of the earth about its axis also affects the depth to which the wind mixing penetrates. Present theories agree that a wind of given force ultimately produces a deeper mixed layer in low latitudes than in high.

This principle is probably part of the explanation of the data shown in figure 2-8, which indicate that strong negative gradients are most apt to be formed in high latitudes. If negative surface gradients are interpreted naively as being the result of solar heating alone this condition is most


unexpected, because heating is greatest at the equator. The necessity for considering all four of the major processes, with the detailed mechanisms causing them, is emphasized by figure 2-8.


Drift Currents

The frictional drag of the wind sets up drift currents which flow at less than 3 percent of the wind velocity. These drift currents do not flow with the wind, but are deflected 45° to the right in the Northern Hemisphere and 45° to the left in the Southern Hemisphere. This deflection is caused by the earth's rotation and is closely related to the influence of the earth's rotation on the depth of mixing, which was just discussed.

Permanent Currents

The redistribution of density resulting from the wind-drift currents in turn maintains the permanent currents. Under the influence of the steady wind systems, such as the trade winds in the low latitudes and the westerlies in high latitudes, these permanent currents form the large-scale current system of the oceans. They are thus partly the indirect result of geographic differences in the heating and cooling of the water and partly the result of wind action. The character of the currents is influenced also by the configuration of the oceans, but in general there are clockwise gyrals in the Northern Hemisphere and counter-clockwise gyrals in the Southern Hemisphere. Smaller currents related to land topography and local climate exist near the continents. A counter current flows eastward between the two westward-flowing equatorial currents.

The permanent currents have several effects on the temperature conditions. Currents with poleward flow tend to carry warm water into cooler regions. Conversely, currents with equatorward flow tend to carry cool water into warmer regions. Within the currents themselves the distribution of

  density produces a temperature gradient such that in the Northern Hemisphere the water on the left side of the current has a lower average temperature than the water on the right side. This condition may be reflected by a thinner mixed layer or even by lower surface temperatures. In the Southern Hemisphere the structure is reversed.

Divergence and Convergence of Surface Currents

Divergence of the surface currents may occur under the influence of the wind. Examples of this effect are found along the western coasts of the continents and in the vicinity of the equator in the eastern parts of the Atlantic and Pacific. In these areas upwelling brings water toward the surface from moderate depths and the thermocline may be shallow or, rarely, absent.

The opposite effect, convergence, occurs in the center of the subtropical gyrals in the Northern and Southern Hemispheres. In these regions the surface water accumulates, and consequently the thermocline may be very deep.

Tidal Currents

Tidal currents in partially isolated, shallow areas have a marked effect on temperature conditions because they also cause turbulent mixing. In areas of strong tidal currents-for example in the English Channel-the water may remain virtually mixed throughout the year, although there is heating and cooling of the water column as a whole.

Internal Waves

Internal waves also affect the temperature distribution. The effect of these waves is reflected in a periodic rise and fall of the thermocline. Periods as long as 24 hours are known to exist, and recent studies have shown that periods of only a few minutes may occur. Whether there is a continuous spectrum of frequencies is not known.

Geographical Variations

The annual cycle in temperature conditions represents the net effect of the annual sequence in

  the various factors described, particularly in the amount of radiation received, the heat losses associated with evaporation, and the character of prevailing winds. In low latitudes where these factors do not vary appreciably there is little

change in conditions throughout the year, except that near the continental boundaries changing monsoon winds may introduce variable conditions.

The annual cycle is most conspicuous in the latitudes of from 40° to 50°. This condition is to be expected, because in these regions the surface experiences the greatest range of temperature. The effects of this great variation in temperature are magnified by the fact that in winter the cooling due to low temperatures is increased by the greater evaporation that occurs at this season. The resultant increase in the density of the surface water facilitates mixing and thus contributes to the seasonal variation.

The annual cycle is even more pronounced in regions near land, and in areas where heavy precipitation occurs and light winds prevail during the spring and summer. These conditions tend to induce even more extreme negative gradients than those shown in figure 2-2. These gradients can also be observed generally in areas of flow toward the equator, in which cool water is being heated-for example, off the California coast.


