restrat.html

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

0.036^o longitude (2 km at 60^oN) 0.63e-3 radians sec^-1 inside / outside yes Laplacian: 10 m²/s

0.1^o longitude (5.55 km at 60^oN) 0.63e-3 radians sec^-1 inside yes Laplacian: 10 m²/s

0.1^o longitude (5.55 km at 60^oN) 0.63e-3 radians sec^-1 inside yes Laplacian: 20 m²/s

0.1^o longitude (5.55 km at 60^oN) 0.63e-3 radians sec^-1 inside yes Laplacian: 30 m²/s

0.1^o longitude (5.55 km at 60^oN) 0.63e-3 radians sec^-1 inside yes Laplacian: 50 m²/s

0.1^o longitude (5.55 km at 60^oN) 0.63e-3 radians sec^-1 inside yes Laplacian: 100 m²/s

0.1^o longitude (5.55 km at 60^oN) 0.63e-3 radians sec^-1 inside yes Laplacian: 10 m²/s , 30 m²/s

0.1^o longitude (5.55 km at 60^oN) 0.63e-3 radians sec^-1 inside yes biharmonic

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
0.036^o longitude (2 km at 60^oN)	0.63e-3 radians sec^-1	inside / outside	yes	Laplacian: 10 m²/s
0.1^o longitude (5.55 km at 60^oN)	0.63e-3 radians sec^-1	inside	yes	Laplacian: 10 m²/s
0.1^o longitude (5.55 km at 60^oN)	0.63e-3 radians sec^-1	inside	yes	Laplacian: 20 m²/s
0.1^o longitude (5.55 km at 60^oN)	0.63e-3 radians sec^-1	inside	yes	Laplacian: 30 m²/s
0.1^o longitude (5.55 km at 60^oN)	0.63e-3 radians sec^-1	inside	yes	Laplacian: 50 m²/s
0.1^o longitude (5.55 km at 60^oN)	0.63e-3 radians sec^-1	inside	yes	Laplacian: 100 m²/s
0.1^o longitude (5.55 km at 60^oN)	0.63e-3 radians sec^-1	inside	yes	Laplacian: 10 m²/s , 30 m²/s
0.1^o longitude (5.55 km at 60^oN)	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 0.1^o 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 0.036^o runs, more SF6 is subducted to 229 m from inside the chimney than from outside.
2) In the 0.1^o 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

0.1^o cos(lat) (5.55 km at 60^oN) 0.5e-3 radians sec^-1 outside no biharmonic

0.1^o cos(lat) (5.55 km at 60^oN) 0.63e-3 radians sec^-1 outside no biharmonic

0.1^o cos(lat) (5.55 km at 60^oN) 1.0e-3 radians sec^-1 outside no biharmonic

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
0.1^o cos(lat) (5.55 km at 60^oN)	0.5e-3 radians sec^-1	outside	no	biharmonic
0.1^o cos(lat) (5.55 km at 60^oN)	0.63e-3 radians sec^-1	outside	no	biharmonic
0.1^o cos(lat) (5.55 km at 60^oN)	1.0e-3 radians sec^-1	outside	no	biharmonic

Conclusions:
1) At 0.1^o 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 0.1^o density gradient must be increased to have similar export to the 0.036^o 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 K_h, K_v = 10, 30 m²/s run is very similar to the K=10 m²/s run.
3) The 0.036^o run is similar to the 20 m²/s run at 1200 m, but not that similar to any of the 0.1^o runs above 600 m; e.g. the 0.036^o run has twice as much export at 400 m.
4) The export of the biharmonic run is generally similar to the 0.1^o 10 m²/s run.