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Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves.…
While the global boundary control of nonlinear wave equations that exhibit blow-up is generally impossible, we show on a typical example, motivated by laser breakdown, that it is possible to control solutions with small data so that they…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
Direct numerical simulations are conducted to study the receptivity and transition mechanisms in a solitary wave boundary layer developing over randomly organized wave-like bottom topography. The boundary layer flow shows a selective…
We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes a sudden upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the…
We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial…
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…
An experimental study is reported of the near-critical reflection of internal gravity waves over sloping topography in a stratified fluid. An overturning instability close to the slope and triggering the boundary-mixing process is observed…
A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…
The problem of the sea wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. Key and novel moment here is the accounting of the asymmetric waves when the face slope steepness…
The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the…
By numerical simulation of exact equations of motion (in terms of conformal variables) for planar non-stationary potential flows of an ideal fluid with a free surface over a strongly non-uniform bottom profile, the effect of nonlinear…
From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
The problem of the long wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. The key and novel moment here is the analysis of the runup of a certain class of asymmetric waves,…
Nonlinear wave interactions affect the evolution of steep wave groups, their breaking and the associated kinematic field. Laboratory experiments are performed to investigate the effect of the underlying focussing mechanism on the shape of…
In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of various classes of damped nonlinear wave equations. Specifically, stabilization the zero steady state solution of initial boundary value…
A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently…