Development of nonlinear two fluid interfacial structures by combined action of Rayleigh-Taylor, Kelvin-Helmholtz and Richtmyer-Meshkov instabilities:Oblique shock

TL;DR

This paper investigates the nonlinear evolution of interfacial structures like bubbles and spikes caused by combined Rayleigh-Taylor, Kelvin-Helmholtz, and Richtmyer-Meshkov instabilities under oblique shock conditions, providing analytical growth rate expressions.

Contribution

It introduces new analytical expressions for the asymptotic growth rates of interfacial structures under combined instabilities caused by oblique shocks, extending previous models.

Findings

Growth rate tends to a constant velocity for oblique shocks.

Interface perturbations can grow monotonically or oscillate depending on velocity shear.

Implications for astrophysical jet formation are discussed.

Abstract

The nonlinear evolution of two fluid interfacial structures like bubbles and spikes arising due to the combined action of Rayleigh-Taylor and Kelvin-Helmholtz instability or due to that of Richtmyer-Meshkov and Kelvin-Helmholtz instability resulting from oblique shock is investigated. Using Layzer's model analytic expressions for the asymptotic value of the combined growth rate are obtained in both cases for spikes and bubbles. However, if the overlying fluid is of lower density the interface perturbation behaves in different ways. Depending on the magnitude of the velocity shear associated with Kelvin-Helmholtz instability both the bubble and spike amplitude may simultaneously grow monotonically (instability) or oscillate with time or it may so happen that while this spike steepens the bubble tends to undulate. In case of an oblique shock which causes combined action of Richtmyer-Meshkov instability arising due to the normal component of the shock and Kelvin Helmholtz instability through creation of velocity shear at the two fluid interface due to its parallel component, the instability growth rate-instead of behaving as $1/t$ as $t \rightarrow \infty$ for normal shock, tends asymptotically to a spike peak height growth velocity $\sim \sqrt{\frac{5(1+A_{T})}{16(1-A_{T})}(\Delta v)^2}$ where $\Delta v $ is the velocity shear and $A_T$ is the Atwood number. Implication of such result in connection with generation of spiky fluid jets in astrophysical context is discussed.