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

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

Bibliographic record

BibTeX Citation

@article{Viotti2014conformalmappingmethod,
  author = {Viotti, C. and Dutykh, D. and Dias, F.},
  title = {The conformal-mapping method for surface gravity waves in the presence of variable bathymetry and mean current},
  journal = {Procedia IUTAM},
  year = {2014},
  volume = {11},
  pages = {110--118},
  doi = {10.1016/j.piutam.2014.01.053},
  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 = {conformal mapping, surface gravity waves, spectral methods}
}