Governing Equations

The dynamics described herein are based solely on the linear inviscid equations of motion for a homogenous fluid. The x-momentum, y-momentum, and conservation of mass equations are du

dy dn

where q is the height of the water surface above equilibrium, H is the water depth, and f is the Coriolis parameter. The momentum equations listed here are nothing more than the application of the Newton's famous equation F = ma, where the terms on the left-hand side represent acceleration terms (unsteady and Coriolis, respectively), and the term on the right-hand side represents the restoring force due to gravity. The same equations can be applied for barotropic and baroclinic motions, where for the baroclinic case, we replace the actual water depth H by the equivalent depth He described earlier.

In describing the effects of the earth's rotation on currents in inland waters, we consider two classes of motion based on the above equations. As we are interested in rotational effects, we first assume f = 0, such that we are sufficiently far away from the equator. For the first class of motions, which we will term 'gravity waves,' we also assume that the body of water under consideration is sufficiently small such that f can be considered constant (i.e., the lake is at a constant latitude) and that the bottom is flat, and therefore the restoring force is due to gravity only. For the second class of motions, which we will term 'vorticity waves,' we assume fis constant as for gravity waves, but we allow for variable water depth. This variable water depth allows for waves that arise due to the conservation of angular momentum. Dynamically, the second class of motions have similar characteristics to planetary Rossby waves in the ocean and atmosphere (i.e., where the latitude is not considered constant). In most cases, gravity waves dominate the dynamics of lakes and hence are explained later in detail. Only a brief summary description is given of the dynamics of vorticity waves, and for additional information the reader is referred to the references in Further Reading.

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