PDE/Analysis seminar Larry Forbes, University of Tasmania The development of unstable interfaces

Description


Speaker: Larry Forbes, University of Tasmania, Australia

Title: The Development of Unstable Interfaces

Abstract:

Until relatively recently, the study of fluid interfaces or free-surfaces has largely been restricted to steady-state flows, where the waves on the interface do not change with time. Waves behind submarines or behind ships moving with constant speed are two famous examples.

As computers have developed, it has now become possible to look at 2D and even 3D unsteady problems, where the fluid interface evolves with time. These unsteady flows have some surprising behaviour, both analytically and numerically. If fluid viscosity is ignored, it is now known that classical flows, such as the Kelvin-Helmholtz Instability between two moving fluids, develop a singularity at the interface within finite time. This is a consequence of assuming an infinitessimally narrow interface, and can even happen between viscous fluids.
Singularities can be avoided essentially by smearing the interfacial zone over some thin, but finite-width, region.

This talk will consider some examples of unsteady fluid flow, characterized by the presence of an unstable interface. We will discuss how fluid viscosity and interface thickness change the singular behaviour predicted by (non-linear) inviscid theory, and permit the interface to overturn. Some recent developments in computer design now mean that computing these complex and unstable fluid flows is now within the reach of many researchers.
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