February 23, 2000, 4.00 pm
Lecture Theatre OF/B9 Oddfellows Hall (Material Science)
The saturation of the Rayleigh-Taylor instability
Prof. David Halpern, Department of Mathematics, University of Alabama
The stability of a two fluid system between two horitontal
plates is considered, where the lighter fluid is at the bottom, and
a plane Couette-type flow between the plates is generated by an
in-plane circular spinless motion of the upper plate.
We derive and numerically study an evolution equation governing the
thickness of the viscous film. The equation has the familiar
Kuramoto-Sivashinsky (KS) form but is modified by an additional
time-dependent factor multiplying the nonlinear term. Numerical
solutions on extended spatial intervals reveal interesting
time-asymptotic regimes in which averaged properties of the extensive
spatiotemporal chaos are not steady but rather oscillate in time.
The results are interpreted along the lines developed earlier for the
simpler case of a film evolution governed by the classical,
time-independent KS equation.
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