Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves

This paper is concerned with a priori $C^\infty$ regularity for three-dimensional doubly periodic travelling gravity waves whose fundamental domain is a symmetric diamond. The existence of such waves was a long standing open problem solved recently by Iooss and Plotnikov. The main difficulty is that, unlike conventional free boundary problems, the reduced boundary system is not elliptic for three-dimensional pure gravity waves, which leads to small divisors problems. Our main result asserts that sufficiently smooth diamond waves which satisfy a diophantine condition are automatically $C^\infty$. In particular, we prove that the solutions defined by Iooss and Plotnikov are $C^\infty$. Two notable technical aspects are that (i) no smallness condition is required and (ii) we obtain an exact paralinearization formula for the Dirichlet to Neumann operator.Comment: Corrected versio

Elastic waves in a soft electrically conducting solid in a strong magnetic field

Shear wave motion of a soft, electrically-conducting solid in the presence of a strong magnetic field excites eddy currents in the solid. These, in turn, give rise to Lorentz forces that resist the wave motion. We derive a mathematical model for linear elastic wave propagation in a soft electrically conducting solid in the presence of a strong magnetic field. The model reduces to an effective anisotropic dissipation term resembling an anisotropic viscous foundation. The application to magnetic resonance elastography, which uses strong magnetic fields to measure shear wave speed in soft tissues for diagnostic purposes, is considered

Numerical modelling of wave penetration in Ostend Harbour

The initial Ostend harbour entrance at the North Sea coast of Belgium is being modified and extended with two new rubble-mound breakwaters. Through an integrated study of the wave penetration in Ostend harbour, the waves are being acquired by prototype measurements and physical and numerical modelling is carried out. Two numerical models are used. SimWave is a numerical model based on Nwogu’s extended Boussinesq equations. The second numerical model is MILDwave, a mild-slope wave propagation model based on the equations of Radder and Dingemans. The present study concentrates on applications of the numerical models, throughout the different design stages and construction phases of the new breakwaters

Wave attenuation in mangrove forests; field data obtained in Trang, Thailand

Mangroves thrive in sheltered intertidal areas in the tropics and sub-tropics. Due to this position at the interface between land and sea, mangroves play an important role in the attenuation of waves. Dissipation of wave energy in mangrove forests is an interesting feature from the viewpoint of coastal protection. Nevertheless, field data are sparse and modeling attempts reveal the need for additional data. This paper presents the results of an extensive field campaign, lasting 6 months, in mangroves along the Andaman coast of Trang Province in southern Thailand. Wave attenuation has been studied along two contrasting transects with different elevation and vegetation characteristics and different orientations towards the Andaman Sea. Along the Kantang transect, which is mostly exposed to swell waves, vegetation densities increased from 4.5 to 9.3 volume-‰ along the transect and on average 63% of the incident wave energy was attenuated over a distance of 246 m. Along the Palian transect, mostly exposed to sea waves instead, vegetation increased from 4.3 to 19 volume-‰ and 72% of the incident wave energy was attenuated over this 98 m transect. It was found that standardized wave attenuation correlates well with incident wave energy, when attenuation is analyzed per vegetation zone. Energy reduction rates of these zones, defined by the gradient of the correlations between the standardized wave attenuation and incident wave energy, are found to increase significantly with vegetation density. Consistently, wave reduction rates, expressing the gradient of the correlation between wave height reduction and incident wave heights, are found to be 0.001-0.014 for the study sites and also show a significant and increasing trend with vegetation densities

Reverse Doppler effect in backward spin waves scattered on acoustic waves

We report on the observation of reverse Doppler effect in backward spin waves reflected off of surface acoustic waves. The spin waves are excited in a yttrium iron garnet (YIG) film. Simultaneously, acoustic waves are also generated. The strain induced by the acoustic waves in the magnetostrictive YIG film results in the periodic modulation of the magnetic anisotropy in the film. Thus, in effect, a travelling Bragg grating for the spin waves is produced. The backward spin waves reflecting off of this grating exhibit a reverse Doppler shift: shifting down rather than up in frequency when reflecting off of an approaching acoustic wave. Similarly, the spin waves are shifted up in frequency when reflecting from receding acoustic waves.Comment: 4 pages, 3 figure

Are "EIT Waves" Fast-Mode MHD Waves?

We examine the nature of large-scale, coronal, propagating wave fronts (``EIT waves'') and find they are incongruous with solutions using fast-mode MHD plane-wave theory. Specifically, we consider the following properties: non-dispersive single pulse manifestions, observed velocities below the local Alfven speed, and different pulses which travel at any number of constant velocities, rather than at the ``predicted'' fast-mode speed. We discuss the possibility of a soliton-like explanation for these phenomena, and show how it is consistent with the above-mentioned aspects.Comment: to be published in the Astrophysical Journa

Is the phase of plane waves an invariant?

Based on the invariance of the phase of waves, plane waves was shown to propagate with negative frequencies in a medium which moves at superluminal speeds opposite to the propagation direction of plane waves. The validity of the invariance of the phase of plane waves was then called into question. A radical change of the conventional concept of plane waves is recently proposed to solve the problem of negative frequency of waves. Here, we point out flaws in that proposal. Thus, the validity of the invariance of the phase of plane waves remains questionable

Balanced dynamics in the Tropics

For the shallow-water equations on an equatorial beta plane, the properties of low-frequency Rossby waves and (mixed) Rossby-gravity waves are investigated. It is shown that in the low-frequency limit the horizontal divergence of these solutions is zero and their geopotential satisfies = f, where f = y is the Coriolis parameter and is the stream function of the non-divergent velocity field. This type of balance is rather different from the geostrophic balance satisfied by Kelvin waves. It can be used to formulate a balanced potential vorticity equation in the single variable that, while filtering out Kelvin waves and inertia-gravity waves, exactly reproduces Rossby waves and Rossby-gravity waves in the low-frequency limit