Analysis and modeling of thermodynamic fluctuations generated by shock-turbulence interaction

We propose simplemodels for the thermodynamic fluctuations in canonical shock-turbulence interaction based on the physical mechanisms observed from linear interaction analysis (LIA). The models are developed in conjunction with the two-equation k − ǫ model. The production of temperature, density, entropy and pressure variances across the shock is modeled in terms of the turbulent kinetic energy (TKE) and their corresponding decay mechanism is modeled as per the relevant physical mechanism observed in LIA. The pressure and the entropy variances are modeled with acoustic and viscous decay mechanisms, respectively. The decay mechanism of temperature variance employs a model of mixed type, which accounts for both the acoustic and the entropymode contributions in the evolution of the temperature variance. The proposed models compare well with the direct numerical simulation (DNS) data.