Turbulence in Supersonic Flow

Abstract

First-order perturbation theory indicates that the Navier-Stokes equations for a compressible, viscous, and heat-conductive gas can have three distinctly different types of disturbance fields, obeying three independent differential equations. These three ''modes" of disturbance fields are: vorticity mode, entropy mode, and sound-wave mode. The modes are independent when the intensities of the fluctuations are small, but they interact at larger intensities when linearization is not permissible. The principal tool for measuring the fluctuating fields is the hot-wire anemometer adapted for supersonic flow. In a supersonic flow the hot-wire anemometer responds to two variables: mass flow fluctuations and stagnation temperature fluctuations. Each of the above three modes contributes to both of these variables. By taking fluctuation measurements at different wire temperatures, the relative sensitivity to the flow parameters varies and a "fluctuation diagram" can be obtained. The character of the fluctuation diagram differs for each mode, and even coexisting modes can be separately determined by anatyzing the fluctuation diagram under certain restrictive conditions. Hot-wire measurements were obtained in various supersonic flows. Pure temperature spottiness (entropy mode) and pure sound-wave fields were explored. Detailed measurements were taken in a turbulent supersonic boundary layer. With the aid of the fluctuation diagram, the intensity of temperature spottiness (entropy mode) and of turbulent velocity fluctuations (vorticity mode) was measured across the layer. Energy spectrum and probability density measurements gave clues concerning the character of the fluctuations.