Coastal-trapped waves and tides at near-inertial frequencies

The nature of the transition in coastal-trapped wave behavior from trapped, subinertial modes to imperfectly trapped, superinertial waves (not modes), is investigated. When formulated purely in terms of pressure, the coastal-trapped wave eigenvalue problem admits a spurious inertial mode that distorts numerical calculations at nearby frequencies. By solving a pair of coupled equations, involving the component of velocity normal to the coastline as well as pressure, this spurious mode is removed. The transition through the inertial frequency is examined analytically by considering the effect on trapped inertial modes of a small frequency increment. It is shown that, to first order in this increment, modes remain trapped. At higher frequencies, the modal approach breaks down and a primitive equation model is used to represent the, now fully three-dimensional, situation. The scattering of energy from an oscillating barotropic alongshore flow by a topographic feature is considered. At superinertial frequencies, internal energy is scattered in all directions, although preferentially alongshore in the direction of coastal-trapped wave propagation. There is not a sudden change in behavior at the inertial frequency. As frequency becomes increasingly superinertial there is a gradual increase in the three-dimensionality of the response and a decrease in the proportion of energy represented by the trapped component. The work highlights the potential for spurs and canyons to generate alongslope-propagating internal tides.