RAYLEIGH-TAYLOR INSTABILITY IN ELASTIC LIQUIDS

In this paper the problem of the stability of an incompressible elasti c fluid at rest above a free surface is considered by carrying out a l inear stability analysis. In the first case considered the Maxwell mod el is used to include elastic effects but inertial effects are neglect ed. A characteristic equation for the growth rate is found showing a d imensionless critical wave number. However, for each fixed wave number in the region of instability, this model is found to predict an unbou nded growth rate at a certain value of the Weissenberg number. It is t hen shown how the introduction of inertial terms smooths out this sing ularity as does the change to a model which introduces a second elasti c parameter, the linear Jeffreys model. Asymptotic expansions are deve loped to show how the singularity is approached in both cases.