Nonlinear stationary internal and surface waves in shallow seas

Abstract

It is known that propagation of the two-dimensional stationary internal gravity waves of arbitrary amplitude can be described by a certain nonlinear equation which contains two arbitrary functions. It is shown that for the solitary waves and for infinitesimal periodic internal waves, these two unknown functions are described by the Vaisala-Brunt frequency. For nonlinear periodic waves with weak nonlinearity and dispersion approximation there is an arbitrary function of the transversal coordinate giving rise to a current. By the additional assumption that this current is reduced to zero, the phase velocity of a nonlinear periodic wave has a unique connection with the amplitude. Further, it is shown that additivity of wave motions of different modes takes place in the present approach.

Two examples of model stratification are considered. A detailed numerical analysis is performed, illustrating propagation of internal waves, based on experimental data for the Arkona basin in the Baltic Sea. The local Richardson numbers have been calculated. It is shown that Ri < 1/4 can occur for solitary waves which may cause organization of some turbulent regions.