the study of wave and its propagation on the water surface is among significant phenomena in designing quay, marine and water structures. therefore, in order to design structures which are exposed to direct wave forces, it is necessary to study and simulate water surface height and the wave forces on the structures body in different boundary conditions. in this study, the propagation of static ...

The most successful equations for the modeling of ocean wave phenomena are the free– surface Euler equations. Their solutions accurately approximate a wide range of physical problems from open–ocean transport of pollutants, to the forces exerted upon oil platforms by rogue waves, to shoaling and breaking of waves in nearshore regions. These equations provide numerous challenges for theoretician...

Asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.From these evolution equations stability analysis ismade for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. Instability condition is obtained and g...

The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here an approximate closure is obtained under the hypotheses of small surface slope, weak horizontal gradients of the water depth and mean current, and weak curvat...

The theory of the water waves is the main subject in coastal hydrodynamics and plays a significant role in applied mathematics and in physics. In these notes we present the basics of the water wave theory. Specifically, after introducing briefly the basic concepts of continuum mechanics, we derive the physical laws describing the physics of an inviscid, incompressible fluid, namely the Euler eq...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

Abstract We derive the Whitham equations from water waves in shallow regime using two different methods, thus obtaining a direct and rigorous link between these models. The first one is based on construction of approximate Riemann invariants for Whitham–Boussinesq system adapted to unidirectional waves. second generalisation Birkhoff’s normal form algorithm almost smooth Hamiltonians bidirectio...