Dynamics of two-dimentional Rayleigh-Taylor bubbles for fluids with a finite density contrast

We study the motion of a two-dimensional coherent structure of bubbles and spikes in the Rayleigh-Taylor instability for fluids with a finite density contrast in the case of a small amplitude initial perturbation. The theoretical and numerical solutions for the system of conservation laws are found, and the dynamics of the bubble shape and velocity in the nonlinear regime is described. Good agreement between theory and simulations is achieved. A comparison to earlier models is performed.