The diurnal change in temperature gradients is essentially similar in principle to the annual cycle, but the temperature changes are smaller and do not extend to such great depths. The incoming

  solar radiation depends on latitude, time of year, time of day, and cloudiness. The diurnal cycle of incoming radiation changes during the year, the variation being least near the equator and increasing toward the poles. Above the polar circles, of course, there are days of complete darkness during winter and continuous daylight during summer. The diurnal change is not necessarily cyclic, as is time annual change, and progressive heating or cooling of the water is characteristic in middle and high latitudes. Within the tropics, where the annual variation is small, diurnal changes are more nearly cyclic.

Even if the total heat absorption is the same, the character of the changes in temperature gradients may be quite different, because these changes depend on the previously existing gradients and on the wind conditions. A negative gradient near the surface is increased by incoming heat unless a strong wind (force 4 or greater) springs up. On time other hand, the changes in an initially mixed (isothermal) layer depend critically on the wind strength. The development of surface gradients is common when the wind force is 3 or less but is rare with winds above force 4. (See figures 2-3, 2-5, and 2-8.) In the trade-wind belts, therefore, development of surface gradients during the day is a rather rare condition-probably another factor to be considered in explaining figure 2-8.

Summary of Conditions for Temperature Gradients
The regional differences in temperature structure can be explained in terms of the factors described. The discussion can be summed up as follows:

An isothermal layer near the surface is the result of mixing. The factors inducing mixing are (1) wind, (2) radiative cooling, (3) evaporation, with its consequent cooling and salinity increase.

Strong negative gradients are the effect of heating a stable surface layer, without much wind mixing.

  Strong winds may tend to prevent the formation of negative gradients.

Positive gradients are produced only in areas where cool, dilute water flows or is formed on top of warm, more saline water. Measurable positive temperature gradients are most common during the fall and winter months in the northwestern Atlantic and Pacific Oceans, where cold, dilute coastal waters are driven offshore by the wind and flow over the warm. but saline ocean water of higher density.

Echo formation from discontinuities in a medium, such as suspended air bubbles in water, has been discussed in chapter 1. In sonar, the principal source of discontinuities that produce   echoes, reverberation, or scattering is the wake of a ship. The acoustic properties of a wake are important because of their influence on transmission and operational procedures.

Wake of U. S. S. Moole (DD).
Figure 2-9. -Wake of U. S. S. Moole (DD) at 20 knots, From 2,500 Feet.

Woke of U. S. S. Ringgold (DD).
Figure 2-10. -Woke of U. S. S. Ringgold (DD) from 300 feet.


Wake of surfaced submarine at 15 knots.
Figure 2-11. -Wake of surfaced submarine at 15 knots.

Swirl behind submarine after crash dive.
Figure 2-12. -Swirl behind submarine after crash dive.



The wake of a ship is most readily seen from the air (figures 2-9 through 2-12). The surface waves that spread out in a V-shape behind the vessel and form a navigational hazard for nearby small craft are relatively inconspicuous from the air. Even the white bow wave, which breaks and sends foam back along the sides of the vessel, is inconspicuous compared to the wake of the turbulent, foamy water that fans out from the screws.

This turbulent wake spreads rapidly for a fraction of the ship's length, and thereafter widens only slightly. The divergence has been measured for various wakes and found to vary from 0.5° to 5°. The foam, which makes it visible from a distance, gradually disappears, but not until long after the ship has passed. The visible wake of a high-speed vessel extends from 20 to as much as 50 ship lengths astern.


It is fairly obvious that the violent disturbance which creates the turbulent wake gives it physical properties that differ to a greater or lesser extent from those of the undisturbed ocean surrounding it. For example, if there is a temperature gradient in the upper part of the ocean, the mixing of the surface water with that of lower layers gives the water in the wake a different temperature from that of the nearby water at the same depth. This effect has been observed by the use of sensitive recording thermometers. The mixing of water from different depths may also result in anomalous density gradients.


