arXiv subjects
Publications and source records attributed to D. I. Kachulin.
We analyze modern operational models of wind wave prediction on the subject for compliance dissipation. Our numerical simulations from the "first principle" demonstrate that heuristic formulas for damping rate of free wind sea due to "white capping" (or wave breaking) dramatically exaggerates the role of this effect in these models.
We derive very simple compact equation for gravity water waves which includes nonlinear wave term (`a la NLSE) and advection term (may results in wave breaking).
We applied canonical transformation to water wave equation not only to remove cubic nonlinear terms but to simplify drastically fourth order terms in Hamiltonian. This transformation explicitly uses the fact of vanishing exact four waves interaction for water gravity waves for 2D potential fluid. After the transformation well-known but cumbersome Zakharov equation is drastically simplified and can be written in X-space in compact way. This new equation is very suitable as for analytic study as for numerical simulation. Localized in space breather-type solution was found. Numerical simulation of collision of two such breathers strongly supports hypothesis of integrability of 2-D free surface hydrodynamics.