Rogue waves associated with resonant slow sloshing waves spontaneously excited in wind-driven water wave turbulence

2020 ◽  
Vol 32 (12) ◽  
pp. 122120
Author(s):  
Ji-Lin Jou ◽  
Wei-Shuo Lo ◽  
Lin I
Keyword(s):  
Water Wave ◽  
Rogue Waves ◽  
Wave Turbulence

scholarly journals ROGUE WAVE ASYMMETRY IN THE DIRECT NUMERICAL SIMULATIONS OF DIRECTIONAL JONSWAP WAVES

2020 ◽  
pp. 48
Author(s):  
Alexey Slunyaev ◽  
Anna Kokorina
Keyword(s):  
Water Wave ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Hydrodynamic Equations ◽  
Laboratory Measurements ◽  
Term Evolution ◽  
Typical Picture ◽  
High Order Spectral Method

The asymmetry between the troughs from the rear and front sides of rogue waves is the particular object of the present study. In our previous simulations of unidirectional waves the typical picture of a rogue waves possesses the trend that most of the rogue waves where characterized by deeper rear troughs. In the present work we broaden the discussion of the rogue wave front-to-crest asymmetry to the directional case. The direct numerical simulation of primitive water equations is an affordable alternative to the in-situ or laboratory measurements, in particularly when the interest is focused on the long-term evolution or on the detailed consideration of the water wave movement in space and time. In this work we simulate irregular surface waves in the hydrodynamic equations using the High-Order Spectral Method, and focus on the so-called rogue waves.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/plseXdjpE6c

scholarly journals Discreteness and its effect on water-wave turbulence

2006 ◽  
Vol 218 (1) ◽  
pp. 24-35 ◽  
Author(s):  
Yuri V. Lvov ◽  
Sergey Nazarenko ◽  
Boris Pokorni
Keyword(s):  
Water Wave ◽  
Wave Turbulence

scholarly journals Different Regimes for Water Wave Turbulence

2011 ◽  
Vol 107 (21) ◽  
Author(s):  
P. Cobelli ◽  
A. Przadka ◽  
P. Petitjeans ◽  
G. Lagubeau ◽  
V. Pagneux ◽  
...  
Keyword(s):  
Water Wave ◽  
Wave Turbulence

scholarly journals Rogue waves, rational solitons and wave turbulence theory

2011 ◽  
Vol 375 (35) ◽  
pp. 3149-3155 ◽  
Author(s):  
Bertrand Kibler ◽  
Kamal Hammani ◽  
Claire Michel ◽  
Christophe Finot ◽  
Antonio Picozzi
Keyword(s):  
Rogue Waves ◽  
Turbulence Theory ◽  
Wave Turbulence

scholarly journals Super compact equation for water waves

2017 ◽  
Vol 828 ◽  
pp. 661-679 ◽  
Author(s):  
A. I. Dyachenko ◽  
D. I. Kachulin ◽  
V. E. Zakharov
Keyword(s):  
Wave Equation ◽  
Water Waves ◽  
Wave Breaking ◽  
Water Wave ◽  
Rogue Waves ◽  
Resonant Interaction ◽  
Zakharov Equation ◽  
Advection Term ◽  
New Equation ◽  
The Many

Mathematicians and physicists have long been interested in the subject of water waves. The problems formulated in this subject can be considered fundamental, but many questions remain unanswered. For instance, a satisfactory analytic theory of such a common and important phenomenon as wave breaking has yet to be developed. Our knowledge of the formation of rogue waves is also fairly poor despite the many efforts devoted to this subject. One of the most important tasks of the theory of water waves is the construction of simplified mathematical models that are applicable to the description of these complex events under the assumption of weak nonlinearity. The Zakharov equation, as well as the nonlinear Schrödinger equation (NLSE) and the Dysthe equation (which are actually its simplifications), are among them. In this article, we derive a new modification of the Zakharov equation based on the assumption of unidirectionality (the assumption that all waves propagate in the same direction). To derive the new equation, we use the Hamiltonian form of the Euler equation for an ideal fluid and perform a very specific canonical transformation. This transformation is possible due to the ‘miraculous’ cancellation of the non-trivial four-wave resonant interaction in the one-dimensional wave field. The obtained equation is remarkably simple. We call the equation the ‘super compact water wave equation’. This equation includes a nonlinear wave term (à la NLSE) together with an advection term that can describe the initial stage of wave breaking. The NLSE and the Dysthe equations (DystheProc. R. Soc. Lond.A, vol. 369, 1979, pp. 105–114) can be easily derived from the super compact equation. This equation is also suitable for analytical studies as well as for numerical simulation. Moreover, this equation also allows one to derive a spatial version of the water wave equation that describes experiments in flumes and canals.

scholarly journals Shallow water wave turbulence

2019 ◽  
Vol 874 ◽  
pp. 1169-1196 ◽  
Author(s):  
Pierre Augier ◽  
Ashwin Vishnu Mohanan ◽  
Erik Lindborg
Keyword(s):  
Reynolds Number ◽  
Structure Function ◽  
Shallow Water ◽  
Water Wave ◽  
Structure Functions ◽  
Wave Turbulence ◽  
Order Structure ◽  
Third Order ◽  
Shallow Water Wave ◽  
The Mean

The dynamics of irrotational shallow water wave turbulence forced at large scales and dissipated at small scales is investigated. First, we derive the shallow water analogue of the ‘four-fifths law’ of Kolmogorov turbulence for a third-order structure function involving velocity and displacement increments. Using this relation and assuming that the flow is dominated by shocks, we develop a simple model predicting that the shock amplitude scales as $(\unicode[STIX]{x1D716}d)^{1/3}$, where $\unicode[STIX]{x1D716}$ is the mean dissipation rate and $d$ the mean distance between the shocks, and that the $p$th-order displacement and velocity structure functions scale as $(\unicode[STIX]{x1D716}d)^{p/3}r/d$, where $r$ is the separation. Then we carry out a series of forced simulations with resolutions up to $7680^{2}$, varying the Froude number, $F_{f}=(\unicode[STIX]{x1D716}L_{f})^{1/3}/c$, where $L_{f}$ is the forcing length scale and $c$ is the wave speed. In all simulations a stationary state is reached in which there is a constant spectral energy flux and equipartition between kinetic and potential energy in the constant flux range. The third-order structure function relation is satisfied with a high degree of accuracy. Mean energy is found to scale approximately as $E\sim \sqrt{\unicode[STIX]{x1D716}L_{f}c}$, and is also dependent on resolution, indicating that shallow water wave turbulence does not fit into the paradigm of a Richardson–Kolmogorov cascade. In all simulations shocks develop, displayed as long thin bands of negative divergence in flow visualisations. The mean distance between the shocks is found to scale as $d\sim F_{f}^{1/2}L_{f}$. Structure functions of second and higher order are found to scale in good agreement with the model. We conclude that in the weak limit, $F_{f}\rightarrow 0$, shocks will become denser and weaker and finally disappear for a finite Reynolds number. On the other hand, for a given $F_{f}$, no matter how small, shocks will prevail if the Reynolds number is sufficiently large.

Effects of discretization of the spectrum in water-wave turbulence

2004 ◽  
Vol 34 (3) ◽  
pp. 199-216 ◽  
Author(s):  
Mitsuhiro Tanaka ◽  
Naoto Yokoyama
Keyword(s):  
Water Wave ◽  
Wave Turbulence
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