Konstantin Koshel

Based on the ideas of statistical topography, the stochastic boundary value problem of the occurrence of anomalously large structures on the sea surface is considered in [1]. The boundary condition on the sea surface is considered as a closed stochastic quasilinear equation in the kinematic approximation. Starting from the stochastic Liouville equation [2], under the assumption of the random nature of the hydrodynamic velocity field within the diffusion approximation, an equation is obtained for a single point in space and simultaneous in time joint probability density of the fields of sea surface elevation and its gradient, taking into account stochastic topographic inhomogeneities of the seabed. It is shown that, for the deep sea, clustering of the field of the gradient modulus of the sea surface occurs with a probability of one, which corresponds to the occurrence of such rare events as anomalously large structures and deep depressions on the sea surface in almost all realizations of the stochastic velocity field. In this paper, we test the assumption that clusters of the gradient modulus lead to the occurrence of anomalously large surface elevations. Numerical modeling of a stochastic quasilinear equation for surface elevation demonstrated that anomalous structures do indeed arise. The mechanism by which such structures arise was also analyzed.