Chapter 29 



VELOCITY AND TEMPERATURE STRUCTURE 



THE WATER in the wake of a ship is usually in mo- 

 tion relative to the surrounding water. In addi- 

 tion, the temperature of the water at different points 

 in the wake is sometimes characteristically diiferent 

 from the temperatures found outside the wake. The 

 variations of temperature and velocity are important 

 physical properties of wakes, and might be expected 

 to account at least in part for the acoustic effects ob- 

 served; furthermore, a study of these physical char- 

 acteristics is of independent military interest. Even if 

 air bubbles are responsible for all the observed 

 acoustic effects of wakes, any theory of the origin and 

 persistence of bubbles must be consistent with known 

 facts about the velocity and temperature structure. 

 The present chapter summarizes the fragmentary 

 evidence which is available on these two subjects. 

 Sections 29.1 and 29.2 discuss the available data on 

 the velocity and temperature, respectively. In Section 

 29.3 the resulting acoustic effects are examined. It is 

 shown that scattering from turbulent but wake-free 

 water is negligible; scattering of sound by water with 

 an irregular temperature distribution may some- 

 times be appreciable, but cannot explain the large 

 acoustic effects observed. Thus, velocity and tem- 

 perature structure alone cannot account for the ob- 

 served acoustic properties of wakes. 



29.1 VELOCITY STRUCTURE OF WAKES 



The simplest wake is that produced by the flow of a 

 fluid past a thin plate parallel to the stream. In this 

 case the plate affects the flow only in a narrow region 

 close to the plate, known as the boundary layer, 

 where the fluid is slowed down. This effect is shown 

 in Figure 1, where the magnitude of the velocity at 

 various points is shown by arrows; for simplicity, 

 only the upper half of the flow pattern is shown. Far 

 behind the plate the velocity distribution still shows 

 the effect of passing by the plate, since the fluid which 

 passed through the boundary layer will be moving 

 less rapidly than the rest of the stream. The arrows in 



Figure 1 represent the average velocities of the fluid 

 relative to the plate. Thus these results are applicable 

 directly to the reciprocal situation, when the thin 

 plate (or ship's hull) is moved through still water. In 

 this situation the water in the wake is left moving in 

 the same direction as the plate. It may be noted that 

 in most cases, the flow in the boundary layer becomes 

 turbulent, in which case the flow in the wake will also 

 be turbulent. 



,.- -v-- 



UNDISTURBED 

 FLOW 



BOUNDARY 

 LAYER 



Figure 1. Velocity structure. 



In addition to the wake produced in this way by 

 passage of a ship through water, there is also the 

 effect produced by the screws. To move the ship for- 

 ward, the screws exert a forward force on the ship 

 which is somewhat greater than the frictional force 

 produced by the flow of water past the hull ; the dif- 

 ference is just equal to the retarding force due to wave 

 action and air resistance. For a submerged submarine, 

 however, the propulsive force is just equal to the fric- 

 tional force produced by the flow of the water around 

 the hull. To produce this propulsive force on the sur- 

 face ship or submarine, the screws exert an equal and 

 opposite force on the water, which is forced back- 

 ward. As a result, the water passing through and 

 around the screws moves in a direction opposite to 

 that of the vessel. The flow of water produced by 

 ship screws has already been discussed in detail in 

 Section 27.1.1 in connection with the formation of air 

 bubbles. 



Thus, close to a ship the wake is made of several 

 component parts: one or more screw wakes, usuaUy 

 called "slipstreams," moving away from the ship as a 

 result of screw action; and the hull wake following 

 the ship as a result of frictional force at the surface of 



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