Exact steady periodic water waves with vorticity

By Adrian Constantin, Walter A. Strauss. 2004

486 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Oceanography

View Paper: https://www.semanticscholar.org/paper/7edad69faec41f1654fd59000af930530aff7a43

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In Applied Mathematics

In Numerical Analysis

In Oceanography

Citations in the corpus

On the global existence and wave-breaking criteria for the two-component Camassa-Holm system (2010, background): “1) models wave-current interactions (see the discussions in [15,25,26] and see also [4,24]).”
A geometric approach to generalized Stokes conjectures (2009, methodology): “Our methods can still be applied when dropping the condition of irrotationality of the flow (see [32], the forthcoming papers [33] and [23], and [8, 9] for a background on water waves with vorticity).”
Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis (2008, background): “5a), and have the same level curves, say = f ( ), for some continuously differentiable function f; see Constantin and Strauss (2004) for a proof of the equivalence of these statements in a similar context with z = 0.”
On Gerstner’s Water Wave (2008, background): “In recent years there has been growing interest in free surface water waves (see [1, 2, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 18, 20, 21, 22, 25, 35, 36]), but the current state of affairs regarding explicit solutions has not advanced much since the last century.”
Symmetry of steady periodic surface water waves with vorticity (2004, background): “However, the existence of regular wave trains for flows with non-constant vorticity can be established (Constantin & Strauss 2002, 2004).”
Global bifurcation of steady gravity water waves with critical layers (2014, background): “Now, global bifurcation has also been carried out for general vorticity under the limitation that there are no stagnation points or critical layers [15], that is, under the condition that ψY < 0, where the vector (ψY ,−ψX) is the fluid velocity in the frame moving with the speed of the traveling wav”
Wave Breaking and Global Existence for a Generalized Two-Component Camassa–Holm System (2010, background): “Notice that the Burns condition [6] gives the shallow-water limit of the dispersion relation for the waves with vorticity and hence determines the speed of propagation of the linear waves [23, 35].”
Pressure beneath a Stokes wave (2009, background): “To prove this claim, it is convenient to introduce new coordinates [8] ̨ D x; ˇ D .”
Steady periodic capillary waves with vorticity (2006, methodology): “In the last few years there has been an increasing amount of research in the area of water waves with vorticity, see [3], [4] regarding the symmetry of rotational water waves, [12], [15], [16], [24] for questions of uniqueness and [1], [2], [5], [6], [25], [26] for existence results.”
The trajectories of particles in Stokes waves (2006, background): “While rigourous results on large amplitude periodic traveling waves with an arbitrary vorticity distribution are available [ 9 , 10] we do not expect that in such rotational flows (with nonvanishing vorticity ω = vx − u y) results on the particle trajectories similar to those established here for ir”
Symmetry of steady periodic gravity water waves with vorticity (2007, methodology): “throughout the fluid [8].”
Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation (2009, methodology): “23) holds, thus confirming the conclusions of [12].”