彗木相撞的不可压缩分层流体模型

An Incompressible Stratified Fluid Model of the Comet's Collision with Jupiter

提出了一个彗木相撞的线性模型。在这个模型中,将木星大气看作是一个分层的、不可压缩和无粘滞的流体层,而与撞击相联的引力波则由一个初始冲力所造成。 采用初始冲压P(r,z,0)代替初始表面形变作为初始条件。发现这种做法使得问题的数学处理更加方便,特别是在计算流体粒子的垂直位移和摄动势能方面,后者可以表为P(r,z,0)的有限傅立叶正弦和余弦变换。 导出了一个联系彗星碰撞参数、木星大气参数和所设初始冲力之间的关系式。还对两种P(r,z,0)的假设形式分析地导出表面波波高。

A linear model of the comet's collision with Jupiter is presented, in which the Jovian atmosphere is considered as a stratified, incompressive and inviscid fluid layer and the gravity wave associated with the impacts is caused by an initial impulse. In stead of adopting an initial surface deformation, we take an initial impulsive pres- sure P(r, z, o) as the initial condition. It is found that this approach is more convenient for the mathematical formulation of the problom, especially for the computation of the verti- cal displacement of the fluid particles and the perturbation potential energy which can be expressed by finite Fourier sine and cosine transform of P(r, z, o). A relationship among cometary impact parameter, Jovian atmosphere parameter and the assumed initial impulse is deduced. We also derive the wave height of the surface wave analytically for two assumed forms of P(r, z, o).