Steady surface water waves on a Beltrami flow are equivalent to two scalar equations for the surface elevation and a surface potential, derived from a variational principle via a nonlocal operator that generalizes the Dirichlet-Neumann operator.
2015 Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water waves equations with vorticity
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A variational formulation for steady surface water waves on a Beltrami flow
Steady surface water waves on a Beltrami flow are equivalent to two scalar equations for the surface elevation and a surface potential, derived from a variational principle via a nonlocal operator that generalizes the Dirichlet-Neumann operator.