grid_scale_considerations

===== Scale considerations in grids: A start from Bob Beardsley =====

http://www.sciencedirect.com/science/article/pii/S0278434307000374 reviewed the need for adequate horizontal resolution regarding both tidal and subtidal current simulations.

The key considerations follow.

====Tidal motion====

Δx ≤ (T√gH)/n

where Δx is the grid size; T is the tidal period; g is the gravity; H is the mean water depth; and n is the number of nodes n is the number of nodes per wavelength. Based on Le Provost et al. (1995)'s analysis, n = 30.

====Subtidal flow====

For subtidal flow, the dynamics over the slope are controlled by a cross-shelf motion scale defined as ∇H/H (http://onlinelibrary.wiley.com/doi/10.1029/CE047p0125/summary; http://www.sciencedirect.com/science/article/pii/S0278434307000374). On an assumption of steady state and no along-isobath variation, http://www.sciencedirect.com/science/article/pii/S0278434307000374 derived this scale through the continuity equation, which was given as

∂U/∂x ~ -1/H dH/dx U = -αU

For non-dimensional scaling, it yielded

U/Lx ~ -αU ⟹ Lx ~ 1/α=H/∇H

where Lx is the cross-shelf motion scale and α=1/HdH/dx. Using a numerical model to produce an analytically-derived barotropic slope current, http://onlinelibrary.wiley.com/doi/10.1029/CE047p0125/summary concluded that in order to reasonably reproduce this flow, the model resolution (Δx) must satisfy the criterion given as

Δx ≤ 0.33 H/∇H = 0.33Lx

which is one-third of the cross-shelf motion scale.

Others to add are external and internal Rossby radius of deformation, probably more.

===References=== http://www.sciencedirect.com/science/article/pii/S0278434307000374

http://onlinelibrary.wiley.com/doi/10.1029/CE047p0125/summary