Suppression mechanism of Kelvin-Helmholtz instability in compressible fluid flows

Kelvin-Helmholtz instability in a compressible dust fluid flow

We report the first experimental observations of a single-mode Kelvin-Helmholtz instability in a flowing dusty plasma in which the flow is compressible in nature. The experiments are performed in an inverted [Formula: see text]-shaped dusty plasma experimental device in a DC glow discharge Argon plasma environment. A gas pulse valve is installed in the experimental chamber to initiate directional motion to a particular dust layer. The shear generated at the interface of the moving and stationary layers leads to the excitation of the Kelvin-Helmholtz instability giving rise to a vortex structure at the interface. The growth rate of the instability is seen to decrease with an increase in the gas flow velocity in the valve and the concomitant increase in the compressibility of the dust flow. The shear velocity is further increased by making the stationary layer to flow in an opposite direction. The magnitude of the vorticity is seen to become stronger while the vortex becomes smaller with such an increase of the shear velocity. A molecular dynamics simulation provides good theoretical support to the experimental findings.

Continuum breakdown in compressible mixing layers

Gas-kinetic simulations of rarefied and compressible mixing layers are performed to characterize continuum breakdown and the effect on the Kelvin-Helmholtz instability. The unified gas-kinetic scheme (UGKS) is used to perform the simulations at different Mach and Knudsen numbers. The UGKS stress tensor and heat-flux vector fields are compared against those given by the Navier-Stokes-Fourier constitutive equations. The most significant difference is seen in the shear stress and transverse heat flux. The study demonstrates the existence of two distinct continuum breakdown regimes, one at low and the other at high convective Mach numbers. Overall, at low convective Mach numbers, the deviation from continuum stress and heat flux appears to scale exclusively with the micro-macro length scale ratio given by the Knudsen number. On the other hand, at high convective Mach numbers, the deviation depends on the global micro-macro timescale ratio given by the product of Mach and Knudsen numbers. We further demonstrate that, unlike shear stresses and transverse heat flux, the deviations in normal stresses and the streamwise heat flux depend separately on Knudsen and Mach numbers. A local parameter called the gradient Knudsen number is proposed to characterize the rarefaction effects on the local momentum and thermal transport. Noncontinuum aspects of gas-kinetic stress-tensor and heat-flux behavior that Grad's 13-moment equation model reasonably captures are identified.

Influence of Knudsen and Mach numbers on Kelvin-Helmholtz instability

The combined influence of rarefaction and compressibility on classical Kelvin-Helmholtz instability is investigated with numerical simulations employing the unified gas kinetic scheme. Five different regimes in the Reynolds-Mach-Knudsen number parameter space are identified. The flow features in various Mach and Knudsen number regimes are examined. Stabilizing action of compressibility leads to suppression of perturbation kinetic energy and vorticity and/or momentum thickness. The suppression due to rarefaction exhibits a different behavior. At high enough Knudsen numbers, even as the perturbation kinetic energy is suppressed, the vorticity and/or momentum thickness grows. The flow physics underlying the contrasting mechanisms of compressibility and rarefaction is highlighted.

Influence of orientation on the evolution of small perturbations in compressible shear layers with inflection points

We investigate the influence of orientation on the evolution of small perturbations in compressible shear layers with inflection points. By using linear analysis, we demonstrate that perturbations along the shear plane are most affected by compressibility. The influence of compressibility gradually diminishes with increasing obliqueness of the perturbations with respect to the shear plane. It is demonstrated that the effective gradient Mach number is an appropriate compressibility parameter. We establish that spanwise perturbations, orthogonal to the shear plane, are impervious to compressibility effects. Direct numerical simulations of compressible mixing layers subject to the perturbations at various obliqueness angles verify the analytical findings.