Steep sharp-crested gravity waves on deep water

A new type of steep two-dimensional irrotational symmetric periodic gravity wave with local singular point inside the flow domain is revealed on inviscid incompressible fluid of infinite depth. The speed of fluid particles in the vicinity of the crest of these waves is greater than their phase speed. Corresponding particle trajectories provide insight into how gravity waves overturn and break.     

Numerical simulation of three-dimensional nonlinear water waves

We present an accurate and efficient numerical model for the simulation of fully nonlinear (non-breaking), three-dimensional surface water waves on infinite or finite depth. As an extension of the work of Craig and Sulem [19], the numerical method is based on the reduction of the problem to a lower-dimensional Hamiltonian system involving surface quantities alone. This is accomplished by introducing the Dirichlet–Neumann operator which is described in terms of its Taylor series expansion in homogeneous powers of the surface elevation. Each term in this Taylor series can be computed efficiently using the fast Fourier transform. An important contribution of this paper is the development and implementation of a symplectic implicit scheme for the time integration of the Hamiltonian equations of motion, as well as detailed numerical tests on the convergence of the Dirichlet–Neumann operator. The performance of the model is illustrated by simulating the long-time evolution of two-dimensional steadily progressing waves, as well as the development of three-dimensional (short-crested) nonlinear waves, both in deep and shallow water.     

Compact equation for gravity waves on deep water

Using the fact of vanishing four waves interaction for water gravity waves for 2D potential fluid, we have significantly simplified the well-known but cumbersome Zakharov equation. The Hamiltonian of the obtained equation is very simple and includes only the fourth order nonlinear term. It raises the question of the integrability of free surface hydrodynamics. This new equation is very suitable both for analytic study and for numerical simulation.     

Modulated periodic stokes waves in deep water

Modulated deep-water 1D Stokes waves are considered experimentally and theoretically. Wave trains are modulated in a controlled fashion and their evolution is recorded. Data from repeated laboratory experiments are reproducible near the wave maker, but diverge away from the wave maker. Numerical integration of a perturbed nonlinear Schrodinger equation and an associated linear spectral problem indicate that under suitable conditions modulated periodic Stokes waves evolve chaotically. Sensitive spectral evolution in the neighborhood of homoclinic manifolds of the unperturbed nonlinear Schrodinger equation is found.     

Nonlinear fast growth of water waves under wind forcing

In the wind-driven wave regime, the Miles mechanism gives an estimate of the growth rate of the waves under the effect of wind. We consider the case where this growth rate, normalised with respect to the frequency of the carrier wave, is of the order of the wave steepness. Using the method of multiple scales, we calculate the terms which appear in the nonlinear Schrödinger (NLS) equation in this regime of fast-growing waves. We define a coordinate transformation which maps the forced NLS equation into the standard NLS with constant coefficients, that has a number of known analytical soliton solutions. Among these solutions, the Peregrine and the Akhmediev solitons show an enhancement of both their lifetime and maximum amplitude which is in qualitative agreement with the results of tank experiments and numerical simulations of dispersive focusing under the action of wind.     

Stochastic simulation of unidirectional intense waves in deep water applied to rogue waves

The results of numerical and laboratory simulation of ensembles of quasi-random unidirectional intense surface gravity waves in deep water have been summarized. The role of nonlinear self-modulation of the waves applied to the problem of ocean rogue waves, as well as the appearance, dynamics, and manifestation of non-linear wave packets in stochastic wave fields, is discussed.     

On the formation of freak waves on the surface of deep water

Numerical simulation of the fully nonlinear water equations demonstrates the existence of giant breathers on the surface of deep water. The numerical analysis shows that this breather (or soliton of envelope) does not loose energy. The existence of such a breather can explain the appearance of freak waves. The text was submitted by the authors in English.     

Generation of surface waves by three-dimensional vortex structures

The oblique interactions of vortex rings with a free surface is discussed. The signature of a submerged turbulent jet on a free surface is presented.     

