Note on the Pressure Fluctuations in Isotropic Turbulence

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 n*(k) thus derived is : rr*(k) -k-7I3 for the intermediate wave-number range and n*(k)_k2 for the low wavenumber 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.