Propagation of long waves due to atmospheric disturbances on a rotating sea

Abstract

Long waves in shallow water in a non-rotating system are not dispersive but in a rotating system they are. This paper investigates the generation and propagation of these dispersive waves in an infinite sea. The mode of generation is by air-pressure gradients or wind stresses applied to the surface. Bottom friction is neglected. The surface elevation due to a stationary force of constant amplitude suddenly applied and maintained at t = 0 over one-half of an infinite sea is shown to approach, through a series of oscillations approximating more or less to an inertia period, a steady-state amplitude decreasing with distance from the generating area, The longitudinal and transverse velocities are also given. The time elapsed from the initial disturbance at a point to the first maximum of elevation decreases with the distance of the point from the edge of the generating area. A generating area whose edge moves forward with the maximum group velocity of the waves is shown to lead to an elevation of ever-increasing height. The effect of a barrier placed at right angles to the direction of propagation is also briefly considered.