Circular Basin

UNDER CONSTRUCTION

Analytical Solution

Dupont (2001) presented an analytical solution for a closed circular domain on an f-plane, with radius , a linear bottom friction, and a spatially variable wind stress equal to , where is the gradient of the wind forcing and is the vertical coordinate. The water surface elevation solution is given by

Failed to parse (syntax error): {\displaystyle \eta =\left\{ \begin{align} & \frac{W{{r}^{2}}\sin 2\theta }{4gHR}\,\,\,\,\text{for}\,\,\,{{f}_{c}}=0 \\ & \frac{W{{f}_{c}}}{RgH\kappa }\left[ \frac{{{R}^{2}}}{8}+\frac{{{r}^{2}}}{4}\left( \frac{\kappa }{{{f}_{c}}}\sin 2\theta -1 \right) \right]\,\,\,\,\text{for}\,\,\,{{f}_{c}}\ne 0 \\ \end{align} \right }

(1)

Setup

The model is run to steady state from zero current and water level initial conditions with , , and both , and . Figure 1 shows the computational grid with 5 levels of refinement from 2000 m to 125 m.

Figure 1. Computational grid.

Results

Table 2. Goodness of fit statistics for the water elevation

Statistic	Value
RMSE	0.0074 m
RMAE	0.0068
R^2	0.991
Bias	0.0017 m

References

• Dupont, F., 2001. Comparison of numerical methods for modelling ocean circulation in basins with irregular coasts. Ph.D. thesis, McGill University, Montreal.

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Test Cases

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