The Role of the Earth’s Rotation: Oscillations in Semi-bounded and Bounded Basins of Constant Depth

Abstract

In Chap. 7 of Volume I, the propagation of surface waves in a layer of a homogeneous fluid referred to an inertial frame was studied. It was shown that superposing the fields of two waves, with the same frequency propagating in opposite directions with the same amplitude can be combined to a standing wave. These standing waves appear as localized oscillations between fixed nodal lines of which the distance defines the semi-wave length with wave humps and wave troughs arising inbetween. Under frictionless conditions imaginary walls can be placed at any position parallel to the wave direction to confine a channel without physically violating any boundary conditions. Similarly, the locations of the nodal lines across the channel turned out to be the positions of standing waves where the longitudinal velocity component vanishes for all time so that vertical walls can equally be inserted at these positions without disturbing the solution. This then formally yields the surface wave solution for the unidirectional motion in a basin of rectangular form and constant depth, see Figs. 7.9 and 7.12 in Chap. 7 of Volume I. These standing wave solutions were subsequently generalized to two-dimensional oscillations in rectangular cells of constant depth in which non-vanishing horizontal velocity components are allowed within the cell that only persistently vanish at the four side walls, thus forming oscillations of true cellular structure (see Figs. 7.14 and 7.15 in Chap. 7 in Volume I). How does the structure of these waves change when the fluid is rotating?