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Colloque Promenade dans la physique d’aujourd’hui / A Stroll through Today’s Physics

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Inclined to exchange: shocking gravity currents
John Hinch (univ. Cambridge)

28 juin 2007

Experiments at Laboratoire FAST have studied the flow which ensues in an inclined pipe which starts with the upper half-length filled with a heavy liquid and the lower half-length filled with a light fluid. This talks aims at providing a little theory for the special regime of slow flows in a nearly horizontal pipe. In a viscous gravity current, the light fluid spreads up along the pipe occupying the upper half of the cross-section while the heavy fluid moves down in a counter current. This viscous spreading is described by a nonlinear advection-diffusion equation for the dependence along the pipe of the height of the flat horizontal interface in the cross-section, very similar to the spreading of a viscous drop on a flat plane. Curiously, the solution of the diffusion equation involves matching a shock wave to a rarefaction wave.

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John Hinch John Hinch (univ. Cambridge)
CMS-DAMTP, Cambridge U.K.