Of most interest at this point are the acoustic properties of the wake. They are probably all associated with the presence of entrained air bubbles. Aerial photographs show, that large numbers of bubbles remain in the wake for several minutes. It is likely that some remain suspended in the water even after the visible foam disappears.

These acoustic properties of the wake are easily demonstrated with sonar gear. Figure 2-13 shows a record of echoes obtained from the wake of the E. W. Scripps. This vessel ran between the echo-ranging vessel and a small sphere, the echoes from

  the small sphere being recorded simultaneously with those from the wake.

Two general conclusions can be drawn from figure 2-13o(1) the wake echo gradually lengthens and becomes fainter, presumably because of the spreading of the turbulent wake and the gradual disappearance of the bubbles, and (2) the sphere

Range recorder trace of wake echoes.
Figure 2-13 -Range recorder trace of wake echoes.


echo is weakened slightly but noticeably by the wake between the sonar and the sphere.

Thus, we may conclude that the wakes of surface vessels have two major acoustic properties-(1) they return echoes that are readily detectable by ordinary sonar gear, and (2) they act as acoustic screens, reducing the intensity of the echoes from targets on the far side of the wake.

Causes of Acoustic Properties of Wakes

The two most obvious differences between a surface wake and the undisturbed ocean are (1) the turbulence of the wake and (2) its content of bubbles. It is therefore reasonable to assume that one or both of these factors are the cause of its acoustic properties.

The possibility that turbulence is the cause of wake echoes is ruled out by theoretical considerations. It is true that when a sound wave passes through turbulent water it is scattered, but two facts exclude the possibility that this scattering is the cause of echoes-(1) the scattering from turbulence is very weak unless there are great differences in velocity between pairs of points separated by 1 wavelength of the sound, and (2) the intensity of the scattered sound depends strongly on the direction of scattering, and the intensity in the backward direction is zero. Thus, although turbulent water scatters sound, it does not return an echo.

Turbulence may be an indirect cause of the echoes by mixing the warmer surface water with that from below. From this mixing, irregular differences of temperature are produced, which cause irregular differences in sound velocity in the turbulent water. However, the magnitude of the expected effect is too small. To produce the observed echoes, temperature differences of nearly 1° F would have to occur between points only 1 wavelength apart. Such large temperature differences are very improbable. Moreover, if they were formed in some way, they would persist for a much longer time than wakes are observed to persist.

Thus, it may be concluded that the air bubbles in a wake are the major cause of the acoustic properties of the wake. Several objections have been urged against this conclusion. One objection is based on the supposed short life of bubbles in water. Bubbles rise to the surface and break, so


  that they disappear from the wake in a short time; their disappearance is also hastened by absorption of air by the sea water. On the other hand, echoes have been obtained from wakes more than 10 minutes after the vessel has passed, and there have been reports of echoes from wakes several hours old. The latter reports may be discounted, because it is very difficult to be certain of the position of a wake so long after the ship has passed, and it is quite possible that a school of fish, for example, might be mistaken for a wake under such circumstances. It is therefore necessary only to show that some bubbles remain suspended for periods of from 10 to 30 minutes.

Experimental evidence on this point was obtained by stirring the water of the pool at U. S. Naval Electronics Laboratory (USNEL) with an outboard motor. The acoustic properties of the water were studied with an echo sounder. It was found that sound was returned from the body of the water after stopping the motor. This return continued even after all the more obvious bubbles and turbulence had disappeared. Closer examination showed, however, that a relatively small number of small bubbles remained suspended. They were very difficult to see except when they drifted into a region of favorable illumination, so that neither their number nor their size could be accurately determined. It was concluded that sufficient bubbles were present to explain the observed effects. This conclusion was based on the consideration that very small bubbles are quite effective in scattering sound and rise very slowly.

The rate of rise of the bubbles which are most effective in scattering is about 1 yard per minute. These results for still water do not apply directly. to wakes or turbulent water. The long-lived bubbles observed in the USNEL pool did not show any marked tendency to rise but were carried in irregular paths by the motion of the water. This condition is analogous to the effect of air currents in keeping dust from settling. It is reasonable to suppose that the moderate turbulence in an old wake has this same effect and prevents the disappearance of the bubbles.

