COHERENT VORTEX MODEL FOR SURFACE PRESSURE-FLUCTUATIONS INDUCED BY THE WALL REGION OF A TURBULENT BOUNDARY-LAYER

Exact solutions of the Navier-Stokes equations describing the interact ion of streamwise vortices with a rigid surface are utilized to develo p a conceptual model for the surface pressure spectrum associated with the wall region of a turbulent boundary layer. The evolution of singl e as well as pairs of coherent streamwise vortices, which principally govern the production of turbulence in the wall region, is considered in the presence of local straining flow induced by larger, outer-layer eddies. The surface pressure signatures of the coherent vortex motion and the associated power spectrum of the pressure are examined. Based on the results of the exact solutions, the surface pressure spectrum of an ensemble of independent coherent structures is modeled using the assumption of ergodicity in the manner described by Townsend and Lund gren for homogeneous turbulence. The free parameters in the model are estimated through comparison with available results from experiments a nd numerical simulations. The model, especially the one involving pair s of streamwise vortices, predicts the high frequency and high spanwis e wave number range of the surface pressure spectrum quite well. Furth er, the probability density function of surface pressure associated wi th the model compares well with experimental results. Interestingly, t he model also suggests that the contribution of the viscous interactio n to low wave number spectral elements accounts for the discrepancy be tween experimental observations at such wave numbers and the predictio n of the Kraichnan-Phillips theorem. (C) 1997 American Institute of Ph ysics.