Approximate treatment of density gradients in Rayleigh-Taylor instabilities

We present an approximate method, based on a moment equation, to derive explicit analytic formulas for the growth rate of Rayleigh-Taylor instabilities in fluids with density gradients. We illustrate with several examples and compare the results with our earlier method of treating a continuous density profile as a large number of fluid layers. The emphasis is on obtaining simple analytic formulas for the largest growth rate.