Modeling of pressure spectra in a turbulent shear flow

Models of turbulent-turbulent and turbulent-shear contributions to pressure spectra in a turbulent shear flow are developed. The spectral model for the turbulent-shear contribution is obtained by directly Fourier transforming the integral solution to Poisson's equation for an isotropic, homogeneous, constant mean shear flow. The turbulent-turbulent model is found in a similar manner with the addition of a quasinormal fourth-order-moment closure approximation. It is found that the turbulent-turbulent contribution is dominant in the high-wavenumber region and possesses a k−7/3 inertial subrange. The shear contribution is dominant in the low-wavenumber region where it increases as k2 for the large scales and rolls off as k−11/3 for scales smaller than the energy containing eddies. Both spectra are related to the type of model chosen for the velocity field; by choosing various spectral forms, it is possible to compute the mean-square pressure of the flow. These results are compared to models for the mean-square pressure developed by Kraichnan, as well as with our own experimental data taken in a 12-in.-round jet and that of several other investigators.