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Prediction of the free-surface elevation for rotational water waves using the recovery of pressure at the bed

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NWWW01 - Nonlinear water waves

In this talk we consider the pressure-streamfunction relationship for a train of regular water waves propagating on a steady current, which may possess an arbitrary distribution of vorticity, in two dimensions. The application of such work is to both nearshore and offshore environments, and in particular for linear waves we provide a description of the role which the pressure function on the sea-bed plays in determining the free-surface profile elevation.

Our approach is shown to provide a good approximation for a range of current conditions, leading to the derivation of expressions for the pressure transfer function, and the related pressure amplification factor, which generalise the well-known formulae for irrotational waves. An implementation of the moderate current approximation renders these expressions more tractable, leading to quite elegant and explicit formulae.

This is joint work with Gareth Thomas.

This talk is part of the Isaac Newton Institute Seminar Series series.

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