Noise Production in a Turbulent Boundary Layer by Smooth and Rough Surfaces

In a turbulent boundary layer, the effective velocity fluctuations amount to about 4% of the free-stream velocity, independent of the curvature of the body and within wide limits independent of the velocity of the flow. The fluctuations in pressure can then be computed from those of the velocity by an equation similar to the standard Bernoulli equation, except that the numerical constant is different. Vortices pass along the receiving hydrophone; they represent pressure pulses that generate a constant power spectrum at low frequencies that decreases approximately inversely proportional to the cube of the frequency at higher frequencies. This information, in conjunction with the pressure equation, makes it possible to compute the power spectrum of the flow noise as a function of the frequency, the boundary layer thickness and the speed of the flow. The flow noise at greater speeds and at higher frequencies turns out to be predominantly generated by the surface roughnesses. A small hydrophone records the local fluctuations at the pressure in the boundary layer; on the other hand, a large hydrophone is very insensitive to the small-scale turbulence. It indicates the true sound pressure that is produced by the generation and the decay of the turbulence and by the vibrations of the walls of the vessel. A large hydrophone therefore reads the same pressure, whether it is placed inside the boundary layer or outside the near field region, not too far away from the turbulent layer. The theoretical conclusions are borne out, qualitatively and quantitatively, by the experimental results obtained with the aid of a rotating cylinder and through measurements in the test section of the Garfield Thomas Water Tunnel.