Analytical solutions to two- and three-dimensional periodic flows for numerical model testing

Analytical solutions to 2D depth-averaged (external mode) and fully 3D (internal mode) periodic flows for numerical model testing are presented in this paper. These solutions take into account the effects of the bottom friction, the horizontal turbulent viscosity, and the vertical turbulent viscosity for the case of 3D flow. The key linkage for the modes is the relationship between the bottom friction coefficients in the 2D and 3D solutions. In the analytical solutions, two parameters are introduced concerning the periodic flows studied, namely, the rate of the horizontal turbulent viscosity and a dimensionless number given by the ratio of this rate to the wave celerity. The effects of the horizontal turbulent viscosity on the wave amplitude and the phase are significant if the square of this number is not much smaller than one. Three cases for numerical model testing are developed according to three different chosen values of the complex wave number. Various results illustrating the solutions to these test cases are also presented. Copyright (C) 2008 John Wiley & Sons. Ltd.