Modeling the operation of scalar wave filters – isotropic wavelets – in the field of wall turbulent pressure pulsations

The results of scalar filtering in the field turbulent wall pressure fluctuations under a homogeneous boundary layer are estimated. The main attention is paid to the operation of extremely compact scalar wave filters formed from two receiving elements – a central circular one and an adjacent external ring 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 quality of filtration in the short-wave zone of the wave spectrum. The prospects of using the investigated receivers in problems of spatial wavelet analysis of turbulent fields of wall pressure pulsations are noted.