Retour Séminaire de EDP - Physique Mathématique
Prediction of the free-surface elevation for rotational water waves using the recovery of pressure at the bed
David Henry
( Cork University ) Salle 2
le 27 mars 2018 à 14:00
In this talk we consider the pressure-streamfunction relationship for two-dimensional water waves which may possess an arbitrary distribution of vorticity. This question represents a highly-complex, intractable mathematical problem which also has immediate practical applications to both nearshore and offshore ocean environments. In the particular setting of 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: the so-called free-surface profile recovery problem. 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 (UCC).