"Fundamental understanding and modeling of multi-fluid miscible Shock-Turbulence Interaction (STI) and the corresponding post-shock turbulence are critically important to many different applications, such as supersonic combustion, nuclear fusion, and astrophysics. This thesis presents a comprehensive study of the multi-fluid Shock-Turbulence flow using accurate flow-resolving, shock-capturing, and shock-resolving simulations. The objective is to develop a better understanding of underlying mechanisms of the variable density fluid effects on shock-turbulence interactions, post-shock turbulence evolution and mixing in high speed flows. Theoretical and numerical analyses of data confirm that all turbulence scales as well as the STI are well captured by the computational method, which is based on a high order hybrid monotonicity preserving-compact finite difference scheme. Linear Interaction Approximation (LIA) convergence tests are conducted to show that shock-capturing numerical simulations exhibit similar converging trend to LIA predictions as more demanding shock-resolving Direct Numerical Simulations (DNS) method. The effects of density variations on STI are studied first by comparing the "Eulerian" results obtained from both Eulerian (grid) and Lagrangian (particle) data for a multi-fluid mixture with the corresponding single-fluid results. The comparison shows that the turbulence amplification by the normal shock wave is much higher and the reduction in turbulence length scales is more significant when strong density variations are present. Turbulent mixing enhancement by the shock is also increased and stronger mixing asymmetry in the post-shock region is observed when there are significant density variations. The dominating mechanisms behind STI influence on post-shock turbulence and mixing are identified by analyzing the transport equations for the Reynolds stresses, vorticity, normalized mass flux, and density specific volume covariance. Statistical analyses of the velocity gradient tensor (VGT) show that the density variations also significantly change the turbulence structure and flow topology. Compared to the single-fluid case, the correlation between rotation and strain is found to be weaker in the multi-fluid case, which is shown to be the result of complex role density plays when the flow passes through the shock. Furthermore, a stronger symmetrization of the joint PDF of second and third invariants of the anisotropic velocity gradient tensor, as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multi-fluid case. Lagrangian dynamics of the VGT and its invariants are studied by considering particle residence times in different flow regions and the conditional mean rate of change vectors. The pressure Hessian contributions to the VGT invariants transport equations are shown to be strongly affected by the shock wave and local density, making them critically important to the flow dynamics and turbulence structure. Lagrangian statistics of non-inertial particles in post-shock turbulence show that the single-particle dispersion rate and anisotropy can be correlated to the development of post-shock Reynolds stress. The particle dispersion in the streamwise direction is found to be non-Gaussian, with the skewness of the dispersion PDF dependent on the density variations. Lagrangian integral time scales of fluid particles with different densities are obtained from velocity autocorrelation functions. Particle pair dispersion generally follows the temporal scaling for isotropic turbulence. In this thesis, the propagation of shock waves in non-uniform density media is also studied. Theoretical analyses show that in both linear and nonlinear regime, there are similarities in shock propagation in non-uniform density fields generated by fluctuations in entropy and compositional fields. The 1D numerical results are shown to agree well with theoretical solutions obtained from classical Chisnell-Whitham theory for weak shocks and linearly varying density fields. For more significantly varying density profiles, the numerical results deviate from the theoretical solutions and exhibit additional long-wavelength oscillations, which are shown to be related to the re-reflected waves. A simplified model (named CWRW) that includes the effects of re-reflected waves is proposed to compensate for the CW model definitions. The results obtained by the proposed CWRW model show significant improvement over the classical CW model. The three-dimensional (3D) effects concerning the shock propagation in 3D non-uniform density media are studied by considering the wavenumber ratio of the streamwise and spanwise length scales in the density field. The asymptotic limits for wavelength ratio approaching zero and infinity are investigated and used to provide a bound for shock propagation in 3D non-uniform media."--Pages ii-iii.
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