[MITgcm-support] OBC problem: spurious boundary jets with C-D coupling

[Mark Hadfield]

I am attempting to apply MITgcm to limited-area ocean simulations around 
New Zealand. (I am also collaborating with Jill Schwarz in her Ross Sea 
work.) My first attempt, loosely based on the lab_sea case, was 
spectacularly unsuccessful. Within a few hours of starting from rest, 
narrow jets developed along the open boundaries. Within a day the 
velocities had developed to several m/s, at which point the model 
crashed with large Eta values where the jets impinged on topography.

To cut a long story short, I have reproduced this problem in a minimal 
test case (below) and established that it occurs when the CD scheme is 
enabled (useCDscheme=.true.) AND the CD scheme coupling time scale, 
tauCD, is set to a value other than its default (which is equal to the 
momentum time step, deltaTMom). My first NZ region simulation is now 
chugging along with the CD scheme disabled and giving sensible results. 
(Unfortunately, it is developing some grid-scale noise in the velocity 
field; I am controlling that with viscosity.)

By the way, does leaving tauCD at its default actually have the effect 
of disabling the CD coupling? The results I have seen suggest this is 
the case, but mitgcm.org won't let me look at the documentation today to 
confirm.

For now, it seems that the CD scheme and OBCs are incompatible and the 
simplest workaround is to disable the CD scheme. I don't know how much 
of a limitation that will be for me. As others have noticed on this 
list, the model leaves the outermost Eta values at zero. I presume the 
CD scheme is accessing those zero values, whereas the ordinary C-grid 
scheme is not. Might this be solved simply with a zero-gradient boundary 
condition on Eta?

In case anyone's interested, the files for the test case are in

    ftp://ftp.niwa.co.nz/incoming/hadfieldm/dmf/work/channel/mitgcm/run01/

The domain is a 600 km x 600 km wide and 2000 m deep, with open 
boundaries on all 4 sides. Coriolis parameter f is set to -1.0E-4 (this 
is the southern hemisphere) and beta is zero. Model grid dimensions are 
40 x 40 x 1. At t = 0, the interior is at rest and a zonal jet is 
imposed at the western and eastern boundaries. The jet is in geostrophic 
balance with a tanh-shaped step in sea surface height, eta:

    eta = Z tanh(y/D)

where y is N-S position relative to the centre of the channel, D is the 
transition zone half-width (60 km) and Z is 0.2 m. So the jet velocity is

    ubar = -(g Z)/(f D cosh(y/D)^2)

where g is gravitational acceleration and f is Coriolis parameter. Peak 
velocity is about 0.32 m/s. (Note that eta is given here for 
completeness but eta data are not supplied to the model.)

To simplify things, we solve for the velocity field only, without 
advection or diffusion:

    saltStepping = .FALSE.
    tempStepping = .FALSE.
    momStepping = .TRUE.
    momAdvection = .FALSE.
    momViscosity = .FALSE.

In the first run...

    ftp://ftp.niwa.co.nz/incoming/hadfieldm/dmf/work/channel/mitgcm/run01/runa/

the CD scheme is enabled and tauCD is left at its default. The velocity 
field adjusts in less than one day to a steady state: the jet spreads 
more or less radially from its source at the western boundary, occupies 
the whole width of the channel in the centre, and converges (is 
confluent?) to its sink on the eastern boundary. The expected symmetry 
is maintained/ The difference in Eta across the jet is what you would 
expect from geostrophy, except that Eta at the exterior points stays zero.

In the second run...

    ftp://ftp.niwa.co.nz/incoming/hadfieldm/dmf/work/channel/mitgcm/run01/runb/

the tauCD is set to twice deltaTmom. Here westward jets develop next to 
the northern and southern boundaries. These jets continue to develop 
over the duration of the simulation (10 d) and by the end the velocity 
field is dominated by a pair of gyres, with westward velocities of ~ 2 
m/s at the boundaries and an eastward return flow of ~ 1 m/s in the centre.


-- 
Mark Hadfield          "Kei puwaha te tai nei, Hoea tahi tatou"
m.hadfield at niwa.co.nz
National Institute for Water and Atmospheric Research (NIWA)


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