Numerical Wave Tanks

Vladimir Zakharov
Department of Mathematics
University of Arizona

Most theoretical and applied problems of Surface Waves cannot be solved analytically, thus the use of massive numerical simulation is inevitable. One can call big complex of numerical codes for modelling of different aspects of Water Waves problems as "Numerical Wave Tanks". At the moment our group developed three such "tanks":

1. "Statistical" Wave Tank. This is a set of codes for solution of the Hasselmann kinetic equation. So far we are able to solve the Hasselmann equation in the 'duration limited" version, in other words, in one spatial point. The "fetch limited " kinetic equations are ill-posed, thus the next step is development of a real spatial- and time- resolving tank.

2. Weakly nonlinear "Dynamical Wave Tank". This is a complex of programs for solving of approximated dynamical equations describing potential flow of ideal fluid with free surface in the limit of small nonlinearity.

3. Strongly nonlinear "Dynamical Wave Tank" designed for solution of exact Euler equations for free surface fluid. So far this program is available only in 2-D Geometry. In this case the technique of conformal mapping is used.

The combined use of all three tanks may make it possible to solve a lot of practical and theoretical problems from explanation of self -similiar wind driven sea spectra to modelling of Freak Wave formation.