Restratification Simulations
by
Dennis McGillicuddy (WHOI) and Larry Anderson (WHOI)

After Jones and Marshall (1997, J. Phys. Oceanogr., vol. 27, p 2276-2287).
 
Table 1.  Simulations varying model resolution and horizontal diffusivity/viscosity
Horizontal grid resolution
Background N (Brunt-Vaisala)
Passive tracer in/outside chimney?
Perturbations to chimney radius?
Horizontal diffusivity/viscosity
0.036o longitude  (2 km at 60oN)
0.63e-3 radians sec-1
inside / outside
yes
Laplacian: 10 m2/s
0.1o longitude  (5.55 km at 60oN)
0.63e-3 radians sec-1
inside
yes
Laplacian: 10 m2/s
0.1o longitude  (5.55 km at 60oN)
0.63e-3 radians sec-1
inside
yes
Laplacian: 20 m2/s
0.1o longitude  (5.55 km at 60oN)
0.63e-3 radians sec-1
inside
yes
Laplacian: 30 m2/s
0.1o longitude (5.55 km at 60oN)
0.63e-3 radians sec-1
inside
yes
Laplacian: 50 m2/s
0.1o longitude  (5.55 km at 60oN)
0.63e-3 radians sec-1
inside
yes
Laplacian: 100 m2/s
0.1o longitude  (5.55 km at 60oN)
0.63e-3 radians sec-1
inside
yes
Laplacian: 10 m2/s , 30 m2/s
0.1o longitude  (5.55 km at 60oN)
0.63e-3 radians sec-1
inside
yes
biharmonic

Notes:
The 200 km x 200 km x 2000 m domain is a flat-bottomed channel (cyclic in x-direction, walls on y boundaries).
Vertical grid resolution is 26 levels, with 10 to 250 m thicknesses.
A linear equation of state is used, and salinity is constant, such that density is proportional to temperature (T).
Background T and N (Brunt-Vaisala frequency) vary linearly with depth.
A cylinder of quasi-well-mixed water is placed in the center of the domain, having a 50 km radius and extending from 0 to 1500 m.
The vertical T gradient within the cylinder is 1% of that outside. (This is done to inhibit further convection within the chimney as
we are interested in the vertical transport of tracer during restratification by advection, not convection.)
A passive tracer ("SF6") is initialized in the top 104 m either inside or outside the chimney, and its evolution followed.
As in Jones and Marshall (1997), 1-grid point random perturbations to the initial cylinder radius are sometimes made.
"Biharmonic" diffusivity refers to that used in the 0.1o North Atlantic simulations, which decrease with latitude: over this
subdomain, diffusivity is between -1.02e+9 and -1.23e+9 m4/s and viscosity is between -3.07e+9 and -3.68e+9 m4/s.

Conclusions:
1) In the 0.036o runs, more SF6 is subducted to 229 m from inside the chimney than from outside.
2) In the 0.1o runs, the diffusivity/viscosity used impacts the spatial and temporal scales of the baroclinic instability.
The chimney quickly disintegrates on the grid-scale if the horizontal diffusivity is small, and very slowly
develops large-scale asymmetries if the horizontal diffusivity is large. In all cases some SF6 is subducted to 229 m.
 
Table 2. Simulations varying background stratification
Horizontal grid resolution
Background N (Brunt-Vaisala)
Passive tracer in/outside chimney?
Perturbations to chimney radius?
Horizontal diffusivity/viscosity
0.1o cos(lat)  (5.55 km at 60oN)
0.5e-3 radians sec-1
outside
no
biharmonic
0.1o cos(lat)  (5.55 km at 60oN)
0.63e-3 radians sec-1
outside
no
biharmonic
0.1o cos(lat)  (5.55 km at 60oN)
1.0e-3 radians sec-1
outside
no
biharmonic

Conclusions:
1) At 0.1o resolution with biharmonic diffusion, the eddy will break up more rapidly if the background N
     (i.e. the horizontal density gradient) is increased.
2) SF6 is initialized outside the chimney in these simulations; negligible SF6 is subducted to 229 m.

Figure 1. SF6 initialized outside the chimney :

Conclusions:
1) The runs with more baroclinic instability export more SF6. The 0.1o density gradient must be increased to have similar export to the 0.036o run.  Nevertheless, very little SF6 from outside the chimney is exported beyond 200 m.

Figure 2. SF6 initialized inside the chimney:

Conclusions:
1) The lower the horizontal diffusivity, the more SF6 that is exported to 1500 m. However highest SF6 values at 229 m occur at intermediate diffusivities. The K=100 m2/s
     run exports very little SF6 below 700 m.
2) The Kh, Kv = 10, 30 m2/s run is very similar to the K=10 m2/s run.
3) The 0.036o run is similar to the 20 m2/s run at 1200 m, but not that similar to any of the 0.1o runs above 600 m; e.g. the 0.036o run has twice as much export at 400 m.
4) The export of the biharmonic run is generally similar to the 0.1o 10 m2/s run.