Continental shelf waves in the presence of a sheared geostrophic current

Abstract

When the effects of a sheared geostrophic current are included, continental shelf waves are modified but retain their essential character, although the direction of phase propagation may be changed by a strong adverse current.However, there is also a continuous spectrnun of modes whose phase speeds lie in the range of the current.These modes have finite amplitudes everywhere,but singular derivatives at the so-called critical layer where the phase speed of the mode equals the speed of the current.The influence of these modes may be studied by methods used in hydrodynamic stability theory.If the phase speeds of any of the free wave modes or the phase speed of the travelling wind stress pattern should lie in the range of the current, the inviscid theory predicts discontinuous velocity occcponents parallel to the coast at the critical layer. In practice, these would be limited by friction,but we should still expect large shears at these regions.