Sound Radiation from High Reynolds Number Turbulence

Abstract

It has been found, on the basis of a recent, anticipatedly exact theory of homogeneous turbulence, that the acoustic power radiated at high Reynolds numbers and low Mach numbers is dominated by the high-frequency contributions from the inertial wave-number range. The inertial range pressure wave-number spectrum in the isotropic case has been found to be P(k) = aρ2εv0k−2, where ρ is density, ε is the dissipation rate by viscosity, per unit mass, and v0 is the rms turbulent velocity in any direction. The universal number a is determined by the theory. The power spectrum of the inertial range radiation per unit mass has been found to be W(ω) = AM5εω−1, where M is the Mach number v0/c and the universal number A is determined by the theory. The total inertial range radiation power is of order AM5εlnR02/3, where R0 is the Reynolds number v04/εν (ν = kinematic viscosity) which characterizes the turbulent macrostructure. In the present paper, an attempt will be made to give an elementary physical interpretation of these results in terms of the dynamical interaction of the sharply defined shear fronts and vortex filaments which make up high Reynolds number turbulence. Some implications for radiation from jets, wakes, and boundary layers will be discussed briefly. (The research described was supported by the Mechanics Branch, Office of Naval Research.)