A Shock Wave Instability Induced on a Periodically Disturbed Interface With Plasma

Abstract

The shock wave instability induced when interacting with a small waviness on an interface was investigated analytically and numerically. The perturbation to the shock was phenomenologically treated assuming this as the consequence of the shock refraction. The instability develops in the form of wave-like stretchings into the lower density medium followed with the loss of stability in the flow behind it, and eventually evolving into an intense vortex structure. The instability mode is aperiodical and unconditional, and either a transition to another stable state or continuous development as a secondary flow is possible. Among other interesting features are: a similarity law in the spatial and temporal evolution of the perturbations with respect to the interface curvature; the instability locus independence of the gas density distribution thus identifying the interface conditions as the sole triggering factor; the role of the density gradient in the instability evolution discriminating between qualitatively different outcomes; and the possibility of decay via non-viscous dumping mechanisms. The phenomenological connection between the shock and the interface stability is discussed.

Critical Science Plan for the Daniel K. Inouye Solar Telescope (DKIST)

“…A number of shock-instability mechanisms have been identified in other settings: MHD wave breaking (Moore et al, 1987), radiative instability of the shock front (e.g. Smith, 1989;Mignone, 2005), and shock-front distortions due to plasma inhomogeneities (Brouillette, 2002;Zhou, 2017, and the references therein; Markhotok, 2018). In order for any of these to occur in the chromosphere, not only must the instability mechanism be feasible, but it must occur on a time scale short compared to shock-damping rates (Hollweg, 1987;Lanzerotti and Uberoi, 1988).…”

Wave Drag Modification in the Presence of Discharges

“…The shock refraction resulting in an increase of the absolute value of the shock velocity along with its vector rotation (at refraction angle γ) occurs at the moment when the shock front crosses the plasma interface. As the refracted shock continues to propagate in hotter medium, its dynamics is determined by the parameter distribution in the plasma volume [17,19,33,35]. Even though the changes in the shock structure become visible only during this time, they are the still consequences of the interaction at both stages: the conditions on the interface are necessary to trigger the front instability, and the gas volume effects provide the means necessary for its positive dynamics.…”

“…The overall pressure drop behind the refracted shock continuously mounting with time is responsible for the sucking effect resulting in the large-scale interface perturbation, moving it closer to the shock. The positive and essentially nonlinear dynamic in the pressure perturbation evolution [17] will support amplification of this global perturbation to the interface and thus determines the pattern in the interface instability structure. With increasing distortion of the interface, Kelvin-Helmholtz (KH) shearing instability may start to contribute resulting in the characteristic mushroom shapes of the interface perturbations [47].…”

“…Regardless of the interaction geometry, the instability mode is aperiodical and unconditional, and thus either a transition to another stable state or continuous development as a secondary flow is possible. The marginal state condition {T 2 /T 1 >(M 1 /M 2 ) 2 ,|χ| > 0} is the only requirement to trigger the instability [17], where the minimum heating requirement accounts for losses due to shock reflections off the interface. Independence of the instability locus on the plasma density distribution identifies the interface conditions as the sole triggering factor, though the density gradient can discriminate between qualitatively different outcomes at later stages of the instability evolution.…”

“…In the interaction between a shock wave and a plasma region produced in a discharge, the initially simply structured planar, bow, or oblique shock wave loses its stability and eventually evolves into a complicated system of distorted and secondary shocks with flow separation regions and formation of vortices in the flow behind the shock [16,17]. The main changes in the "shock-plasma" system include the shock's acceleration and its front distortion gradually increasing with time, followed with its weakening until it becomes unidentifiable [18,19]; motion of the shock away from the body in the presence of heating [20]; substantial gas/plasma parameter redistribution in the flow behind the shock, particularly considerable reduction of gas pressure; a vortex system forming in the aftershock flow [12]; remarkable positive dynamics in the vortex strength as the shock propagates well beyond the interface suggesting not only boundary but volume effects as well; the time delays in the effects on the flow relative to the discharge on-off times and a finite pressure rise time [21]; and finally a strong distortion or collapse of the plasma region [22].…”