Direct Numerical Simulation of Shock-wave/Isotropic Turbulence Interaction

We conduct direct numerical simulations (DNS) of shock/isotropic-turbulence interactions (SITI), in which the turbulence is highly compressible. We find, consistent with previous studies using weakly compressible turbulence, that turbulent kinetic energy and spanwise vorticity fluctuations become persistently amplified upon passage through a shock wave and that the spanwise Taylor microscale becomes persistently diminished. In addition, we find that the directional bias predictably introduced by the shock wave into the initially isotropic flow persists to some degree well downstream; and we also find that the shape of the shock wave becomes distorted by the passing turbulence to such a degree that sections of it may be found far upstream of its average position, causing statistical changes attributable to shock interaction to begin unexpectedly early. I. Introduction The interaction of turbulence with shock waves occurs in many external and internal fluid flows, including but not limited to flows over the surfaces of fast-moving vehicles and flows within the engines of such vehicles. Strong coupling between the two phenomena and strong nonlinearities in the interaction dynamics can lead to substantial changes in the structures of both the shock wave, which may impinge on surfaces at altered locations and with altered intensities, and the passing turbulence, which may cause physical mechanisms such as energy transfer to behave di!eren tly throughout the entire downstream region. The simplest shock/turbulence interaction configuration is that of homogeneous isotropic turbulence interacting with a steadily moving normal shock wave, but because of diculties in forming such a configuration experimentally and adequately resolving it numerically, a much larger body of work exists for interactions of shock waves with turbulent boundary layers than for interactions with isotropic turbulence. While studies of shock/turbulent-boundary-layer interactions are of great importance from the standpoints of both physics and engineering, concurrent studies of shock/isotropic-turbulence interactions (SITI) can help to elucidate which physical processes are common to shock/turbulence interaction in general and which may be unique to interactions that include boundary layers.