Note on the Pressure Fluctuations in Isotropic Turbulence

Abstract

The spectrum of the pressure fluctuations in isotropic turbulence is theoretically studied on the basis of an assumption that the joint probability distribution of turbulent velocities is normal, making use of an approximate representation for the interrelation between the longitudinal velocity correlation and the velocity spectrum. The three-dimensional pressure spectrum _??__*(k) thus derived is: _??__*(k) _??_ k^-7/3 for the intermediate wave-number range and _??__*(k)_??_k² for the low wave-number range, corresponding to the velocity spectra F_*(k) _??_ k-^5/3 and F_*(k) _??_ k, respectively. These theoretical results are compared with the pressure spectra observed in the westerlies zone of middle latitudes with fairly good agreement.