2.5D magnetohydrodynamic simulation of the Kelvin-Helmholtz instability around Venus—Comparison of the influence of gravity and density increase

Abstract

We present a numerical study of the 2.5D Kelvin-Helmholtz instability and its vortices, where an initial plasma configuration appropriate for the situation around unmagnetized planets is assumed. We solve the set of ideal magnetohydrodynamic equations numerically with the total variation diminishing Lax-Friedrichs algorithm. Our density profile is such that the mass density increases toward the planet. A high density leads to smaller growth rates of the instability and, thus, has a stabilizing effect for the boundary layer. Moreover, we include source terms in the equations, enabling us to study the influence of gravity. Our results show that gravity affects the evolution of the Kelvin-Helmholtz instability. However, the effect is not very significant. We thus conclude that the density increase toward the planet stabilizes the boundary layer around Venus more than gravity does.

Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

“…During its life-cycle, a small perturbation whose wavelength along the interface between two fluids is longer than the shear layer width, will experience linear and nonlinear growth stages to a saturation point followed by a post-saturation evolution, whereafter, may evolve into turbulent mixing through mass-momentum-energy transport and cascades of interacting vortices. Those studies also demonstrate that density ratio [35][36][37][38][39], viscosity [39][40][41], surface tension [38,39,42], magnetic field [43,44], and compressibility [37,43,45,46] suppress the evolution, while the velocity difference [38,47], and the density transition layer [47,48] favor the evolution. Despite these significant progresses to date, there still remains several fundamental issues that deserve special attention.…”

“…Owing to its extreme importance in fields including, but not limited to, listed above, the KHI has been investigated extensively through experiments, theoretical analysis and more recently by numerical simulations during the past decades [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. Those studies indicate the following scenarios.…”

“…[76,77]. While, in previous studies, nearly all numerical investigations were based on hydrodynamic equations at the Euler level [8,10,18,25,26,[33][34][35][36][37]48] which assume that the system is always in its local thermodynamic equilibrium.…”

The Kelvin-Helmholtz Instability at Coronal Mass Ejection Boundaries in the Solar Corona: Observations and 2.5D MHD Simulations

“…We solve the ideal MHD equations numerically with the so-called TVD Lax-Friedrichs scheme (Tóth & Odstrčil 1996). The numerical algorithm was already used in previous studies on the Kelvin-Helmholtz instability (Amerstorfer et al 2010;Möstl et al 2011;Zellinger et al 2012).…”

Magnetohydrodynamic Modeling Investigations of Kelvin–Helmholtz Instability and Associated Magnetosonic Wave Emission along Coronal Mass Ejections

“…We believe including a higher density value in the CME region may cause significant changes in the evolution of the KHI and MHD wave emission. Studies in the past have shown that an increase in the density gradient decreases the KHI growth and thus has a stabilizing effect on the shear flow boundary (Amerstorfer et al 2010;Zellinger et al 2012). However, the background magnetic fields on either side of the boundary were set to zero or purely perpendicular to the boundary and thus the effect of a parallel component of the background magnetic field was not included in these past studies.…”