Critical free surface flow over topography

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• Mark Blyth (University of East Anglia)
• Monday 11 November 2019, 16:00-17:00
• CMS, MR15.

If you have a question about this talk, please contact Matthew Priddin.

Two-dimensional free-surface flow over a localised bottom topography is examined with an emphasis on calculating steady, forced solitary-wave solutions. In particular we focus on the case of a Gaussian dip topography. Most of the focus is on the weakly-nonlinear limit where a forced KdV equation is applicable, and the problem essentially boils down to solving a forced nonlinear ODE with a single parameter that quantifies the amplitude of the topography. This equation has a rich solution space with a large (probably infinite) number of solution branches. Asymptotic analysis for small topography amplitude reveal some interesting features, for example an internal boundary layer which mediates a change from exponential to algebraic decay of the free-surface in the far-field. Traditional boundary-layer theory fails beyond the first two solution branches, where the surface profiles feature multiple waves trapped over the topography. The stability of the steady solutions will also be briefly discussed.

This talk is part of the Waves Group (DAMTP) series.

This talk is included in these lists:

• CMS, MR15
• Waves Group (DAMTP)

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