RAYLEIGH-TAYLOR INSTABILITY IN ELASTIC LIQUIDS

In this paper the problem of the stability of an incompressible elastic fluid at rest above a free surface is considered by carrying out a linear stability analysis. In the first case considered the Maxwell model is used to include elastic effects but inertial effects are neglected. A characteristic equation for the growth rate is found showing a dimensionless critical wave number. However, for each fixed wave number in the region of instability, this model is found to predict an unbounded growth rate at a certain value of the Weissenberg number. It is then shown how the introduction of inertial terms smooths out this singularity as does the change to a model which introduces a second elastic parameter, the linear Jeffreys model. Asymptotic expansions are developed to show how the singularity is approached in both cases.