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On the mechanics of lake circulation Fofonoff, Nicholas Paul

Abstract

Four aspects of the problem of describing the phenomena governing the flow pattern in a lake are investigated with the aid of simple mathematical models. Analogies are pointed out between the two-dimensional models and the corresponding problems in the elastic deformation of thin rigid plates. A. The dependence of the flow pattern in a longitudinal vertical cross-section of a lake on a given temperature distribution within the lake is studied with the aid of a two-dimensional lake model of semicircular vertical cross-section. A stream function satisfying the two-dimensional non-homogeneous biharmonic equation is introduced. Solutions are found consisting of a through flow function having a source and sink at the ends of the diameter plus a circulation function which is obtained in terms of a Green's function and the horizontal density gradient. The total stream function satisfies the conditions of no slipping at a solid boundary and zero stress at a free surface. Two cases of simple density structure are considered, and streamlines are drawn for several ratios of circulation to through flow. B. The departure of the lake surface from the horizontal required to maintain a pressure head sufficient to overcome eddy viscosity is estimated by considering the pressure distribution in the case of the through flow function introduced above. C. The effect of Coriolis forces on the flow in a canal is investigated with the aid of a three-dimensional semi-oylindrical model. It is shown that the effect on the shape of the canal surface is negligible. For a sufficiently low value of vertical density stratification the effect of Coriolis forces may show up in the tilting of constant density surfaces. D. The effect of wind stress on circulation in a vertical lake cross-section is investigated mathematically with the aid of a two-dimensional model. The results are found to agree quite closely with experiments on the deformation of a semicircular plate recently reported in the literature.

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