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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Numerical Analysis Seminars: Convective instabilities in a fluid overlying a porous material

Presented by Antony Hill, Nottingham University

28 November 2008 15:15 in CM107

The instability of parallel flows and in particular Poiseuille or
Couette flow has been a major problem in fluid mechanics for a long
time. The reason to study such systems is motivated by their numerous
industrial and geophysical applications. We study the Poiseuille flow
instability problem, where a Newtonian fluid overlies a porous material
saturated with the same fluid. By introducing a transition layer between
the homogeneous fluid and porous layers in the model (a three layer
approach), we show that the difficulties associated with the two layer
approach may be overcome.

We will also discuss the development of energy techniques to assess the
nonlinear stability thresholds of fluid/porous problems. This is done in
the context of another rich area of fluid/porous research; that of
thermal convection. We show that for the nonlinear Stokes problem, the
linear instability and unconditional nonlinear stability thresholds
coincide, demonstrating that the linear theory accurately emulates the
physics of the onset of convection.

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