Statistics of overpressure fluctuations behind a weak shock wave interacting with turbulence

The overpressure fluctuations behind a weak shock wave interacting with turbulence are studied by wind tunnel experiments, where a spherical shock wave propagates in grid turbulence. The experiments are conducted for various values of the shock Mach number MS0 of the shock wave and turbulent Mach number MT of the grid turbulence. The experimental results show that the root-mean-squared peak-overpressure fluctuation divided by the averaged peak-overpressure, σΔp/⟨Δp⟩, where the inherent noise caused by the experimental facility is removed, follows a power law of MT2/(MS02−1). The probability density functions of the overpressure fluctuations are close to the Gaussian profile for a wide range of MT2/(MS02−1). A shock deformation model based on the deformation due to nonuniform fluid velocity is proposed for the investigation of the influences of turbulence on the shock wave. The deformation changes the cross-sectional area of the ray tube, which is related to the shock Mach number fluctuation of the area. The model for a weak shock wave yields the relation σΔp/⟨Δp⟩≈(1/3)[MT2/(MS02−1)]1/2, which agrees well with the experimental results. The model also predicts the Gaussianity of the peak-overpressure fluctuations behind the shock wave interacting with Gaussian velocity fluctuations. Good agreements between the model and experiments imply that the change in the shock wave characteristics by the interaction with turbulence is closely related to the shock wave deformation caused by the fluctuating turbulent velocity field.