36.1 Eddy-topography interactions and neptune

Option neptune implements the following. Based on statistical mechanics arguments, Holloway (1992) proposed that interaction between mesoscale eddies and topography results in a stress on the ocean with two important consequences: first, the ocean is not driven towards a state of rest and secondly, the resulting motion may have scales much larger than the scale of the eddies. Somewhat suprisingly, this interaction^36.1 can generate coherent mean flows on the scale of the topography. The magnitude of this topographic stress is dependent on the correlation between pressure p and topographic gradients $\nabla H$ which is largely unknown but even if the correlation is 0.1, the resulting topographic stress would be comparable in magnitude to that of the surface wind.

If the view is taken that equations of motion are solved for moments of probable flow (because of imperfect resolution) then those moments are forced in part by derivatives of the distribution entropy with respect to the realized moments. The entropy gradient is estimated as begin proportional to a departure of the realized moments from a state in which the entropy gradient is weak. This latter state is approximated by a transport streamfunction $\psi^\star$ and maximum entropy velocity $u^\star$ given by

$$\psi^\star -fL^\prime H$$ = (36.1)

$$u^\star \hat{z} \times \nabla\psi^\star$$ = (36.2)

where f is the Coriolis term, H is depth, and $L^\prime$is O (10 km). If model resolution is coarse relative to the first deformation radius, $u^\star$ is independent of depth. Instead of eddy viscosity driving flow towards rest, flow is driven towards $u^\star$using an eddy viscosity of the form $A\nabla^2 (u^\star - u)$. Note that topographic influence on flow^36.2 is not strongest near bottom topography. Instead, the flow implied by $\psi^\star$ only approximates a maximum entropy system given eddies and topography. Since this approximation is admittedly crude, further refinements are open to researchers.

There is legitimate concern about the stepwise resolution of bottom topography in level models such as MOM and its predecessors. Option neptune is an attempt to instruct the model about physical consequences due to topography and eddies which are nearly unachievable even at the most ambitious resolutions. The hope is that if the model can be suitably informed about the effect of topography, it matters little if that topography is only ``approximately'' represented.