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 (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\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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