Pressure Fluctuations in Turbulent Flow over a Flat Plate

The pressure fluctuations exerted on a flat plate by a turbulent boundary layer flow are investigated. The approximate dependence of the mean-square intensity, spatial scale, and frequency scale on Mach number and distance from transition point are estimated through the use of similarity arguments. The wave number spectrum of the pressure fluctuation distribution over the surface of the plate is expressed in terms of transforms of two-point velocity correlations and expressions are derived for the driving force exerted on a rectangular piston set in the surface of the plate. It is found that the integral over the boundary surface of the two-point quadratic correlation function of the pressure fluctuation should vanish, with the result that the mean-square force per unit area exerted on a large area of the surface should tend to zero as the area increases indefinitely. An idealized model of turbulent boundary layer flow is constructed and used to relate the spectrum and correlation function of the surface pressure distribution to the corresponding functions for a homogeneous turbulent flow. Application of the theory to Laufer's data on turbulent channel flow indicates that the dominant contribution to the pressure fluctuations should depend only on the mean velocity profile and the two-point quadratic correlation of the fluctuating velocity component perpendicular to the boundary surface. On the basis of the seriously incomplete data available the rms pressure fluctuation from this source is tentatively estimated. The treatment of the present paper is based on the assumptions of (1) adiabatic conditions, (2) small compressibility, and (3) slow rate of growth of the boundary layer.