Propeller Cavitation as a Source of Bubbles

The second objection to air bubbles as the cause of acoustic properties in wakes is based on the fact that echoes are obtained from the wakes of


Cavitating propeller.
Figure 2-14 -Cavitating propeller.

submerged submarines and the idea that most of the bubbles in a wake come from the breaking bow wave. Aerial photographs strongly suggest that, this idea is not correct, because most of the foam appears to come directly from the screws. This idea is borne out by the observation that the wake laid by a vessel under sail is less acoustically active than the wake of the same vessel under power.

Hence, most of the bubbles are caused probably by cavitation at the propellers. Photographs of this phenomenon are shown in figures 2-14 and 2-15. In figure 2-14, the water in the jet is moving away from the observer. The back of each blade is half covered with cavitation bubbles and a cavitation void which extends for some distance behind the blade, whereas the face of each blade is clean. In figure 2-15, the cavitation of the rotation of the propeller and the flow of the water in the jet from left to right gives a spiral pattern to the vortices.

The bubbles are formed far from the air-water interface and are not sucked under from the atmosphere. The mechanism of cavitation is apparently similar to that of boiling. Because of the motion of the screws the hydrostatic pressure is reduced; the boiling point of water is lowered by this reduced pressure and boiling occurs. For example, pure water boils at 60° F if the pressure is reduced much below one-sixtieth of an atmosphere.

  However, sea water is not pure. In the present discussion, dissolved air is the most important impurity. Dissolved air is present in such quantities that sea water boils at 60° F whenever the pressure is reduced much below 1 atmosphere. The bubbles produced by this boiling are filled principally with air, rather than water vapor. Once formed, these bubbles are apparently quite stable-that is, the rate at which the air is redissolved is very slow.

Even in the wakes of surface vessels, much of the foam is probably the result of cavitation, and only a part of it is probably caused by air dragged under from the atmosphere. In the wakes of submerged submarines the only sources of air other than cavitation might conceivably be leaky high-pressure air lines.

Dependence of Cavitation on Depth and Speed

Cavitation depends critically on propeller rpm. A given propeller at a given depth of submergence produces no bubbles unless its speed exceeds a certain critical value; when the speed exceeds No, the number of bubbles formed increases very rapidly, but not according to any known law.

The critical speed itself, however, depends in a simple manner on h, the depth of the propeller beneath the sea surface. Expressed as an equation, this dependence is

No2/h = constant.  (2-1)

Figure 2-15 -Tip vortices emanating From a propeller.
Figure 2-15 -Tip vortices emanating From a propeller.


Thus, if a given propeller begins to cavitate at 50 rpm when at a depth of 15 feet, it begins to cavitate at 100 rpm when at a depth of 60 feet and at 200 rpm when at a depth of 240 feet.

The constant in equation (2-1) depends on the design of the propeller, and on any accidental changes in its shape that may occur in service. A scratch or nick caused by some accident usually reduces appreciably the value of the critical speed. One remarkable property of cavitation is that the bubbles themselves scratch and scar the metal surface on which they are formed.

This theory of the relation between cavitation and the acoustic properties of wakes has certain consequences that can be qualitatively checked. Thus, the wake of a submerged submarine should return echoes, but the echoes should be considerably weaker than when the ship is moving on the surface. They should also become progressively weaker as the depth of submergence increases. Finally, they should increase rapidly with propeller speed. All these conclusions are in general agreement with experience.

The propellers are probably not the only source of cavitation bubbles. Because the ship as a whole is moving through the water, cavitation can occur at other places. In general, the smaller the object, the lower is the critical speed at which cavitation occurs. Thus, small fittings or handrails on the deck of a submarine may become sources of cavitation bubbles when submerged.


The theoretical discussion of the acoustic properties of water containing air bubbles is complicated, and the studies are not complete. To present the general ideas of the theory without confusion, it is convenient to introduce certain terms for the description of water containing bubbles.

In foamy water the average distance between neighboring bubbles is less than the average diameter of the bubbles. The walls separating the bubbles may occasionally be very thin, as with soap suds. The acoustic theory of foamy water has not been studied, but lack of this information is not important because wakes probably contain foamy water only at the air-water surface, where the bubbles tend to accumulate.

