彗木相撞的可压缩分层流体模型

提出一个彗木相撞的修正了的线性模型．在这个模型中,将木星大气视为一个转动的、分层的、可压缩和无粘滞的流体层．结果表明,虽然大部分撞击能量仍然转换成内波能量,但不能忽视可压缩效应．

A Compressive Stratified Fluid Model of the Comet's Collision with Jupiter

In order to explain the waves arising from the collisions of Comet Shoemaker-Levy 9 with Jupiter, we present a revised linear model in which the gravity wave propagation associated with the impacts is caused by an initial impulse and the Jovian atmosphere is considered as a rotating stratified, compressive and inviscid fluid layer. By means of a procedure similar to that adopted in Gill's book (1982), two derived equations (8) and (9) involving only the perpendicular component of perturbation velocity and the perturbation pressure can be obtained. In terms of the new variables defined by (11) and (12), the equations turn into (13) and (14). As pointed out by Dowling (1995), the Jovian atmosphere is a thin sheet of fluid and the shallow-water model can be used. It also means that the hydrostatic approximation can be used and the basic equations become (15) and (16). These equations have separable solutions of the form (17). It is stressed that we take an initial impulsive pressure prescribed at the surface of Jupiter as the initial condition rather than an initial surface deformation. This approach is expedient for the mathematical formulation of the problem, for instance, the vertical displacement of a fluid particle can be expressed by an integral transform of the potential energy and thereupon can be calculated. It is also shown by the calculations that although the contribution of the compressibility in the participation of impact energy is larger than that of the surface waves, which indicates the effect of compressibility can not be ignored, the energy of the internal waves is still the main part, i.e. most of the impacting energy is converted into the energy of internal waves.