Influence of initial wave flow velocity on seiches in a confined marine basin

Abstract

The influence of initial wave flow velocity on seiches in a model basin with the Azov Sea characteristic size is investigated. The investigation was carried out by using the previously obtained time-periodic analytic solutions of the long wave equations. Two variants of initial conditions are considered. In the first variant, the initial wave flow velocity doesn’t equal zero and the initial deviation of the free surface from the undisturbed level equals zero. In the second variant, when $t=0$ the wave flow velocity and free surface deviation does not equal zero. It was found that in both variants of initial conditions the spatial structure of sea level fluctuations and the characteristics of the wave flows are similar, which present in the case when the initial wave flow velocity are zero and initial free surface deviation is a non-zero. Along with it the positions of the nodal lines are the same. The direction of wave flows at the half-period time ($0\leqslant t<\tau /2$) is constant. Then it reverses and saves during the following half-period ($\tau \geqslant t\geqslant \tau /2$). For the variant when at the initial time there are non-zero deviation of the free surface and the wave flows velocity, it is found that the sea level maximum increases, beginning from time $t=0$ and reaches the biggest value in 0.1 of the period. The amplitude of the level fluctuations is more than the amplitude of the initial elevation 1.4 times. Also, the maximum of the wave flow velocity module exceeds the maximum of the initial velocity module 1.4 times. It was shown that a reduce to ten times of initial wave flow velocity leads to 1.4 times maximum deviation reduction for the first mode and 1.5 times - for the fourth mode.