Journal ArticleDOI
Large-amplitude steady rotational water waves
Joy Ko,Walter A. Strauss +1 more
TLDR
Two-dimensional, finite-depth periodic water waves with general vorticity and large amplitude are computed in this paper, and the mathematical formulation and numerical method that allow us to compute a continuum of such waves with arbitrary vortivities are described.Abstract:
Two-dimensional, finite-depth periodic water waves with general vorticity and large amplitude are computed The mathematical formulation and numerical method that allow us to compute a continuum of such waves with arbitrary vorticity are described The problems of whether extreme waves exist, where their stagnation points occur, and what qualitative features such waves possess are addressed here with particular emphasis on constant vorticityread more
Citations
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Analyticity of periodic traveling free surface water waves with vorticity
Adrian Constantin,Joachim Escher +1 more
TL;DR: In this paper, it was shown that the prole of a periodic traveling wave propagating at the surface of water above a at bed in a flow with a real analytic vorticity must be real analytic, provided the wave speed exceeds the horizontal flow velocity throughout the flow.
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Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation
TL;DR: In this paper, the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable, which leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.
Journal ArticleDOI
Steady water waves with a critical layer
TL;DR: In this article, the authors construct small-amplitude steady periodic water waves with constant vorticity, which do not exist in the irrotational setting, and give a full description of the particle paths.
Journal ArticleDOI
On Gerstner's Water Wave
TL;DR: In this paper, a simple approach is presented to show that Gerstner's flow is dynamically possible: each particle moves on a circle, but the particles never collide and fill out the entire region below the surface wave.
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Global bifurcation of steady gravity water waves with critical layers
TL;DR: In this article, a Riemann-Hilbert problem approach is used to recast the governing equations as a one-dimensional elliptic pseudodifferential equation with a scalar constraint.
References
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Journal ArticleDOI
Exact steady periodic water waves with vorticity
TL;DR: In this article, the authors considered the classical water wave problem described by the Euler equations with a free surface under the influence of gravity over a flat bottom and constructed two-dimensional inviscid periodic traveling waves with vorticity.
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Steep, steady surface waves on water of finite depth with constant vorticity
TL;DR: In this article, steady surface waves on a shearing flow are computed for the special case where the flow has uniform vorticity, i.e. in the absence of waves the velocity varies linearly with height.
Journal ArticleDOI
Symmetry of steady periodic surface water waves with vorticity
Adrian Constantin,Joachim Escher +1 more
TL;DR: For large classes of vorticities, this article showed that a steady periodic gravity water wave with a monotonic profile between crests and troughs must be symmetric.
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Wave-current interactions: an experimental and numerical study, part 2 - nonlinear waves
TL;DR: In this article, a numerical model is constructed for use in the finite depth regime, extending the work of Dalrymple (1973, 1977) and this is used to predict the wavelength and the particle velocities under the waves.