Explicit solutions for a long-wave model with constant vorticity

Segal, Benjamin L.; Moldabayev, Daulet; Kalisch, Henrik; Deconinck, Bernard

doi:10.1016/j.euromechflu.2017.04.008

Cited by 8 publications

(5 citation statements)

References 40 publications

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“…Similar structures and trajectories can also be found in depression solitary waves, and a typical example is shown in figure 15(b) with parameters c = −3.03, h = 3 and Ω = 3. It is remarked that closed streamlines were also computed in weakly nonlinear models for rotational gravity waves at much lower computational costs (see, for example, the numerical studies on the Benjamin equation by Segal et al (2017)). However,richer flow structures, such as nested cat's-eyes, can be expected in the fully nonlinear equations and beneath complicated wave profiles.…”

Section: Solitary Wavesmentioning

confidence: 99%

Progressive flexural–gravity waves with constant vorticity

2020

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Section: Solitary Wavesmentioning

confidence: 99%

Progressive flexural–gravity waves with constant vorticity

2020

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“…As a consequence, it has received much attention in both mathematical and numerical studies, regarding e.g. the existence and stability of steadily progressing wave solutions (Teles Da Silva & Peregrine 1988; Vanden-Broeck 1996; Segal et al 2017; Dyachenko & Hur 2019; Hur & Wheeler 2020; Blyth & Părău 2022), the flow structure beneath waves (Ribeiro, Milewski & Nachbin 2017), or the focusing of transient waves by an adverse current (Choi 2009; Moreira & Chacaltana 2015).…”

Section: Introductionmentioning

confidence: 99%

A Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticity

Guyenne

Kairzhan²,

Sulem³

2022

J. Fluid Mech.

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This paper is a study of the water wave problem in a two-dimensional domain of infinite depth in the presence of non-zero constant vorticity. A goal is to describe the effects of uniform shear flow on the modulation of weakly nonlinear quasi-monochromatic surface gravity waves. Starting from the Hamiltonian formulation of this problem and using techniques from Hamiltonian transformation theory, we derive a Hamiltonian Dysthe equation for the time evolution of the wave envelope. Consistent with previous studies, we observe that the uniform shear flow tends to enhance or weaken the modulational instability of Stokes waves depending on its direction and strength. Our method also provides a non-perturbative procedure to reconstruct the surface elevation from the wave envelope, based on the Birkhoff normal form transformation to eliminate all non-resonant triads. This model is tested against direct numerical simulations of the full Euler equations and against a related Dysthe equation derived recently by Curtis, Carter & Kalisch (J. Fluid Mech., vol. 855, 2018, pp. 322–350) in the context of constant vorticity. Very good agreement is found for a range of values of the vorticity.

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“…As a matter of fact, there is sufficient evidence that vorticity may have a strong impact on the propagation of wave in a variety of circumstances. For instance, it was recently shown that vorticity has a major influence on the modulational stability of quasi-periodic wavetrains [6,75] as well as the streamline pattern and pressure profiles in shallow water waves [1,5,57,63,64,73]. In addition, the significant influence of vorticity in the modelling of surface waves has been demonstrated in recent studies of wave-current interaction [74], the interaction of vortex patches and point vortices with the free surface [9,66], the influence of non-constant vorticity on small amplitude waves [37] and the generation of vorticity in long-wave models [4].…”

Section: Introductionmentioning

confidence: 99%

Delta shock waves in shallow water flow

2017

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The thesis is centred on nonlinear Partial Differential Equations that appear in the modelling of shallow water waves. In particular, the Riemann problem for such models is investigated and the results, to the best of my knowledge, are original. In a case where the result appear in a previous work, acknowledgements and references are made accordingly. The thesis has not been submitted for other degree or diploma in any other university. The content of this thesis is in two parts. Part I consists of general background information about water wave theory and summary of the main research results. Part II consists of the following papers written during the work of the thesis:

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Explicit solutions for a long-wave model with constant vorticity

Cited by 8 publications

References 40 publications

Progressive flexural–gravity waves with constant vorticity

Progressive flexural–gravity waves with constant vorticity

A Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticity

Delta shock waves in shallow water flow

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