Nonlinear scaling of fluctuation kinetic energy for shock–vorticity wave interaction

Abstract

Turbulent kinetic energy (TKE) is a quantity of primary importance in shock–turbulence interaction (STI). Linear interaction analysis (LIA) serves as a theoretical method to predict the amplification of TKE in STI. LIA is constrained by low-amplitude fluctuations and neglects nonlinear effects. In this paper, we explore the nonlinear amplification of the kinetic energy of fluctuations in the interaction between a vorticity wave and a shock wave that serves as a building block flow for STI. A weakly nonlinear framework (WNLF) is introduced to analyze nonlinear effects in fluctuation kinetic energy (FKE) and identify the dominant physical mechanisms driving its amplification. The theoretical framework is validated through high-accuracy numerical simulations of shock–vorticity wave interactions. The simulation results are compared with the predictions derived from the WNLF for a range of intensities and inclinations of shock-upstream vorticity fluctuations at different Mach numbers, and WNLF is found to successfully scale the numerical data for FKE, thus confirming the validity and applicability of the framework. According to WNLF findings, at lower supersonic Mach numbers, the intermodal interaction between vorticity–vorticity modes is important, whereas the interaction between vorticity and acoustic modes becomes dominant at higher Mach numbers. Using the intermodal interactions, a model based on WNLF is proposed to predict TKE amplification in STI. In comparison to direct numerical simulation, the WNLF based model predicts the TKE amplification for moderate turbulent Mach number and lower supersonic flow Mach numbers. This is a significant improvement over the LIA results available in the literature.