Spectral features of wall pressure fluctuations beneath turbulent boundary layers

Publisher Website
Google Scholar
Abstract
Experimental measurements of the frequency spectra and frequency cross‐spectra of the wall pressure fluctuations beneath a turbulent boundary layer were made in a low‐noise flow facility. The data, taken over a range of flow speeds, clearly display a dimensionless frequency (ωδ/uτ=50) at which the spectra achieve a maximum and a low‐frequency range with an approximately ω2 rolloff. The scaling laws for the low‐, mid‐, and high‐frequency regions of the spectrum are established. The cross‐spectral data, obtained over a range of streamwise separations (0.21≤ξ/δ≤16.4), allow for the computations of the decay Γ(ξ,ω) and convection velocity Uc(ξ,ω) of the wall pressure field. These data show the existence of two distinct wave number groups: a high wave number group that scales on the similarity variable k1ξ=ωξ/Uc(ξ,ω) associated with turbulent sources in the log region of the boundary layer, in which eddies decay in proportion to their size, and a low wave number group that defines the cutoff for the large‐scale turbulence contributors in the outer region of the boundary layer. The convection velocity data support the conjecture that the major turbulent contributions to the low and high wave number groups come from the outer and inner layers, respectively. These new results, when examined collectively, firmly establish the spectral features of the wall pressure fluctuations, including the low‐frequency range, which is highly sensitive to (passive) structures in the outer flow. The locations for the turbulent sources of the wall pressure field are proposed.