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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.
Cited literature [14 references]
https://hal.archives-ouvertes.fr/hal-00855780
Contributor : Denys Dutykh Connect in order to contact the contributor
Submitted on : Friday, August 30, 2013 - 9:28:02 AM
Last modification on : Monday, October 11, 2021 - 10:16:53 AM
Long-term archiving on: : Thursday, April 6, 2017 - 10:38:41 AM
Contributor : Denys Dutykh Connect in order to contact the contributor
Submitted on : Friday, August 30, 2013 - 9:28:02 AM
Last modification on : Monday, October 11, 2021 - 10:16:53 AM
Long-term archiving on: : Thursday, April 6, 2017 - 10:38:41 AM
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