Oceanic Tides: A Physical Explanation and Modeling

Abstract

Common misconceptions about tides encountered in the literature are briefly discussed. A physically transparent simple but rigorous derivation of tide-generating forces is suggested, followed by a dynamical treatment of the tidal wave in a simplified model of the ocean as a water shell of equal depth wholly covering the globe. Novelty of our approach consists in representing tide-generating forces as two quadrupole systems of oscillating forces with axes of symmetry making 45$^{\circ}$ angle with one another. The dynamical response of the ocean to these time-dependent forces is found as steady-state forced oscillations in a linear system. The treatment is appropriate for a wide readership, including non-specialists and enthusiasts interested in the phenomenon. A set of simulations is developed to aid understanding the phenomenon of tides, which is of great general interest due to its cosmic nature.