Flow Topology and Alignment Analysis of Passive Scalar Mixing in Shock Turbulence Interaction

We present a flow topology and alignment analysis of passive scalar mixing in shock-turbulence interaction. Shock-capturing Direct Numerical Simulations (DNS) are utilized, targeting different shock Mach numbers, M (1.28 to 5), turbulent Mach numbers, M_t (0.1 to 0.4, including wrinkled- and broken-shock regimes), and scalar Schmidt numbers, Sc (0.5 to 2), while keeping the Taylor microscale Reynolds number constant (Re_λ≈40). The downstream evolution of the PDFs of the P, Q and R invariants of the velocity gradient tensor is first analyzed together with conditional averages of the scalar dissipation rate. Changes across the shock of local flow topology, defined by joint PDFs on QR planes at different values of P, and the corresponding conditional scalar statistics, are then investigated. A novel barycentric map representation is introduced to study the alignments between strain-rate eigenvectors and vorticity, scalar gradient, and streamwise direction, highlighting the observed changes of these alignment across the shock and the relaxation region that follows. The effects of different flow parameters (M, M_t and Sc) on topology and alignments will be discussed, along with implications for sub-grid scale models.