Highlights► We study the Kelvin–Helmholtz instability at boundary layers around of Venus. ► The stability of the induced magnetopause and the ionopause is examined. ► The ionopause seems to be stable due to a large density jump across this boundary. ► The instability evolves into its nonlinear phase on the magnetopause at solar maximum. ► Loss rates are therefore lower than previously assumed.

[1] The paper presents the detailed numerical investigation of the "double-gradient mode," which is believed to be responsible for the magnetotail flapping oscillations-the fast vertical (normal to the layer) oscillations of the Earth's magnetotail plasma sheet with a quasiperiod 100-200 s. The instability is studied using the magnetotail near-equilibrium configuration. For the first time, linear three-dimensional numerical analysis is complemented with full 3-D MHD simulations. It is known that the "double-gradient mode" has unstable solutions in the region of the tailward growth of the magnetic field component, normal to the current sheet. The unstable kink branch of the mode is the focus of our study. Linear MHD code results agree with the theory, and the growth rate is found to be close to the peak value, provided by the analytical estimates. Full 3-D simulations are initialized with the numerically relaxed magnetotail equilibrium, similar to the linear code initial condition. The calculations show that current layer with tailward gradient of the normal component of the magnetic field is unstable to wavelengths longer than the curvature radius of the field line. The segment of the current sheet with the earthward gradient of the normal component makes some stabilizing effect (the same effect is registered in the linearized MHD simulations) due to the minimum of the total pressure localized in the center of the sheet. The overall growth rate is close to the theoretical double-gradient estimate averaged over the computational domain.

A linear MHD instability of the electric current sheet, characterized by a small normal magnetic field component, varying along the sheet, is investigated. The tangential magnetic field component is modeled by a hyperbolic function, describing Harris-like variations of the field across the sheet. For this problem, which is formulated in a 3D domain, the conventional compressible ideal MHD equations are applied. By assuming Fourier harmonics along the electric current, the linearized 3D equations are reduced to 2D ones. A finite difference numerical scheme is applied to examine the time evolution of small initial perturbations of the plasma parameters. This work is an extended numerical study of the so called “double gradient instability”, – a possible candidate for the explanation of flapping oscillations in the magnetotail current sheet, which has been analyzed previously in the framework of a simplified analytical approach for an incompressible plasma. The dispersion curve is obtained for the kink-like mode of the instability. It is shown that this curve demonstrates a quantitative agreement with the previous analytical result. The development of the instability is investigated also for various enhanced values of the normal magnetic field component. It is found that the characteristic values of the growth rate of the instability shows a linear dependence on the square root of the parameter, which scales uniformly the normal component of the magnetic field in the current sheet.

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.

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