Free waves in stratified lakes

Free waves in stratified lakes

Modal frequencies and structures are determined analytically, for a two-layer lake consisting of a circular basin and concentric annular shelf, in which stratification is confined to the basin. Bottom friction is incorporated into the model, surface divergence is neglected and no restriction is placed upon the frequency. Such lakes can support five types of modes: internal Kelvin waves, shelf waves, inertial oscillations, super-inertial [formula omitted], where ω is the frequency and f the Coriolis parameter) Poincare-like modes and sub-inertial (σ<1), evanescent Poincare modes which do not propagate. Results are presented for σ = σ(μ), where μ is the lower layer depth expressed as a fraction of the height of the basin wall. Like the dispersion curves of their analogues in the coastal ocean, they can approach each other closely, but do not actually intersect. At such points their properties are exchanged. Use of the low frequency approximation filters out all but the sub-inertial modes. It is adequate for the internal Kelvin mode but can misrepresent both the frequency and structure of the shelf mode. A step lake (which consists of a flat shelf and basin of different depths) is found to be deficient in the sense that the phase speed of the shelf mode is unaffected by the introduction of bottom friction, whereas over depth profiles with continuous gradients, their phase speeds are reduced.