Linear stability of stratified fluids and the associated nonlinear eigenvalue problem

Richard Kollar, IMA

It's a problem that has long puzzled fluid dynamicists: How long does it take the waves in a container of fluid to settle? To date there is no complete mathematical analysis; the air/liquid/wall contact line and surface tension complicate things. But for "supercritical" fluids at high pressure (important in several industrial processes, such as decaffeination of coffee) modeled by the incompressible Navier-Stokes equations, the sharp distinction between liquid and vapor disappears. Viscosity can be expected to damp internal waves with a characteristic exponential relaxation time associated with the slowest decaying mode of the system. This work proves that, surprisingly, there is no slowest decaying mode in such stratified fluids. (This is a joint work with R. L. Pego and K. F. Gurski.)