Generalizations of the Wedderburn number: Parameterizing upwelling in stratified lakes

The effect of lake geometry on wind-induced upwelling, in a two-layer stratified lake with a variable bottom slope and generic planar shape is investigated. (1) The traditional linearized classification parameter for upwelling, the Wedderburn number, is extended to include finite amplitude effects in a rectangular basin; this extension is important when the Wedderburn number is , , 3. (2) The Wedderburn number is generalized to incorporate the influence of a bottom slope and a variable-width basin for both the linear (large Wedderburn number) and nonlinear (small Wedderburn number) assumptions. Laboratory and numerical experiments of a two-layer stratification were performed and used to validate these extensions. (3) Both extensions are combined to derive a methodology to estimate the interface displacement in real lakes where both geometry effects may act together, and this methodology is used to discuss the response of the thermocline to the onset of wind in Lake Como and Mundaring Weir reservoir. In most cases, symmetry of the basin geometry along the fetch is the key characteristic that defines tilting of the interface for real lakes. Asymmetries in terms of bottom slopes induce shortening or stretching of the effective internal fetch, while a larger excursion of the interface results in narrower upwind areas of the lake due to horizontal redistribution of displaced water volumes. This paper gives the correct definition of the length scales to define the Wedderburn number for any stratified basin.