scholarly journals Two-dimensional rogue waves on zero background in a Benney-Roskes model

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Lijuan Guo ◽  
Jingsong He ◽  
Lihong Wang ◽  
Yi Cheng ◽  
D. J. Frantzeskakis ◽  
...  
Keyword(s):  
Rogue Waves ◽  
Two Dimensional

Quasi-three-dimensional simulation of crescent-shaped waves

2020 ◽  
Author(s):  
Alexander Dosaev ◽  
Yuliya Troitskaya
Keyword(s):  
Water Waves ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rogue Waves ◽  
Boundary Integral ◽  
Main Direction ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Wave Interactions

<p>Many features of nonlinear water wave dynamics can be explained within the assumption that the motion of fluid is strictly potential. At the same time, numerically solving exact equations of motion for a three-dimensional potential flow with a free surface (by means of, for example, boundary integral method) is still often considered too computationally expensive, and further simplifications are made, usually implying limitations on wave steepness. A quasi-three-dimensional model, put forward by V. P. Ruban [1], represents another approach at reducing computational cost. It is, in its essence, a two-dimensional model, formulated using conformal mapping of the flow domain, augmented by three-dimensional corrections. The model assumes narrow directional distribution of the wave field and is exact for two-dimensional waves. It was successfully applied by its author to study a nonlinear stage of of Benjamin-Feir instability and rogue waves formation.</p><p>The main aim of the present work is to explore the behaviour of the quasi-three-dimensional model outside the formal limits of its applicability. From the practical point of view, it is important that the model operates robustly even in the presence of waves propagating at large angles to the main direction (although we do not attempt to accurately describe their dynamics). We investigate linear stability of Stokes waves to three-dimensional perturbations and suggest a modification to the original model to eliminate a spurious zone of instability in the vicinity of the perpendicular direction on the perturbation wavenumber plane. We show that the quasi-three-dimensional model yields a qualitatively correct description of the instability zone generated by resonant 5-wave interactions. The values of the increment are reasonably close to those obtained from the exact equations of motion [2], despite the fact that the corresponding modes of instability consist of harmonics that are relatively far from the main direction. Resonant 5-wave interactions are known to manifest themselves in the formation of the so-called “horse-shoe” or “crescent-shaped” wave patterns, and the quasi-three-dimensional model exhibits a plausible dynamics leading to formation of crescent-shaped waves.</p><p>This research was supported by RFBR (grant No. 20-05-00322).</p><p>[1] Ruban, V. P. (2010). Conformal variables in the numerical simulations of long-crested rogue waves. <em>The European Physical Journal Special Topics</em>, <em>185</em>(1), 17-33.</p><p>[2] McLean, J. W. (1982). Instabilities of finite-amplitude water waves. <em>Journal of Fluid Mechanics</em>, <em>114</em>, 315-330.</p>

New Patterns of the Two-Dimensional Rogue Waves: (2+1)-Dimensional Maccari System

2017 ◽  
Vol 67 (6) ◽  
pp. 601 ◽  
Author(s):  
Gai-Hua Wang ◽  
Li-Hong Wang ◽  
Ji-Guang Rao ◽  
Jing-Song He
Keyword(s):  
Rogue Waves ◽  
Two Dimensional

scholarly journals Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

2014 ◽  
Vol 470 (2164) ◽  
pp. 20130576 ◽  
Author(s):  
Anjan Kundu ◽  
Abhik Mukherjee ◽  
Tapan Naskar
Keyword(s):  
Theoretical Models ◽  
Rogue Waves ◽  
Two Dimensions ◽  
Ocean Current ◽  
Hole State ◽  
Two Dimensional ◽  
Nls Equation ◽  
Frequency Correction ◽  
Dimensional Equation ◽  
Directional Preference

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

Doubly Localized Two-Dimensional Rogue Waves in the Davey–Stewartson I Equation

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
Jiguang Rao ◽  
Athanassios S. Fokas ◽  
Jingsong He
Keyword(s):  
Rogue Waves ◽  
Two Dimensional
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