On a Model for Surface Pressure Fluctuations Induced by the Wall Region of a Turbulent Boundary Layer

Local solutions of the Navier-Stokes equations describing the interaction of a streamwise vortex with a rigid surface are utilized to develop a conceptual model for the surface pressure spectrum associated with the wall region of a turbulent boundary layer. The interaction of single as well as pairs of coherent streamwise vortices, which principally govern the production of turbulence in the wall region, with the surface beneath is considered, under conditions of axial stretching of the vortex structures. For a range of Reynolds numbers, it is shown that definite smaller structures can arise from the interaction with strengths comparable to that of the primary vortex. The surface pressure signatures of the coherent vortex motion and the associated power spectrum of the pressure is examined. Based on the results of the local solutions, the surface pressure signatures and the corresponding pressure spectrum of an ensemble of independent coherent structures are modeled using the assumption of ergodicity in the manner described by Townsend (1951) and Lundgren (1982, 1993) for homogenous turbulence. The model requires specification of a set of values of the free parameters in the viscous solution. The range of values of these free parameters is estimated through comparison with available results from experiments and numerical simulations. Although the model is rather simplified, it appears to predict the convective wavenumber range of the spanwise spectrum fairly well. The effect of transverse curvature on the surface pressure spectrum is considered.