  In bubbly water the average distance between neighboring bubbles is considerably greater than the average diameter of the bubbles but much less than the wavelength of the sound involved. For practical purposes, water may be considered to be bubbly if it contains less than 1 part per 1,000 (by volume) of air and foamy if it contains much more than this amount. The bubbles are dispersed if the average distance between neighbors is greater than both 1 wavelength of the sound and the average diameter. Thus, a portion of a wake may be dispersed for ultrasonic frequencies and bubbly for sonic frequencies.

It would be useful to have information concerning the foamy, bubbly, and dispersed regions of typical wakes. Unfortunately, there is relatively little information of this sort other than that which can be obtained from the inspection of aerial photographs or deduced indirectly from acoustic measurements. The wake probably reaches the dispersed state between 5 and 10 ship lengths astern of the screws; it is foamy only in the immediate neighborhood of the screws or at the air-water surface.

Scattering and Absorption of Sound in Wakes

Except for some details, the theory of dispersed wakes is similar to the theory of reverberation.

Consider a region where the acoustic energy of a sound beam is flowing into a dispersed wake. The bubbles remove power from the beam at a rate that depends upon the intensity of the sound in the beam and the total effective cross section of the bubbles. Of the power removed from the beam, a fraction is reradiated as sound. The quantity of energy reradiated is determined by a factor called the scattering cross section of the bubbles.

The remainder of the power that is removed from the beam is converted into heat-that is, absorbed by the air of the bubbles and, to a lesser extent, by the water surrounding them. The quantity of energy converted into heat is determined by the absorption cross section of the bubbles. Thus the total effective cross section is a combination of scattering and absorption cross sections. Note that the total effective cross section determines the screening effect caused by a wake, whereas the strength of the wake echo is determined by the scattering cross section.


Interpretation of Scattering Experiments

Historically the study of scattering and absorption has played an important part in the development of various branches of physics. This development is especially evident in those branches dealing with radiations that are not perceptible by the unaided human senses-such as X-rays; α rays; β rays; γ rays; cosmic rays; and more recently, neutron rays. The scattering of visible light explains the color of the clear sky and other meteorological phenomena. The scattering of sound waves had not been studied in any systematic manner before World War II. During the war such studies were begun and are still far from complete.

The modern knowledge of the structure of matter, atoms, and nuclei is based largely on scattering experiments. Experiments on the scattering of sound and radio waves are unlikely to contribute much to this fundamental knowledge concerning the imperceptible structure of matter. Such experiments almost certainly will contribute much to the knowledge of the inaccessible parts of the ocean and the atmosphere. Thus studies of reverberation and of the scattering of sound by wakes are considered to be very important, even apart from immediate practical objectives.

The interpretation of the experiments has been the subject of much careful thought, and has resulted in many major advances in knowledge. However, examples of misinterpretations by conscientious and able experimenters are also numerous.

The most common error is the measurement of extraneous radiation along with radiation that is intended to be measured. In measuring the intensity of sound transmitted through a wake, it is most important to shield the hydrophone from all sound that passes beneath the wake.

The interpretation of many laboratory experiments has been simplified by the use of opaque screens to shield the detector from extraneous radiation. Sometimes these screens have not been completely opaque. Often their edges have been the source of scattered radiation. In performing scattering experiments at sea, it is not possible to use such screens, so that the probability of extraneous sound is particularly great. Another error is the application of theoretical

  equations to circumstances that do not conform to the assumptions made in deriving them.


A series of experiments on the wakes of destroyers and destroyer escorts was performed by the University of California, Division of War Research (UCDWR).3 The procedure was as follows: One vessel carried a hydrophone and was dead in the water, while a destroyer ran past it on a straight course at a fixed speed. As soon as the destroyer had passed, a small launch got underway and carried the sound source from one side of the wake to the other. In this way it was possible to measure the intensity of the sound both when the wake intervened between source and receiver and when the source was on the same side of the wake as the receiver. After allowance was made for the difference in range when the source was on one side or the other of the wake, the apparent transmission loss caused by the wake was determined.

