Anisotropic pressure correlation spectra in turbulent shear flow

We measured the correlation spectrum Q̂ ₚ (k) of pressure fluctuations in a driving mixing layer with a Taylor-scale Reynolds number Rλ up to 700 by a newly developed pressure probe with spatial and temporal resolutions that are sufficient to analyse inertial-subrange statistics. The influence of the mean velocity gradient tensor Sᵢⱼ in the mixing layer, which is almost constant near its centreline, is studied using an idea similar to that underlying the linear response theory developed in statistical mechanics for systems at or near thermal equilibrium. If we write the spectrum Q̂ ₚ (k) as Q̂ ₚ (k)= Q̂ ₚ⁽⁰⁾ (k)+ Δ Q̂ ₚ (k) , where Q̂ ₚ⁽⁰⁾ (k) is the isotropic Kolmogorov spectrum in the absence of mean shear, then for small Sᵢⱼ the deviation Δ Q̂ ₚ (k) due to the shear is approximately linear and is determined by a few non-dimensional universal constants in addition to Sᵢⱼ , k and the mean energy dissipation rate. We also measured the pressure–velocity and velocity–velocity correlation spectra. Deviations from isotropy due to shear are shown to be approximately proportional to Sᵢⱼ at large Rλ .