Seiches in a Narrow Lake, Uniformly Stratified in Three Layers

This paper gives a theoretical analysis of the longitudinal seiches (or standing waves) in a narrow thermally stratified lake. A mathematical model of the lake is postulated consisting of three horizontal layers of water, density varying uniformly with depth in each. The model gives a good representation of the stratification encountered in nature, and leads to a relatively simple analytical solution of the hydrodynamical equations. The theory is applied to find the periods and modes of ordinary and internal seiches in the northern basin of Lake Windermere. The results show that in addition to seiche oscillations centred at thermocline level (predicted by a model of the lake consisting of two horizontal homogeneous layers of water) there are modes of oscillation in which the vertical displacement of water is greatest in the lower depths of the lake below the thermocline. It seems likely that the presence of such modes could explain the vertical oscillations of temperature, of large amplitude and complex wave form, observed in those depths. Further investigations are required to test this hypothesis.