Numerical experiments to investigate the effects of quadratic friction on the propagation of tides in a channel

Abstract

Numerical solutions of the equations of hydrodynamics are sought for cases of increasing complexity, to provide a precise and quantitative understanding of the effects of quadratic friction on tidal motion. These confirm previous inferences, namely the dependence of the damping on the amplitude of the component, the unequal damping of the components in a group, the uniform damping of the minor ones and not their extinction. They show the strong contribution of a net current to friction, and supply explicit solutions for the compound harmonics. They help simulate the creation of “radiational tides” by following the interference of a pair of harmonics in the presence of a larger one. They also allow to make explicit the interaction of the diurnal components K 1 and O 1 with M 2, which cannot be discerned from tidal records. Another experiment shows that the presence of a diurnal component may sharpen the “radiational effect” within a triad of semidiurnal harmonics. They finally reveal that in a travelling wave, the speed as well as the damping, of the current and of the vertical displacement, do differ in zones of strong friction. The results obtained should describe the specific effects of quadratic friction along the shelf of oceans and in rivers.