It is not certain that the result is free from error. In the first place, when the sound soured is on the far side of the wake, it is possible that some sound may pass under the wake and reach the hydrophone. This error was minimized by suspending both source and hydrophone about one-half the depth of the wake. In spite of this precaution, it must be emphasized that the values of transmission loss so obtained are possibly too low.

This source of error can be eliminated by making the measurement while the source is in the wake, but in that case the value obtained may be too large because of the effect of bubbles in reducing the output of the source. To some extent this value is counterbalanced because only part of the wake is between the source and the receiver. The true value probably lies between the two measured values.


Dependence on Age of Wake

Early experiments were performed with a single vessel, the U. S. S. Jasper, which ran on a straight

3 Sound Transmission Through Destroyer Wakes, OEMsr-30, Service Project NS-141, Report M-189, UCDWR, March 8, 1944.

course, then circled and echo-ranged on its own wake.4 These experiments showed that the level of the echo decreased fairly rapidly with the age of the wake. The results of various experiments ranged from 1.5 db per minute to 8 db per minute, with an average of about 4 db per minute. The levels of the echoes were compared with those of reverberation on the same day at the same range from the sonar. On one day this range was about 235 feet and the echoes were about 40 db higher than either volume or surface reverberation. These two kinds of reverberation were about equal at this range. On another occasion the range was 140 feet and the echo was 17 db higher than surface reverberation. A sea state 2 and wind force 3 prevailed on this occasion.

In view of the variability of reverberation from day to day, these observations have little absolute significance but serve to give some idea of the strength of echoes from the wake of a small slow-speed vessel. The values obtained for the rate of decrease of the wake echo have greater claim to validity and are in good agreement with other observations.

The difficulties inherent in performing experiments on wakes at sea led to an extended series of experiments in San Diego Harbor. A 40-foot motor launch was used to lay the wakes, which extended from the surface to a depth of about 5 yards.5 There was some evidence that sound reflected from the bottom increased the strength of the echo. To minimize this effect, only echoes obtained at ranges of less than 100 yards are included in the following averages.

TABLE 3. -Dependence of Wake Strength on Age of Wake

Frequency (kc) Time of maximum echo (sec) Wake strength at time of maximum echo (db)
15 30 -2.9
24 50 +3.1
30 70 +8.4

Echoes were obtained by using 15-kc, 24-kc, and 30-kc sound. These echoes did not reach their

4 Carl F. Eckart, Echoes from Wakes, NDRC C4-sr30-498. UCDWR, August 29, 1942. 5 Richard R. Carhart and George E. Duvall, Acoustic Measurements of Surface Wakes in San Diego Harbor, OSRD 1628, NDRC 6.1-sr 30-961, Report U-62. UCDWR, May 8, 1943.
  Variation of the wake echo level with age of the
wake, for various ping lengths at 24 kc.
Figure 2-16 -Variation of the wake echo level with age of the wake, for various ping lengths at 24 kc.

maximum values until some time after the passage A the launch through the sound beam. Average values of the time of the maximum echo are shown in the second column of table 3. Thereafter, the echo intensity diminished at an average rate of about 7 db per minute for all three frequencies. The wake strength at the time of the maximum echo level was computed for each experiment, and average values are shown in the third column of table 3.

Figure 2-16 gives further information concerning the behavior of wake echoes. The early period, during which the echo from the wake increases in level, is clearly evident, as is the later period during which the echo level decreases at a rate of about 1.8 db per minute.

Dependence on Ping Length

Figure 2-16 also brings out a dependence of echo level on ping length. The theoretical discussion has emphasized the analogy between wake echoes and reverberation. Essentially the wake is a part of the ocean from which the reverberation is especially high. If the ping length is shorter than the width of the wake the distinction between reverberation and wake echoes disappears. The number of scatterers returning echoes at any moment is determined, not by the extent of the wake but by the ping length.

