A sparse recovery technique for the turbulent boundary layer wavenumber-frequency spectrum with non-uniformly spaced array of pressure transducers

Abstract

Historically, determination of wavenumber-frequency spectra of turbulent wall pressure fluctuations has employed the use of evenly spaced linear arrays of sensors. The reason for this is that even spacing of pressure samples in both the temporal and spatial domains facilitates analysis by direct application of 2-D Fourier transforms. The spacing of pressure measurements directly impacts the resolution of the resulting wavenumber-frequency spectra. This rigid spacing requirements of traditional methods may preclude analysis altogether with even a single sensor failure within the array. Rather than determining sensor locations based on the simplest analysis method, the sparseness of the wavenumber-frequency spectra can be leveraged to allow non-uniform sampling in both temporal and spatial domains. Sparse recovery techniques as an analysis tool for wavenumber-frequency spectra will be demonstrated both theoretically and experimentally for uniformly spaced arrays, uniformly spaced arrays with missing measure...