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In order to understand and predict coastal flooding processes in rocky environments, it is necessary to take into account bottom roughness, which plays a key role in wave transformation processes and in general coastal dynamics. The present…
We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation.…
Knowledge about the characteristics of the atmospheric boundary layer is vital for the understanding of redistribution of air and suspended contents that are particularly driven by turbulent motions. Despite many modelling studies, detailed…
Linear properties of kinetic Alfv\'{e}n waves (KAWs) and kinetic slow waves (KSWs) are studied in the framework of two-fluid magnetohydrodynamics. We obtain the wave dispersion relations that are valid in a wide range of the wave frequency…
The purpose of this article is to clarify the Cauchy theory of the water waves equations as well in terms of regularity indexes for the initial conditions as for the smoothness of the bottom of the domain (namely no regularity assumption is…
The statistical properties of a large number of weakly nonlinear waves can be described in the framework of the Weak Turbulence Theory. The theory is based on the hypothesis of an asymptotically large system. In experiments, the systems…
The geometries of surface wave modes are determined by the highly nontrivial interplay of capillarity and wetting effects at the boundaries of their domain. Aside from idealised scenarios, this commonly leads to unknown boundary conditions,…
The nonlinear Schr\"odinger equation in the weakly nonlinear regime with random Gaussian fields as initial data is considered. The problem is set on the torus in any dimension greater than two. A conjecture in statistical physics is that…
Inhomogeneities in the wave field due to wave groups, currents, and shoaling among other ocean processes can affect the mean water level. In this work, the classical and unsolved problem of continuously computing the set-down and the…
Dynamics of the Fermi-Pasta-Ulam (FPU) system on a two-dimensional square lattice is considered in the limit of small-amplitude long-scale waves with slow transverse modulations. In the absence of transverse modulations, dynamics of such…
Nonlinear water waves interacting with quasi-one-dimensional, non-uniformly periodic bed profiles are studied numerically in the deep-water regime with the help of approximate equations for envelopes of the forward and backward waves.…
Coronal waves are an important aspect of the dynamics of the plasma in the corona. Wavefront dislocations are topological features of most waves in nature and also of magnetohydrodynamic waves. Are there dislocations in coronal waves? The…
Periodic waves in the fractional Korteweg-de Vries equation have been previously characterized as constrained minimizers of energy subject to fixed momentum and mass. Here we characterize these periodic waves as constrained minimizers of…
The time evolution emanating from "internal dam-break" initial conditions is studied for a class of models of stratified Euler fluids in configurations close to two-homogeneous layers separated by a thin diffused interface. Direct numerical…
Under certain mode-matching conditions, small-amplitude waves can be trapped by coupling to solitons of nonlinear fields. We present a model for this phenomenon, consisting of a linear equation coupled to the Korteweg-de Vries equation. The…
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 present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels,…
Smooth periodic travelling waves in the Camassa--Holm (CH) equation are revisited. We show that these periodic waves can be characterized in two different ways by using two different Hamiltonian structures. The standard formulation, common…
We study the nonlinear evolution of very oblique small-scale Alfv\'en waves with $k_\perp d_i\gtrsim 1$. At these scales, the waves become significantly compressive, unlike in MHD, due to the Hall term in the equations. We demonstrate that…
The DLVO theory and electrical double layer (EDL) theory are the foundation of colloid and interface science. With the invention and development of surface forces apparatus (SFA) and atomic force microscope (AFM), the measurements and…