On the Kelvin-helmholtz Instability of the Earth’s Magnetopause

-The effect of the finite thickness of the shear layer on the Kelvin-Helmholtz instability of the Earth’s magnetopause boundary is investigated. The thickness of the layer stabilizes the boundary with respect to short wavelength perturbations, which were previously found to be unstable in the zero thickness analysis. Compressibility effects further stabilize the layer. The effects of the magnetic field on the instability are also discussed. INTRODUCTION The hydromagnetic Kelvin-Helmholtz (K-H) instability has been discussed by various authors in connection with the solar wind and its interaction with the Earth’s magnetic field. Fejer (1964) and McKenzie (1970) considered the K-H instability of the magnetopause in regard to the viscous interaction between the solar wind and the magnetosphere. The magnetopause instability phenomenon was also used to explain the semi-annual magnetic field variation (Boller and Stolow ,1970), and the occurrence of ultra low frequency micropulsations in the magnetic field (Dungey and Southwood, 1970). In regard to the physics of the solar wind itself the instability has been discussed in connection with solar wind heating and the smoothing of velocity gradients between fast and slow streams (Coleman, 1969; Jokipii and Davis, 1969). Southwood (1968) showed that the magnetopause is unstable at low and middle latitudes even for small values of the flow velocity. For these cases the flow velocity is not closely aligned with the Earth’s magnetic field and has a large component in the equatorial plane. In these low latitude regions we find a large north-south oriented magnetic field inside the magnetosphere. On the other hand, the field in the magnetosheath is much smaller and oriented in a different direction. The instability was shown to develop in regions along the equatorial plane just away from the subsolar point. The flow velocity in these regions is small compared to the local speed of sound. Lerche (1966) showed that the hydromagnetic analysis of the K-H instability of shear layers of zero thickness leads to an inconsistency. The stability criterion depends on the phase velocity of the various modes and therefore the highest growth rate occurs for the shortest wavelength disturbances. However, for very short wavelength perturbations the thickness of the shear layer should be taken into account. In this paper we study the effect of the finite thickness of the shear layer on the K-H instability of the magnetopause. In the following section we introduce the model and formulate the problem. Since the flow velocity in the region of instability is small compared to the sound speed we first perform the incompressible flow analysis. The effect of compressibility is then shown next. In order to analyze the magnetosphere boundary instability problem properly Lerche (1966) also felt that the collisionless Vlasov equation together with the Maxwell’s equations should be used. As we have no way of determining the form of the particle distribution function in the turbulent magnetosheath region this approach is theoretically very difficult, if not impossible. Thus we shall use a hydromagnetic model and limit ourselves to an order of magnitude estimate of the mascroscopic behavior of the magnetosphere boundary.