Nonlinear shallow-water oscillations in a parabolic channel : exact solutions and trajectory analyses

摘要: A new exact solution of the nonlinear shallow-water equations is presented. The corresponds to divergent and non-divergent free oscillations in an infinite straight channel parabolic cross-section on rotating Earth. It provides a description one-dimensional subclass flows paraboloidal basins considered by Ball (1964), Thacker (1981), Cushman-Roisin (1987) others which velocity field varies linearly free-surface displacement quadratically with spatial coordinates. In contrast previous solutions describing circular elliptic basins, oscillation frequency found depend, part, amplitudes relative vorticity curvature. This result consistent Thacker's (1981) numerical finding that when surface flow curved, depends amplitude motion. Solutions for parcel trajectories are also rare class potentially valuable as validation test models Eulerian Lagrangian frameworks.