Sound Radiation from a Turbulent Boundary Layer

If the restriction of incompressibility in the turbulence problem is relaxed, the phenomenon of energy radiation in the form of sound from the turbulent zone arises. In order to calculate this radiated energy, it is shown that new statistical quantities, such as time-space correlation tensors, have to be known within the turbulent zone in addition to the conventional quantities. For the particular case of the turbulent boundary layer, indications are that the intensity of radiation becomes significant only in supersonic flows. Under these conditions, the recent work of Phillips is examined together with some experimental findings of the author. It is shown that the qualitative features of the radiation field (intensity, directionality) as predicted by the theory are consistent with the measurements; however, even for the highest Mach number flow, some of the assumptions of the asymptotic theory are not yet satisfied in the experiments. Finally, the question of turbulence damping due to radiation is discussed, with the result that in the Mach number range covered by the experiments, the energy lost from the boundary layer due to radiation is a small percentage of the work done by the wall shearing stresses.