Rogue wave

About: Rogue wave is a research topic. Over the lifetime, 2977 publications have been published within this topic receiving 70933 citations. The topic is also known as: freak wave & monster wave.

N-solitons, breathers, lumps and rogue wave solutions to a (3+1)-dimensional nonlinear evolution equation

Abstract: Based on Hirota bilinear method, N -solitons, breathers, lumps and rogue waves as exact solutions of the (3+1)-dimensional nonlinear evolution equation are obtained. The impacts of the parameters on these solutions are analyzed. The parameters can influence and control the phase shifts, propagation directions, shapes and energies for these solutions. The single-kink soliton solution and interactions of two and three-kink soliton overtaking collisions of the Hirota bilinear equation are investigated in different planes. The breathers in three dimensions possess different dynamics in different planes. Via a long wave limit of breathers with indefinitely large periods, rogue waves are obtained and localized in time. It is shown that the rogue wave possess a growing and decaying line profile that arises from a nonconstant background and then retreat back to the same nonconstant background again. The results can be used to illustrate the interactions of water waves in shallow water. Moreover, figures are given out to show the properties of the explicit analytic solutions.

Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation

Abstract: We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields.

Can bottom friction suppress ?freak wave? formation?

Abstract: The paper examines the effect of the bottom stress on the weakly nonlinear evolution of a narrow-band wave field, as a potential mechanism of suppression of ‘freak’ wave formation in water of moderate depth. Relying upon established experimental studies the bottom stress is modelled by the quadratic drag law with an amplitude/bottom roughness-dependent drag coefficient. The asymptotic analysis yields Davey–Stewartson-type equations with an added nonlinear complex friction term in the envelope equation. The friction leads to a power-law decay of the spatially uniform wave amplitude. It also affects the modulational (Benjamin–Feir) instability, e.g. alters the growth rates of sideband perturbations and the boundaries of the linearized stability domains in the modulation wavevector space. Moreover, the instability occurs only if the amplitude of the background wave exceeds a certain threshold. Since the friction is nonlinear and increases with wave amplitude, its effect on the formation of nonlinear patterns is more dramatic. Numerical experiments show that even when the friction is small compared to the nonlinear term, it hampers formation of the Akhmediev/Ma-type breathers (believed to be weakly nonlinear ‘prototypes’ of freak waves) at the nonlinear stage of instability. The specific predictions for a particular location depend on the bottom roughness ks in addition to the water depth and wave field characteristics.

Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations

Abstract: odinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations Only the lowest order solutions from 1 to 5 are considered A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al [Phys Rev E 86, 056601 (2012)] In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well

Freak Wave Kinematics

Abstract: Prototype records of extreme single waves recorded on the Danish Continental Shelf have been analysed in detail. Statistical calculations show that these waves do not belong to the traditional short term statistical distributions used for ocean waves. The waves are too high, too asymmetric and too steep.