Numerical Analysis Seminars: Transitional flows and dynamos: nonlinear optimisation of velocity fields for instability
14 November 2014 14:00 in CM105
A common pursuit is to optimise a number of control parameters in order to suppress or avoid the appearance of an instability, e.g. for drag reduction. In recent years, however, it has become possible to use similar variational methods as a means to determining the most direct route to instability. This involves the construction of a variational problem where the `parameter'-space is now huge, being the entire space of possible velocity fields. This field, if corresponding to a flow, must be subject to the constraints of boundary conditions and the governing equations.
The natural application to shear flows has enabled us to identify the minimal flow structures that lead to instability,
i.e. to the transition to turbulence. For the dynamo instability one seeks a velocity field that leads magnetic energy growth, and it has been possible to put a lower bound on the `power' of the driving flow.
Whilst powerful at first sight, the variational method suffers a number of difficulties that the settings above highlight.
Pringle, C.T., Willis, A.P., and Kerswell, R.R., Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos, J. Fluid Mech., 702, 415-443 (2012).
Willis, A.P., Optimization of the magnetic dynamo, Phys. Rev. Lett. 109, 251101 (2012)
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