The conformal-mapping method for surface gravity waves in the presence of variable bathymetry and mean current

Claudio Viotti 1 Denys Dutykh 1, 2, * Frédéric Dias 1, 3
* Corresponding author
1 School of Mathematical Sciences [Dublin]
2 LAMA - Laboratoire de Mathématiques
3 CMLA - Centre de Mathématiques et de Leurs Applications
Abstract : The conformal mapping formulation for the free-surface Euler equations in the presence of non homogeneous, yet stationary bathymetry is here derived and numerically implemented. The differences arising with respect to the more familiar flat-bottom and deep-water versions of the method are examined in detail. It is also shown how the loss of translational invariance due to the variable bottom profile naturally leads to consider a further extension of the method, which accounts for the superposition - otherwise immaterial - of an irrotational mean stream. As it is illustrated by numerical examples, the formulation presented is suitable for the study of fully nonlinear wave-topography and wave-current interactions realized by combining mean current and variable bathymetry.
Keywords : surface gravity waves conformal mapping spectral methods
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Claudio Viotti, Denys Dutykh, Frédéric Dias. The conformal-mapping method for surface gravity waves in the presence of variable bathymetry and mean current. Procedia IUTAM, cElsevier, 2014, 11, pp.110-118. ⟨10.1016/j.piutam.2014.01.053⟩. ⟨hal-00855780⟩

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