A chrystal-model describing gravitational barotropic motion in elongated lakes

Abstract

A spatially one-dimensional model which extends the classical Chrystal equation and replaces the Kelvin wave dynamics approach is presented. It consists of a system of partial differential equations having the arc-length of a preselected lake axis and the time as independent variables and permits qualitatively and quantitatively correct prediction of gravitational waves in rotating systems. The general linear model accounting for bottom friction and atmospheric momentum input is specialized to a “first order” model and subsequently to a straight and ring shaped channel of constant depth. For the latter, a comparison of the dispersion relation of Kelvin-, Poincare- and inertial-type waves with that of the two-dimensional tidal operator indicates that curvature effects of the lake can usually be ignored. Finally, results on co-range and co-tidal lines, obtained for lake of Lugano using extended models of different order prove that the simplest first order extension of the Chrystal equation is capable of predicting these with sufficient accuracy.