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.
Domains
Physics [physics] Mechanics [physics] Fluid mechanics [physics.class-ph] Engineering Sciences [physics] Mechanics [physics.med-ph] Fluids mechanics [physics.class-ph] Physics [physics] Physics [physics] Fluid Dynamics [physics.flu-dyn] Physics [physics] Physics [physics] Computational Physics [physics.comp-ph]
Origin : Files produced by the author(s)
Loading...