Neptune effect (dynnept.F90)

The "Neptune effect" (thus named in [Holloway, 1986]) is a parameterisation of the potentially large effect of topographic form stress (caused by eddies) in driving the ocean circulation. Originally developed for low-resolution models, in which it was applied via a Laplacian (second-order) diffusion-like term in the momentum equation, it can also be applied in eddy permitting or resolving models, in which a more scale-selective bilaplacian (fourth-order) implementation is preferred. This mechanism has a significant effect on boundary currents (including undercurrents), and the upwelling of deep water near continental shelves.

The theoretical basis for the method can be found in [Holloway, 1992], including the explanation of why form stress is not necessarily a drag force, but may actually drive the flow. [Eby and Holloway, 1994] demonstrate the effects of the parameterisation in the GFDL-MOM model, at a horizontal resolution of about 1.8 degrees. [Maltrud and Holloway, 2008] demonstrate the biharmonic version of the parameterisation in a global run of the POP model, with an average horizontal grid spacing of about 32km.

The NEMO implementation is a simplified form of that supplied by Greg Holloway, the testing of which was described in [Holloway and Wang, 2009]. The major simplification is that a time invariant Neptune velocity field is assumed. This is computed only once, during start-up, and made available to the rest of the code via a module. Vertical diffusive terms are also ignored, and the model topography itself is used, rather than a separate topographic dataset as in [Maltrud and Holloway, 2008]. This implementation is only in the iso-level formulation, as is the case anyway for the bilaplacian operator.

The velocity field is derived from a transport stream function given by:

$$\psi = -fL^2H$$ (6.31)

where $L$ is a latitude-dependant length scale given by:

$$L = l_1 + (l_2 -l_1)\left ( {1 + \cos 2\phi \over 2 } \right )$$ (6.32)

where $\phi$ is latitude and $l_1$ and $l_2$ are polar and equatorial length scales respectively. Neptune velocity components, $u^*$, $v^*$ are derived from the stremfunction as:

$$u^* = -{1\over H} {\partial \psi \over \partial y} , v^* = {1\over H} {\partial \psi \over \partial x}$$ (6.33)

!-----------------------------------------------------------------------
&namdyn_nept  !   Neptune effect (simplified: lateral and vertical diffusions removed)
!-----------------------------------------------------------------------
   ! Suggested lengthscale values are those of Eby & Holloway (1994) for a coarse model
   ln_neptsimp       = .false.  ! yes/no use simplified neptune

   ln_smooth_neptvel = .false.  ! yes/no smooth zunep, zvnep
   rn_tslse          =  1.2e4   ! value of lengthscale L at the equator
   rn_tslsp          =  3.0e3   ! value of lengthscale L at the pole
   ! Specify whether to ramp down the Neptune velocity in shallow
   ! water, and if so the depth range controlling such ramping down
   ln_neptramp       = .true.   ! ramp down Neptune velocity in shallow water
   rn_htrmin         =  100.0   ! min. depth of transition range
   rn_htrmax         =  200.0   ! max. depth of transition range
/

The Neptune effect is enabled when ln_neptsimp=true (default=false). ln_smooth_neptvel controls whether a scale-selective smoothing is applied to the Neptune effect flow field (default=false) (this smoothing method is as used by Holloway). rn_tslse and rn_tslsp are the equatorial and polar values respectively of the length-scale parameter $L$ used in determining the Neptune stream function (6.32) and (6.33). Values at intermediate latitudes are given by a cosine fit, mimicking the variation of the deformation radius with latitude. The default values of 12km and 3km are those given in [Eby and Holloway, 1994], appropriate for a coarse resolution model. The finer resolution study of [Maltrud and Holloway, 2008] increased the values of L by a factor of $\sqrt 2$ to 17km and 4.2km, thus doubling the stream function for a given topography.

The simple formulation for ($u^*$, $v^*$) can give unacceptably large velocities in shallow water, and [Maltrud and Holloway, 2008] add an offset to the depth in the denominator to control this problem. In this implementation we offer instead (at the suggestion of G. Madec) the option of ramping down the Neptune flow field to zero over a finite depth range. The switch ln_neptramp activates this option (default=false), in which case velocities at depths greater than rn_htrmax are unaltered, but ramp down linearly with depth to zero at a depth of rn_htrmin (and shallower).