Recent Modeling of Turbulent Wall Pressure and Fluid Interaction With a Compliant Boundary

Abstract

The relation of wall-pressure amplitude to fluctuating Reynolds-stress source amplitudes in the boundary layer is reviewed for inviscid, slightly compressible flow along a rigid planar boundary. An orthotropic wall-similarity model for source spectra is constructed and applied in this framework to derive a rough model for the wavevector-frequency spectrum of turbulent wall pressure, including radiative wavenumbers. By extension to a compliant boundary, with nonlinear, fluctuating Reynolds stress omitted, an expression is given for fluid-loading impedance and energy exchange in the presence of flow with arbitrary mean velocity profile, in terms of a solution to the homogeneous equation for pressure on a rigid wall. For a compliant boundary driven by fluctuating Reynolds stresses, a formal general relation for wall motion and pressure is derived with a view to the possible effect of nonlinear terms involving wall motion on the amplitude of wall pressure at sub-convective wavenumbers.