front_relax

Relaxation of a front in a channel : simplest example that uses GM-Redi parameterization

A 2-D, y-z set-up is used to mimic a zonally symmetric, reentrant channel with a baroclinicly unstable initial density front.
As meso-scale eddies are not resolved in this 2-D set-up, the GM-Redi parameterization is used to represent their effects.

Overview:

This experiment contains 5 set-ups (with corresponding input[.*]/ dir) that can be run with the same executable (built from build/ dir using customized code from code/); binary input files have been generated using matlab script gendata.m from the corresponding input dir. All five set-ups use a simple EOS ( $\rho' = -\rho_0 ~ \alpha_T ~ \theta'$ ) and treat salt as a passive tracer ; without any surface forcing, the density front is expected to flatten (GM effect) while salinity spread along isopycnal (Redi diffusion).

The primary test, using input files from input/ dir, is the simplest one, with flat bottom, non-uniform resolution in both direction (15 levels from 50 m to 400 m thick near the bottom and, in Y-direction, 32 grid-points with about 10 km spacing) and stratified every-where (background $N = 2\times 10^{-3} ~s^{-1}$, see matlab script input/gendata.m), avoiding the need for tapering or clipping.
It uses the skew-flux formulation of GM with same Redi and GM diffusivity ( GM_background_K = 1000 $m^2/s$, see: input/data.gmredi). Note that 10 dead levels were added (below the bottom) to allow to use the same executable (compiled with Nr = 25) for all 5 set-ups.

The secondary test input.in_p/ dir is the same as the primary test but converted to use P-coordinates instead of height coordinates. For the purpose of comparing P and Z coordinates, gravity and reference density rhoNil are set to round number (respectively 10 and 1000) to facilitate conversions. It uses the advective form of GM with same Redi and GM diffusivity (see: input.in_p/data.gmredi).

The next two secondary set-ups, input.mxl/ and input.bvp/ are very similar, sharing the same binary input files from input.mxl/ dir ; they use the full 25 level model to represent a 10 level, 200 m thick mixed layer on top of a stratified warm bowl of water. The input.mxl/ illustrates the use of the transition-layer tapering scheme 'fm07' with the skew-flux formulation of GM with same Redi and GM diffusivity ( GM_background_K = 1000 $m^2/s$, see: input.mxl/data.gmredi) and a flat bottom while the secondary test input.bvp/ has a sloping bottom and uses the Boundary-Value Problem (GM_useBVP=T, with 5 modes: GM_BVP_modeNumber=5,) of the GM advective form with same Redi and GM diffusivity (see: input.bvp/data.gmredi). In addition, in this later test, the sub-meso parameterization is activated (GM_useSubMeso=T).

The last secondary test input.top/ shares some similarity with the previous one (similar warm bowl, use BVP with GM advective form) except that the model top is depressed by 50 m near the center, as it would under, e.g., a floating ice-shelf. Also the mixed layer is thinner (60 m only) and very weakly stratified ( $N = 10^{-6} ~s^{-1}$ ) and vertical resolution is slightly different, reaching a maximum depth of 2.5 km (vs only 2 km in the previous 2 set-ups).

Instructions:

Configure and compile the code:

  cd build
  ../../../tools/genmake2 -mods ../code [-of my_platform_optionFile]
  make depend
  make
  cd ..

To run primary test:

  cd run
  ln -s ../input/* .
  ../build/mitgcmuv > output.txt

There is comparison output in the directory:

results/output.txt

To run any of secondary $sc test ($sc in: in_p, mxl, bvp, top):

  cd run
  rm *
  ln -s ../input.$sc/* .
  ln -s ../input/* .
  ./prepare_run          #- only for "bvp" test
  ../build/mitgcmuv > output.txt

Note that the "prepare_run" step is only needed for bvp test.

There is comparison output in the directory:

results/output.$sc.txt

Notes:

1. Comparison between P and Z coordinates:

   The results from the secondary set-up input.in_p/, using Pressure coordinate, can be compared to the Z-coordinate, primary set-up input/, providing one uses the same pkg/gmredi parameters (same 'data.gmredi'), e.g.:

   • Using GM advective form, with 'data.gmredi' from input.in_p/ for both runs.

   • Using the GM skew-flux form, with 'data.gmredi' from input/ for both runs.

   Note that, when comparing output, the vertical index k of 3-D variables needs to be flipped ; the SSH (in m) comparison is between output variable 'Eta' (in-Z) and 'PHL' (in-P) divided by 10 (=gravity); and the bottom pressure (in Pa) is between 'PHL' (in-Z) multiplied by $1000 = \rho_0$ and 'Eta' (in-P).
   Most of the differences (e.g., after 20 time-steps, T,S max-diff are: $1.4\times 10^{-4}$, $2.3 \times 10^{-5}$ and RMS: $6.6 \times 10^{-5}$, $9.6 \times 10^{-6}$ ) come from the dynamics and not from GM since without dynamics (un-commenting line 34: momStepping=.FALSE., in both set-up data files) the differences are down to machine precision (RMS of T,S diff: $1.5 \times 10^{-14}, ~ 1. \times 10^{-15}$ ).

2. Testing GM or Redi diffusion alone in either of the 2 set-ups above:

   To test GM alone, without isopycnal diffusion, just un-comment: GM_isopycK = 0., in data.gmredi.
   And to test Redi diffusion alone, without GM, just set: GM_isopycK = 1000., and comment out GM_background_K setting in data.gmredi. Also changing the initial salinity to a centered patch (using file Sini_Patch.bin instead of Sini_Ydir.bin) better illustrates the Redi effects on a passive tracer.

3. Switching from a Y-Z to X-Z set-up

   Since none of the 5 set-up use any feature specific to Y-direction, all using 'f-plane' (f0 = 1.E-4, beta=0), the same set of input files could be used by the X-Z model instead of the current Y-Z model (simply switching sNx,nSx,nPx <-> sNy,nSy,nPy in SIZE.h) to produce similar results (flipping U & V with 1 minus sign). The only minor adjustment to input files is related to the setting of delX, delY in the parameter file data, which also need to be switched, e.g., for the primary set-up:

    delXfile='dy.bin',
    delY=1*10.E3,
   

   instead of:

    delX=1*10.E3,
    delYfile='dy.bin',
   

   This may be used to verify implementation of X-fluxes versus Y-fluxes.