Variational approach for linear growth rate of Rayleigh-Taylor instability with continuous density profile

The stabilization effect on Rayleigh-Taylor instability of density gradient was studied, with the variational and finite element approach to solve the Chandrasekhar equation. The growth rates under different density profiles were gained for ideal incompressible fluids and compared with those derived by the modified Lindl formula. The largest difference between of the results the numerical simulation and the formula happens when the perturbation wave length equals to the density scale length, and the peak value of the perturbation lies at the points where the scale length function meets its extreme. The two results agree well when the pertubation wave number appoaches infinity or infinitesimal. The pertubation velocities were also got in the simulation.