Reminiscences on the study of wind waves

The wind blowing over sea surface generates tiny wind waves. They develop with time and space absorbing wind energy, and become huge wind waves usually referred to ocean surface waves. The wind waves cause not only serious sea disasters but also take important roles in the local and global climate changes by affecting the fluxes of momentum, heat and gases (e.g. CO₂) through the air-sea boundary. The present paper reviews the selected studies on wind waves conducted by our group in the Research Institute for Applied Mechanics (RIAM), Kyushu University. The themes discussed are interactions between water waves and winds, the energy spectrum of wind waves, nonlinear properties of wind waves, and the effects of surfactant on some air-sea interaction phenomena.     

Excitation of reverse waves by cubic interaction between a swell and wind waves

Summary The generation of a reverse wave by a swell interacting in the third order with a widely divergent field of wind waves is considered using an averaged shortened equation. Nonstationarity and noncoherence of this mechanism produce a linear spatial growth of intensity and a wide directional spectrum for reverse waves. Theoretical estimates are in a good accordance with the known results of remote radar field measurements.     

Absorption of gravitational waves by water

Summary The present report outlines the research on quantitative processing of absorption of gravitational waves in water. The absorption spectrum lies in the frequenciesf=0.479·10¹⁴ Hz, 1.098·10¹⁴ Hz and 1.127·10¹⁴ Hz and the highest value of absorption constant β in that spectrum is=10⁻³⁴/cm (when the gravitational wave is advanced 10²⁹ km it equals=1/e).

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Riassunto Il presente lavoro si svolge sulla ricerca del procedimento quantitativo di assorbimento di onde gravitazionali in acqua. Lo spettro di assorbimento sta nelle frequenzef=0.479·10¹⁴ Hz,f=1.098·10¹⁴ Hz e 1.127·10¹⁴ Hz e il più alto valore della costante di assorbimento β in tale spettro è=10⁻³⁴/cm (quando l'onda gravitazionale è avanzata 10²⁹km, esso è uguale a 1/e).

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Резюме Работа посвящена поискам количественного анализа поглощения гравитационных волн в воде. Спектр поглощения распложен при частотахf=0.479·10¹⁴ Гц, 1.098·10¹⁴ Гц и 1.127·10¹⁴ Гц. Наибольшая величина постоянной поглощения β в этом спектре составляет=10⁻³⁴ см⁻¹ (когда гравитационная волна проходит 10²⁹ км и затухает вe раз).

     

The generation of wind waves on clean water and in the presence of an oil film

The conditions of the resonant excitation of waves on a liquid surface by a horizontal air flow that has a decreasing velocity in the direction of motion were established, such that steady waves occurred when the period of the escape of a chain of eddies that is generated in a viscous layer of an air flow coincided with the period of natural oscillations, which is determined by the dispersion relationship for a group of waves. The dependence of the lengths of steady waves on the air-flow velocity over the surface of clean water and water with a light oil film was obtained. The resulting model was tested experimentally.     

Superresolution of three-dimensional optical imaging by use of evanescent waves

We simulate a three-dimensional optical diffraction tomography experiment in which superresolution is achieved by illuminating the object with evanescent waves generated by a prism. We show that accounting for multiple scattering between the object and the prism interface is mandatory to obtain superresolved images. Because the Born approximation leads to poor results, we propose a nonlinear inversion method for retrieving the map of permittivity of the object from the scattered far field. We analyze the sensitivity to noise of our algorithm and point out the importance of using incident propagative waves together with evanescent waves to improve the robustness of the reconstruction without losing the superresolution.     

Nonlinear growth rate of wind water waves and their excitation near the stability threshold

The amplitude dependences of the growth rate of water waves generated by turbulent wind are theoretically investigated within the framework of a quasilinear approximation.Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 206–210, March–April, 1995.     

Scattering of electromagnetic waves by three-dimensional arbitrary shaped magnetodielectric body

Using the method of discrete sources, we solve the problem of electromagnetic wave scattering by an arbitrarily shaped magnetodielectric body. The capabilities of the developed software are briefly described. We present some numerical results aimed at analyzing the influence of magnetic properties of absorbing scatterers and deviations of the scatterer shape from the axisymmetric one on the bistatic cross section. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 4, pp. 348–356, April 2006.