A linear regression model for the wavenumber‐frequency spectrum of the turbulent boundary layer pressure fluctuations

Abstract

The rationale of using a linear regression model for estimating the wavenumber‐frequency spectrum of the turbulent boundary layer pressure fluctuations is presented. The contention is that the wavenumber‐frequency spectra, normalized by the convected ridge value at the respective frequency, are the same for all frequencies if the wavenumber is expressed in terms of a nondimensional wavenumber. The nondimensional wavenumber is the streamwise wavenumber that is normalized by the convected wavenumber at the respective frequency. The normalized wavenumber spectrum is then approximately represented by a set of discrete spectral coefficients. The linear regression model relates the response of a measuring system to these discrete spectral coefficients. The spectral coefficients are determined by least‐square minimization of a set of randomly collected response data.