Wake Strengths of Submarines

Many difficulties are encountered in experiments on the wakes of submerged submarines. The problems of navigation and seamanship involved in the


maneuvers are not always solved successfully, even by the ablest submariners. These practical difficulties and the low levels of the wake echoes account for the conflicting reports that have been made on the subject.

On one occasion echoes from the wake of an S-type submarine were recorded with standard echo-ranging gear operated at 24 kc. When this submarine was running at a depth of 45 feet, contact was maintained with the wake at a distance of 3,000 feet astern of the screws. At depths of 90 and 125 feet, the lengths of the contacts were 700 and 300 feet, respectively.

On a second occasion, an attempt was made to use a recording echo sounder for the study. This instrument had been successfully used in the study of the wakes of surface vessels. Consequently, it was mounted on a launch, and the fleet-type submarine ran on a straight course designed to carry it directly under the launch. This maneuver proved difficult to execute, but echoes from the hull of the submarine were obtained several times. The depth of the submarine varied from 65 to 200 feet. Echoes from the wake were never obtained at distances more than from 50 to 100 feet astern of the screws.

It had been hoped that this experiment would show whether the wake has a tendency to rise to the surface, as might be expected if bubbles are the primary cause of its acoustic activity. The results are inconclusive. It has been reported that, on several occasions, the wake of a submarine running at a depth of from 45 to 60 feet could be seen from the deck of a nearby surface vessel. This visibility was apparently due more to turbulence, which disturbed the surface, than to bubbles.

On a third occasion, 15 experiments were performed to measure the wake strength of a fleet-type submarine running at various depths of from 45 to 400 feet. None of these experiments yielded echoes that were positively identified as caused by the wake, although echoes from the hull of the vessel were obtained. Some few echoes may have come from a short distance astern of the screws. Frequencies of 20 kc and 45 kc were used; 45-kc echoes from the wake would have been recorded provided they were not more than 14 db below those from the submarine itself. At 20 kc, the echoes from the wake would have been recorded

  provided they were not more than 28 db below those from the submarine itself.

The operational problems were reduced to manageable proportions by the following procedure: The submarine started on the surface, running a course parallel to that of the echo-ranging vessel. The echo-ranging vessel ran at a slow speed, so that the submarine overtook it and passed through the sound beam while still on the surface and at a range of from 100 to 300 yards. About 90 seconds after passage the submarine dived rapidly to 90 feet and slowed down. Simultaneously the surface vessel increased speed and overtook the submerged submarine about 10 minutes later. It was found that these operations could be carried out satisfactorily except that it was difficult to adhere to the prearranged time schedule and that the submarine's submerged course often diverged appreciably from the course of the surface vessel. The timing of events was critical because of the limited supply of film in the magazine of the recording oscillograph.

Data recorded during such an experiment are summarized in figure 2-17. The lower half of the

Wake strength of a submarine.
Figure 2-17 -Wake strength of a submarine.

figure shows the distance astern in feet. Note that the wake strength while the submarine was running on the surface was from -10 to -15 db. This wake strength was momentarily increased as the echo-ranging vessel passed the site of the dive, where the venting of air from the ballast tanks presumably increased the bubble content of the wake. After the submarine reached the depth of 90 feet the wake strength varied between -20 and -30 db, even while the distance astern remained practically constant at about 900 feet.


TABLE 4 -Wake Strengths of Submarines
Submarine type Frequency (kc) Wake strength surfaced, 9 knots (db) Wake strength submerged 6 knots (db) Depth (ft)
S 60 -18 -26 90
S 45 -13 -24 90
Fleet 45 -13 -20 90
S 45   -33 45
S 20   -20 45
  As the echo-ranging vessel overtook the submarine the wake strength again increased to -20 db.

The results of other experiments with submarines are listed in table 4. Ping lengths of from 8 to 24 yards were used in all the work summarized. Even when the submarine is running on the surface, the strength of its wake is very small. This fact can probably be explained by the low speeds at which the submarine moves.


Previous Chapter
Previous Chapter
Sonar Home Page
Sonar Home Page
Next Chapter
Next Chapter


Copyright © 2013, Maritime Park Association.
All Rights Reserved.
Legal Notices and Privacy Policy
Version 3.00