Amplification of turbulence through multiple planar shocks

TL;DR

This paper analyzes how multiple planar shocks amplify isotropic turbulence using linear theory, exploring effects of shock timing, strength, and ordering on turbulence amplification and anisotropy.

Contribution

It introduces a theoretical framework for understanding turbulence amplification through multiple shocks, including effects of shock timing, strength, and ordering, and their impact on turbulence anisotropy.

Findings

Amplification depends on shock strength and timing.

Shock ordering can significantly alter turbulence amplification.

Post-shock mean fields can be identical despite different turbulence amplification.

Abstract

We study the amplification of isotropic, incompressible turbulence through multiple planar, collisional shocks, using analytical linear theory. 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-equation-of-state, 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, the generated anisotropy -- itself a function of shock strength -- can feedback on amplification by further shocks, altering choices for maximal or minimal amplification. In addition for this case, 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.