Effects of Pressure Gradients on Turbulent Boundary Layer Wave Number Frequency Spectra

Abstract

pp. 93‐113). The use of ± as an outer length scale is shown to produce distinct trends in the convection velocities. The autospectra for the respective cases are scaled on inner and outer variables, with outer variables collapsing the data over a narrow frequency range. The effects of spatial averaging due to the e nite transducer size are taken into account. Estimations of the wave number frequency spectra are obtained by spatially transforming the cross spectra, and taking into account the variation of convection velocity with spatial separation. A distinct trend in these spectra are displayed, with an asymmetric convective ridge that broadens as the pressure gradient changes from favorable to adverse. Uncertainties in the estimation of the spectra are discussed. The results are applicable to the e ow-induced radiated noise of undersea vehicles and the self-noise of sonar systems. Nomenclature d = wall-pressure sensor diameter d + = nondimensional sensor diameter = dus /m G(n , x o) = cross spectrum k = streamwise wave number Rh = Reynolds number based on momentum thickness= Uoh /m Uo = freestream velocity uc = convection velocity us = friction velocity = p (s w/q ) a = decay constant for the cross spectrum d = boundary-layer thickness d ¤ = boundary-layer displacement thickness h = boundary-layer momentum thickness j = nondimensional streamwise wave number = i kd