The Kelvin-Helmholtz instability at Venus: What is the unstable boundary?

Abstract

The Kelvin-Helmholtz instability gained scientific attention after observations at Venus by the spacecraft Pioneer Venus Orbiter gave rise to speculations that the instability contributes to the loss of planetary ions through the formation of plasma clouds. Since then, a handful of studies were devoted to the Kelvin-Helmholtz instability at the ionopause and its implications for Venus. The aim of this study is to investigate the stability of the two instability-relevant boundary layers around Venus: the induced magnetopause and the ionopause. We solve the 2D magnetohydrodynamic equations with the total variation diminishing Lax-Friedrichs algorithm and perform simulation runs with different initial conditions representing the situation at the boundary layers around Venus. Our results show that the Kelvin-Helmholtz instability does not seem to be able to reach its nonlinear vortex phase at the ionopause due to the very effective stabilizing effect of a large density jump across this boundary layer. This seems also to be true for the induced magnetopause for low solar activity. During high solar activity, however, there could occur conditions at the induced magnetopause which are in favour of the nonlinear evolution of the instability. For this situation, we estimated roughly a growth rate for planetary oxygen ions of about 7.6 × 10(25) s(-1), which should be regarded as an upper limit for loss due to the Kelvin-Helmholtz instability.

Fig. 1

Total pressure as a function of solar zenith angle for different terminator pressures.

Fig. 2

Mass density, velocity, magnetic field and plasma pressure along the obstacle surface as a function of the solar zenith angle and for different terminator total pressures.

Fig. 3

Normalized total pressure and normalized magnetic field as a function of solar zenith angle along the obstacle surface.

Fig. 4

Maximum growth rate γ as a function of the solar zenith angle θ for ρ₁ = 10 (upper plot) and ρ₁ = 100 (lower plot). The legend is valid for both plots.

Fig. 5

Time evolution of the maximum of ln(E_y) of every time step for Π₀ = B₀ = 1.0 and for different ρ₁.

Fig. 6

Time series of the density.

Fig. 7

Normalized growth rate as a function of normalized wave number for different densities for Π₀ = B₀ = 1.0. The asterisks and the diamonds give the values of the growth rate calculated for B₁ = 1.1 and B₁ = 0.5, respectively.

Fig. 8

Normalized maximum growth rate (upper plot) and corresponding normalized linear growth time (lower plot) as a function of the density ratio for Π₀ = 1.0 and B₀ = 1.0. The symbols denote the values obtained numerically, the line represents a logarithmic fit.