Circular Basin: Difference between revisions
Jump to navigation
Jump to search
| Line 6: | Line 6: | ||
{{Equation| <math> \eta = | {{Equation| <math> \eta = | ||
\begin{cases} | \begin{cases} | ||
\frac{W{{r}^{2}}\sin 2\theta }{4gHR}, & \mbox{if } | \frac{W{{r}^{2}}\sin 2\theta }{4gHR}, & \mbox{if } 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], & \mbox{if } | \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 } f_c \ne0 \\ | ||
\end{cases} </math> |2=1}} | \end{cases} </math> |2=1}} | ||
Revision as of 22:48, 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.