摘 要
在磁性流體中，當速度切(velocity shear)足以克服磁場張力時，存在於速度切層中的小振幅表面波將會被速度切不穩定所增強，而速度切不穩定又可以稱為Kelvin-Helmholtz(K-H)不穩定。我們使用二維磁流體模擬碼來研究切不連續面上的K-H不穩定，發現快波馬赫數不同時，切不連續面上的磁流體表面波會有不同的非線性發展。當切不連續面兩側的快波馬赫數均小於1時，表面波因為K-H不穩定而發展成渦流結構或扭結狀表面波。當某一側的快波馬赫數大於1時，表面波會發展成非線性快波平面波(nonlinear fast-mode plane wave)。我們使用錐狀磁聲波面(magnetosonic cone)的理論模型來解釋非線性快波平面波的形成機制，而這個磁聲波椎體類似一架超音速飛機在中性氣體中造成的錐狀聲波面(sonic cone)。我們將模擬結果應用到地球磁層頂，討論磁層頂受太陽風影響所可能造成的非線性波結構。
本論文也包含了兩個針對K-H不穩定所做的初步研究。其中一個是以一不均勻的成長率(non-uniform growth rate)為條件的線性波分析，得到了與模擬結果吻合的不均勻成長率的理論解。我們也對K-H不穩定所伴隨的能量傳播作了初步的研究，而結果顯示，對低馬赫數K-H不穩定而言，大部分能量的傳播被侷限在速度切層附近，但是對高馬赫數K-H不穩定而言，大部分的能量可以隨著平面波的擴展而被傳播至遠離速度切層的區域。因此，在無碰撞電漿中(collisionless plasma)，高馬赫數K-H不穩定可以提供一個穩定有效率的能量傳播機制。

Abstract
If a velocity shear is large enough to overcome the magnetic tension force, small amplitude surface waves found in the velocity shear layer in a magnetohydrodynamic (MHD) plasma will be amplified by a velocity shear instability, which is also called Kelvin-Helmholtz (K-H) instability. The MHD K-H instability on a tangential discontinuity (TD) with a finite thickness is studied by means of a two-dimensional MHD simulation in the thesis. It is found that the nonlinear evolution of the K-H instability depends on the fast-mode Mach number of the surface wave obtained in the plasma rest frame. When the fast-mode Mach numbers on both sides of the TD are less than 1, the surface waves will be amplified by the K-H instability and grow into vortex structures or kink-type surface waves. When the fast-mode Mach number on either side of the surface wave is greater than 1, the surface disturbances associated with the K-H instability can generate fast-mode nonlinear plane waves on that side of the TD. A theoretical model of the magnetosonic cone, similar to the sonic cone generated by a supersonic aircraft, is proposed to explain the formation of the nonlinear plane waves in the high-Mach-number K-H instability. Applications of the simulation results to the magnetopause and to the solar wind are discussed in this thesis.
Preliminary results of two controversial issues associated with the K-H instability are also addressed in this thesis. The first one is to examine whether the linear growth rate of the K-H instability should be uniform in a non-uniform medium as commonly presumed in previous studies. The analytical solutions of the non-uniform growth rates obtained in this thesis are in good agreement with the simulation results that the growth rate is non-uniform. The second one is a study of the energy transport on the K-H instability. Results of the energy transport indicate that most of the energy transfer process takes place near the velocity shear layer for the low-Mach-number K-H instability. For the high-Mach-number K-H instability, a huge amount of the energy is transported away from the velocity shear layer with the expanding of the nonlinear plane waves. Thus, it is suggested that the high-Mach-number K-H instability can provide a steady and efficient mechanism, more efficient than previous studies have found, for the energy transport in the collisionless space plasma.

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