Related papers: A mathematical model for rogue waves using Saint-V…

This article introduces a physically realistic model for explaining how electromagnetic waves can be internally generated, propagate and interact in strongly magnetized plasmas or in nuclear magnetic resonance experiments. It studies high…

We formulate a model of the two-way interactions between surface gravity waves and ocean currents. The model couples the transport of wave action in the four-dimensional (horizontal) position--wavevector phase space with the…

We study rogue wave excitation dynamics on a double-plane wave background through deriving rogue wave solution on the background. The results indicate that rogue wave still can be excited successfully from resonant perturbations with the…

Erosion of rocky coasts spontaneously creates irregular seashores. But the geometrical irregularity, in turn, damps the sea-waves, decreasing the average wave amplitude. There may then exist a mutual self-stabilisation of the waves…

We report direct observations of surface waves from a stereo camera system along with concurrent measurements of wind speed during an expedition across the Southern Ocean in the austral winter aboard South African icebreaker…

We construct rogue wave solutions on the double periodic background for the Hirota equation through one fold Darboux transformation formula. We consider two types of double periodic solutions as seed solutions. We identify the squared…

The paper presents a model of a dynamic crack with a wavy surface. So far, theoretical analysis of crack front waves has been performed only for in-plane perturbations of the crack front. In the present paper, generalisation is given to a…

Ocean wave energy is a new renewable energy resource which is going to become one of the reliable and alternative resources for fossil fuels during recent decades. The majority of studies have focused on extract wave energy at an effective…

The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogue waves on the ocean caused by nonlinear focusing, is analyzed by direct numerical simulations based on two-phase Navier-Stokes equations. A…

Rogue waves are known to be much more common on jet currents. A possible explanation was put forward in [ [V. Shrira and A. Slunyaev, Nonlinear dynamics of trapped waves on jet currents and rogue waves, Phys. Rev. E 89, 041002, 2014]]: for…

In this paper we propose an extended Kundu-Eckhaus equation (KEE) for modeling the dynamics of skewed rogue waves emerging in the vicinity of a wave blocking point due to opposing current. The equation we propose is a KEE with an additional…

Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schr\"odinger equation is often used to model rogue waves; it…

With the aim of assessing internal wave-driven mixing in the ocean, we develop a new technique for direct numerical simulations of stratified turbulence. Since the spatial scale of oceanic internal gravity waves is typically much larger…

We consider four turbulent models to simulate the boundary mixing layer of the ocean. We show the existence of solutions to these models in the steady-state case then we study the mathematical stability of these solutions.

Direct numerical simulations of turbulent flow in a channel with one rigid and one viscoelastic wall are performed. An Eulerian-Eulerian model is adopted with a level-set approach to identify the fluid-compliant material interface. Focus is…

The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the…

Rogue waves on the periodic background are considered for the nonlinear Schrodinger (NLS) equation in the focusing case. The two periodic wave solutions are expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are…

This paper presents a class of turbulence models written in terms of fractional partial differential equations (FPDEs) with stochastic loads. Every solution of these FPDE models is an incompressible velocity field and the distribution of…

A simple analytical model is developed for the current induced by the wind and modified by surface wind-waves in the oceanic surface layer, based on a first-order turbulence closure and including the effect of a vortex force representing…

Rogue waves are solitary waves with extreme amplitudes, which appear to be a ubiquitous phenomenon in nonlinear wave propagation, with the requirement for a nonlinearity being their only unifying characteristics. While many mechanisms have…