Doctoral Dissertation

Since Lord Kelvin[1871] and Helmholtz[1868] firstly pointed out that a relative motion of two media causes an unstable wave at the boundary between them, many theoretical and experimental efforts have been devoted to understand its property over the last century. And today, the growing wave at such an interface is well known as Kelvin-Helmholtz (K-H) instability after the names of the first two contributors. Because of its universal property, the applications are involved in diverse areas; the K-H instability appears not only in geophysical phenomena but also in the space and astrophysical phenomena. Among a numerous applications of the K-H instability the present dissertation mainly focuses on the interaction between the solar wind and the earth magnetosphere.
High conductivity of plasma around the earth justifies the frozen-in condition, and thus the earth's intrinsic magnetic field can shield from the solar wind plasma directly penetrating into the earth atmosphere. However, the evidences that indicate the existence of the solar wind plasma inside the earth magnetosphere give us long standing problems. Especially, the indication of the direct penetration of the solar wind plasma across the low latitude boundary at the flanks of the magnetosphere, that cannot be explained by the established reconnection (open magnetosphere) model, still requires a new theoretical model. In this decade, the low latitude boundary therefore has been a subject of mass transport from the solar wind to the earth magnetosphere and many theoretical approaches have attempted to explain it. In this context, the K-H instability, which is considered to be unstable at that region, has been a candidate for this model because its non-linear development is characterized by mixture of two media. The simple vortex evolution, however, cannot explain the broad mixing area, and another mechanism is needed for this kind of issues. In this study, I again shed a new light on the K-H instability by showing that it can transport the solar wind mass in the widely spread region by computational manners. The main results of the dissertation are summarized as follows.

Cross-field diffusion across a homogeneous velocity shear layer

Mixing process of both the ion and electron across a transverse magnetic field by K-H instability is studied by using full particle simulation. The simulation results indicate that the mixing area increases with time as the K-H develops. The most mixed regions for both the ion and electron are restricted within the interface at which two plasma populations face. The increase in mixing area is mainly contributed from the stretched path length of the interface, while the cross-field diffusion in the direction perpendicular to the interface indicates that the electrons diffuse to follow the ions. Electrostatic waves induced by thermal fluctuation scatter electrons and the interface of two electron population is deformed into fine structures to fills up the ion mixing area.

Turbulent mixing and transport across a stratified velocity shear layer

Two-dimensional simulations of K-H instability in a non-uniform density medium show strong developments of turbulence through non-linear instabilities. Ideal MHD simulation results indicate that the difference in density between two media plays a crucial role on the fast turbulent mixing and transport. The onset of the turbulence is triggered not only by the secondary K-H instability but also by the Rayleigh-Taylor (R-T) instability at the density interface inside the normal K-H vortex. The secondary R-T instability alters macroscopic structure by transporting dense fluids to tenuous region, while the secondary K-H instability is just a seed for the turbulence. Full particle simulation is also conducted and reproduces the similar result of the ideal MHD's except that the secondary R-T instability grows during the first turning over motion of the normal K-H instability. Strong electrostatic field caused by the secondary R-T instability scatters ions and deforms electron density interface and as a result the mixing area increases fast and extends spatially as compared to the result in the uniform density case.

Dawn-dusk asymmetry in the non-linear development of the K-H instability

The full particle simulations of the K-H instability in the stratified shear layer show the asymmetry in the non-linear development between the positive and the negative velocity shear cases. In the positive shear case the onset of the secondary instability which leads the system to the turbulence appears in the early non-linear stage of the K-H instability. On the other hand, the apparent transition from the laminar to the turbulent flows does not appear in the negative shear case. This asymmetry was interpreted as a result of an asymmetry in the finite Larmor radius (FLR) effect at the outer edge of the vortex. The difference in the FLR effect appears at the newly induced velocity shear layer in the non-linear stage of the K-H instability. In the positive shear case (B_0\cdot\Omega_0 > 0) the outer edge of the vortex in the negative y region, where is R-T unstable, becomes a positive shear. The FLR effect weakly stabilize the onset of the secondary instability, particularly the R-T instability. On the other hand, in the negative shear case (B_0 \cdot \Omega_0 < 0), the R-T unstable region becomes a negative shear layer that increases effectively the ion gyro radius. The enhanced FLR effect strongly stabilizes the onset of the secondary R-T instability.

The present onset mechanism and the formation of the broad mixing layer give the new understanding of the mass transport mechanism from the solar wind via the low latitude boundary.