Gandzha I. Peculiarities of propagation of steep gravity waves on the surface of fluid

The thesis deals with a theoretical study of the progressive potential periodic steady two-dimensional symmetric gravity waves of large amplitude (steep waves) on the surface of the fluid of arbitrary uniform depth, in the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible. The thesis provides a numerical evidence for the existence of a new type of approximate singular solutions to the canonical model, which were called the "irregular waves". When the numerical accuracy of these approximate solutions is improved, their behavior demonstrates that the crests of irregular waves form sharp corners for any wave amplitude, for which they exist, whereas only the limiting wave of maximum amplitude shows such a feature in the case of Stokes waves. The irregular solutions found may provide an explanation for the experimental observation that gravity waves usually break before the limiting Stokes wave amplitude is attained, that is, at much lesser amplitudes.The thesis also presents the first numerical confirmation for the conjecture of Grant (1973) that a 120$^