Weakly non-linear free oscillations in a basin of variable depth

Weakly non-linear free oscillations in a basin of variable depth filled with non-viscous fluid are investigated in terms of the long waves theory using the perturbation technique. Solutions to the initial two approximations for the horizontal velocity component and free surface departure are numerically derived. An attempt is made to determine the area of applicability of the linear theory by applying a parabolic bottom profile to the basin.Translated by V. Puchkin.