Topographic influence on special modes with narrow amplification diagrams in harbor oscillations

Abstract

In studies of harbor oscillations, modes with extremely-narrow resonant peaks and long response times (i.e., extreme modes) are common. With the advent of extreme modes, a nodal line appears at the entrance, which results in a very weak flow at the entrance and significantly reduces the exchange efficiency of wave energy between the harbor and the sea. However, previous studies are limited to harbors with a constant water depth, and the topographic influence on extreme modes is unclear.In this work, an extended mild-slope equation and a fully nonlinear Boussinesq equation are adopted to study the influence of the topography inside the harbor on extreme modes. The frequency-domain results indicate that the topographies of the symmetrical axes not passing through the entrance have a great influence on the angle between the nodal line and entrance, thereby leading to considerable changes in the resonant peak widths. However, the other topographies have little influence on this angle, resulting in negligible changes in the resonant peak widths. The time-domain results show that the wave nonlinearity can reduce the time required for the oscillation to reach a steady state, and various topographies result in different reduced times.