Abstract
This chapter presents the basic ideas behind how turbulent motions are represented in lake models. The notion of Reynolds averaging is presented, and used to demonstrate the turbulence closure problem. The Reynolds stress is derived and the eddy viscosity closure is presented. The notion of spatial averaging is presented as an alternative to Reynolds averaging, and the large-eddy simulation idea is derived. It is shown that the large eddy simulation equivalent of the Reynolds stress is algebraically more complicated, and the well known Smagorinsky model for eddy viscosity is presented. Two dimensional motions of rotation modified, dispersive shallow water equations are used to demonstrate slow-fast dynamics, and to illustrate how much is lost when the eddy viscosity is chosen to be too high.
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