fied models of anisotropic flow. For the case of a steady mean shear {dU 1 /dx 2 ) with 

 superimposed isotropic turbulent fluctuations of rms value u and correlation scale 

 L, p s ex puL(dU 1 /dx 2 ). This anisotropic model is probably closer than is isotropic 

 turbulence alone to the actual flows in a turbulent jet or in the wake of a cylinder. 



Mention should be made of the periodic fluctuations in pressure, of very large 

 amplitude, existing in the wake close to a cylinder shedding vortices. Blokhintzev [41] 

 has calculated the magnitude of these fluctuations, by assuming that the wake is a 

 steady Karman vortex street. The calculated pressure fluctuation along the centerline 

 of the wake is given by p = 0.07pt/ 2 ; along this line the fluctuation is primarily at 

 twice the shedding frequency. The calculated value agrees quite well with the value 

 measured by Strasberg and Cooper [49] at this frequency for distances within 3 cylinder 

 diameters of the cylinder. At the shedding frequency, the fluctuations are even larger; 

 close to the cylinder, values were observed as large as p = 0.3 p U 2 . Further down- 

 stream, the measured values decrease as the periodic fluctuations degenerate into 

 random turbulence. 



The pressure fluctuations in a free turbulent region is a topic worthy of con- 

 siderable additional attention. The practical importance of these pressure fluctuations 

 can be indicated by an example of their magnitude. In the wake of a cylinder in water 

 at a speed of 5 meters/sec (10 knots), the rms pressure fluctuation 24 cylinder diam- 

 eters downstream is estimated to be about 5 x 10 3 dyne/cm 2 . This pressure corresponds 

 to a level more than 70 decibels above the ambient noise in the sea at sea state 2. 



Pressure in the near field. — The fluctuating pressures outside a turbulent region 

 are much smaller than those mentioned above. In the near field close to a turbulent 

 region, however, their magnitudes can be significant. Jorgensen [21] has measured the 

 pressure fluctuation outside a free turbulent jet of water. The spectral density of the 

 pressure, measured 4 jet diameters off the axis and 4 diameters downstream from the 

 mouth of the jet, is shown in Fig. 20. The bottom and left scales are non-dimensional, 

 but dimensional scales have been put along the top and right side for a jet diameter 

 of 0.6 inch at a speed of 30 knots. For these specific conditions, the fluctuations at 

 500 cy/sec are some 30 db above the ambient noise at sea state 2. 



Radiated pressure fluctuations. — In the radiation field far from an unbounded 

 region of unsteady flow, the pressure fluctuations are even smaller than in the near 

 field. The sound radiated by an unsteady flow has received perhaps more attention 

 than any other form of flow noise, because of its importance in connection with high- 

 speed jet aircraft. At the speeds encountered in water, however, the radiated pressure 

 fluctuations are completely negligible. 



The negligible values of the sound pressure radiated by turbulence in water 

 are illustrated by the case of the turbulent jet. Fitzpatrick and Lee's [51] measurements 

 with air jets give for the rms sound pressure, in the direction of average intensity, 



p s = 2XlO- s P UKU/c) 2 (D/r), (23) 



where D is the diameter of the orifice, and U the mean efflux velocity. At a speed of 

 15 meters/sec (30 knots) and a distance of 100 jet diameters, the rms sound pressure 

 is only about 0.005 dyne/cm 2 ; at least 40 decibels below the ambient noise in sea 

 state 2. 



The influence of boundaries. — The discussion to this point has been concerned 

 with flows in an unbounded space. If boundaries are present, the sound field is of 

 course modified by the boundaries. If the boundaries are within the unsteady region, 

 sound radiation can be associated directly with the boundaries, and this boundary 

 radiation can be much stronger than the radiation from the unsteady motion itself. 



The complete relations describing the sound field generated by an unsteady 



268 



