Tides and tidal friction in a hemispherical ocean centred at the equator

Abstract

A numetical model is constructed of the tides in a hemispherical ocean centred at the equator. This is used to study the role of resonances and friction in determining the rms amplitude of the tide and the energy dissipated by the tides. Without friction, all of the resonances of the ocean may be excited by the tidal forces but when a realistic amount of friction is present most of the resonances merge into a smooth background. Remaining are the ones whose velocity fields best match the tidal forces. These are also important in determining the energy dissipated by the tides. When an energy decay time of 30 hr is used, the model is in good agreement with the tides of the North Pacific and with Lambeck's estimate of the energy dissipated by the M2 tide. However, the energy dissipated is very dependent on two of the remaining resonances lying within two radians per day of the tidal band. If the remaining resonances were distributed in a more random fashion an energy dissipation rate of one third of the calculated value is not impossible. If this were also true for the world's oceans, it would put the Gerstenkorn event near the time of formation of the solar system.