Modeling the Operation of Scalar Wave Filters—Isotropic Wavelets—in the Field of Wall Turbulent Pressure Fluctuations

Abstract— The results of scalar filtering in the field turbulent wall pressure fluctuations under a homogeneous boundary layer are estimated. The article focuses to the operation of extremely compact scalar wave filters formed from two receiving elements—a central circular one and an adjacent external annular one. Such a two-element receiver operates as a wave filter and can be treated as an isotropic wavelet if the recorded total signal under coherent pulsating action on the elements is zero. It is established that two-element wavelet filters are capable of providing a satisfactory solution to the problem of estimating the characteristics of a scalar spectrum. The filtering results are close for different smooth distributions of local sensitivity over the radius. The outer diameters of the two-element receivers are approximately 1.5 wavelengths to which the wave filter is tuned. Three-element scalar wave filters–wavelets with two ring elements and an external diameter of approximately 2.2 lengths of the recorded wave are capable of significantly improving the filtering quality in the short-wavelength zone of the wave spectrum. The prospects of using the investigated receivers in problems of spatial wavelet analysis of turbulent fields of wall pressure fluctuations are noted.