39 research outputs found
Steady waves in flows over periodic bottoms
We study the formation of steady waves in two-dimensional fluids under a
current with mean velocity flowing over a periodic bottom. Using a
formulation based on the Dirichlet-Neumann operator, we establish the unique
continuation of a steady solution from the trivial solution for a flat bottom,
with the exception of a sequence of velocities . The main contribution
is the proof that at least two steady solutions for a near-flat bottom persist
close to a non-degenerate -orbit of non-constant steady waves for a flat
bottom. As a consequence, we obtain the persistence of at least two steady
waves close to a non-degenerate -orbit of Stokes waves arising from the
velocities for a flat bottom