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Subsections

3.9.2 Discrete Numerical Configuration

The domain is discretised with a uniform grid spacing in the horizontal set to $ \Delta x=\Delta y=20$  km, so that there are sixty grid cells in the $ x$ and $ y$ directions. Vertically the model is configured with a single layer with depth, $ \Delta z$ , of $ 5000$  m.

3.9.2.1 Numerical Stability Criteria

The Laplacian dissipation coefficient, $ A_{h}$ , is set to $ 400 m s^{-1}$ . This value is chosen to yield a Munk layer width Adcroft [1995],


$\displaystyle M_{w} = \pi ( \frac { A_{h} }{ \beta } )^{\frac{1}{3}}$     (3.6)

of $ \approx 100$ km. This is greater than the model resolution $ \Delta x$ , ensuring that the frictional boundary layer is well resolved.

The model is stepped forward with a time step $ \delta t=1200$ secs. With this time step the stability parameter to the horizontal Laplacian friction Adcroft [1995]


$\displaystyle S_{l} = 4 \frac{A_{h} \delta t}{{\Delta x}^2}$     (3.7)

evaluates to 0.012, which is well below the 0.3 upper limit for stability.

The numerical stability for inertial oscillations Adcroft [1995]


$\displaystyle S_{i} = f^{2} {\delta t}^2$     (3.8)

evaluates to $ 0.0144$ , which is well below the $ 0.5$ upper limit for stability.

The advective CFL Adcroft [1995] for an extreme maximum horizontal flow speed of $ \vert \vec{u} \vert = 2 ms^{-1}$


$\displaystyle S_{a} = \frac{\vert \vec{u} \vert \delta t}{ \Delta x}$     (3.9)

evaluates to 0.12. This is approaching the stability limit of 0.5 and limits $ \delta t$ to $ 1200s$ .

next up previous contents
Next: 3.9.3 Code Configuration Up: 3.9 Barotropic Gyre MITgcm Previous: 3.9.1 Equations Solved   Contents
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