Related papers: Predictability Horizon of Oceanic Rogue Waves
The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water.…
Strong-type inhomogeneous Strichartz estimates are shown to be false for the wave equation outside the so-called acceptable region. On a critical line where the acceptability condition marginally fails, we prove substitute estimates with a…
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…
We show the existence and investigate the dynamics and statistics of rogue oscillations (standing waves) generated in the frame of the nonlinear quantum harmonic oscillator (NQHO). With this motivation, in this paper, we develop a…
General rogue waves in the Davey-Stewartson-I equation are derived by the bilinear method. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then…
Based on the soliton solution on a continuous wave background for an integrable Hirota equation, the reduction mechanism and the characteristics of the Peregrine rogue wave in the propagation of femtosecond pulses of optical fiber are…
We report a phenomenon that physical perturbations sometimes can benefit the certainty of a free-fall motion with chaotic modes, albeit, as commonly believed, they can ruin it. We statistically compare those factors that may lead to…
One way to predict hurricane numbers would be to predict sea surface temperature, and then predict hurricane numbers as a function of the predicted sea surface temperature. For certain parametric models for sea surface temperature and the…
The goals of the present work are to: (i) investigate the dynamics of oceanic frontogenesis by taking advantage of the geometric mechanics underlying the class of Vertical Slice Models (VSMs) of ocean dynamics; and (ii) illustrate the…
Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves…
In this study we discuss the shapes and statistics of the rogue (freak) waves emerging due to wave-current interactions. With this purpose, we use a simple governing equation which is a nonlinear Schrodinger equation (NLSE) extended by R.…
We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of…
In this paper a new concept, namely the critical predictable time $T_c$, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are…
An algorithm for determining stationary periods for time series of random sea waves is proposed in this work. This is a problem in which changes between stationary sea states are usually slow and segmentation procedures based on…
The horizon is a classical concept that arises in general relativity, and is therefore not clearly defined when the source cannot be reliably described by classical physics. To any (sufficiently) localised quantum mechanical wave-function,…
Boundary layer processes drive the air-sea exchange of momentum, heat, and moisture that powers and shapes hurricanes. The height of the boundary layer is a critical parameter in engineering and meteorological models of hurricane wind…
By mean of generalized Fourier series and Parseval's equality in weighted $L^{2}$--spaces, we derive a sharp energy estimate for the wave equation in a bounded interval with a moving endpoint. Then, we show the observability, in a sharp…
The processes that generate rogue waves on the sea surface remain a mystery. Despite their different natures, the nonlinear bending waves generated in a thin elastic plate share some similarities with waves on the surface of the sea. For…
We show that new types of rogue wave patterns exist in integrable systems, and these rogue patterns are described by root structures of Okamoto polynomial hierarchies. These rogue patterns arise when the $\tau$ functions of rogue wave…
Many adaptive optics systems operate by measuring the distortion of the wavefront in one wavelength range and performing the scientific observations in a second, different wavelength range. One common technique is to measure wavefront…