An incompressible stratified fluid model of Comet Shoemaker-Levy 9's collision with Jupiter

A linear model of Comet Shoemaker-Levy 9's collision with Jupiter is presented, in which the Jovian atmosphere is taken to be a stratified, incompressible and inviscid fluid layer and the gravity wave associated with the impacts is caused by an initial impulse. Instead of adopting an initial surface deformation, we take an initial impulsive pressure P(r, z, 0) as the initial condition. It is found that this approach is more convenient for the mathematical formulation of the problem, especially for the computation of the vertical displacement of the fluid particles and the perturbation potential energy which can then be expressed by finite Fourier sine and cosine transform of P(r, z, 0). A relationship among parameters of the impact and the Jovian atmosphere 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, 0).