On the Diffusion of Sound Waves in a Turbulent Atmosphere

Abstract

The diffusion of sound waves in a homogeneous, isotropic turbulent medium is discussed. The spectrum of the turbulence in wave number and frequency is assumed to be of the form E(k,ω)∼λλ2+ω2k4e−4k/k0. Here, k0 is the wave number of the energy-bearing eddies and 1/λ is the autocorrelation period of the turbulence. This spectrum produces a diffusion of the sound wave in both direction and frequency, as the wave progresses. The quantity λ is evaluated by analogy with the harmonic oscillator which is excited by random noise. The autocorrelation time in this case is given by τ ≡ average energy stored/average energy lost per second, which for the case of turbulence is 1/λ = 〈u2〉/ε = 8/15νk02, where ν = kinematic viscosity. The autocorrelation times as evaluated in this way are compared with those measured in turbulent flow. The limitation of speech intelligibility out of doors by the effect of the frequency diffusion will also be discussed. [Supported by Contract NAw-6463 with the National Advisory Committee for Aeronautics.]