Amplification of Turbulence by Multiple Planar Shocks

We study the amplification of isotropic, incompressible turbulence through multiple planar shocks, using results from Linear Interaction Analysis (Ribner 1953). There are two limiting cases we explore. The first assumes shocks occur rapidly in time such that the turbulence does not evolve between shocks. Whereas the second case allows enough time for turbulence to isotropize between each shock. For the latter case, through a quasi-EOS, we show that the weak multi-shock limit is agnostic to the distinction between thermal and vortical turbulent pressures, like an isotropic volumetric compression. When turbulence does not return to isotropy between shocks, we find that amplification is sensitive to the shock ordering. We map how choices of shock strength can impact these amplification differences due to ordering, finding, for example, shock pairs which lead to identical mean post-shock fields (density, temperature, pressure) but maximally distinct turbulent amplification.