Circular Basin: Difference between revisions
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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 | 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 | ||
{{Equation| <math> \eta = | {{Equation| <math> \eta = | ||
\begin{cases} | |||
\frac{W{{r}^{2}}\sin 2\theta }{4gHR}, & \mbox{if } x<8 \\ | |||
\end{ | \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], & \mbox{if } 8 \leq x \leq 12 \\ | ||
\end{cases} </math> |2=1}} | |||
= Setup = | = Setup = | ||
Revision as of 22:47, 11 May 2011
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
| (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.
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.