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Instability

Controlling instability growth

Original name flow_instab.tiff Credit: Nick Jamieson

When conditions change, some steady flows start to oscillate. These oscillations can develop into nonlinear phenomena such as turbulence. This is sometimes useful and sometimes not. Using tools from linear algebra, dynamical systems, and optimal control, we can predict the shape of oscillations, how they will develop, and how to control them, for example by suppressing or enhancing their growth.

 Top: Contours of the vertical velocity of the most unstable motion that develops on the flow around a cylinder at Reynolds number 50. This develops into von Kármán vortex shedding as the amplitude increases.

Bottom: Contours of the regions of the flow that are most receptive to forcing if one wants to stimulate or suppress von Kármán vortex shedding. The most receptive regions are at the points where the boundary layer around the cylinder separates.