Interface evolution: Water waves in 2-D

Interface evolution: Water waves in 2-D

We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in the normal direction has the proper sign, an assumption which is also known as the Rayleigh-Taylor condition. The well-posedness of the full water wave prob...

On Nonlinear Water Waves in a Channel

Maple ' s 2 - D Math Interface

There are various ways of entering 2-D math as input. The easiest way is to select the 2-D input mode, and the characters will be typeset as you type. For example, typing 'x', '^' and '2' in sequence results in appearing on the input line. You can also select output that is already in typeset form and then copy and paste it into an input line, or you can enter an expression in 1-D form, select ...

Evolution of water waves generated by subaerial solid landslide

Waves generated by aerial and subaerial landslides are studied experimentally, theoretically and numerically. A set of experiments are done in a wave tank of 18 m long, 0.65 m wide and 1.5 m deep. Numerical simulations are in good agreement with the experiments. Based on numerical and experimental results, we derive different scaling laws which show a good agreement with the experiments and the...

Instability and evolution of nonlinearly interacting water waves.

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrödinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term ...