On the thermohaline circulation
in semi−enclosed marginal seas
Michael Spall
WHOI
Don’t try to describe the ocean if you’ve never
seen it
And don’t ever forget that you just may wind
up being wrong
Jimmy Buffett
Questions :
How do regions of deep convection in the
interior of the basin interact with the
boundary currents that communicate with
the open ocean ?
What processes control the vertical and
lateral heat flux ?
What processes control the vertical mass flux ?
Where do these fluxes take place ?
What determines their magnitude ?
Consider an idealized semi−enclosed
marginal sea
600
500
cooling
region
Y (km)
400
300
200
100
open ocean
50
100
150
200
250 300
X (km)
350
400
450
1. cooling in the interior of the marginal sea
active for 2 months, no forcing for 10 months
2. restore T(z) to a uniform stratification in the
"open ocean"
3. integrate the model for 10 years
diagnose last three years
MIT hydrostatic primitive equation model
(Marshall et al. 1997; Adcroft et al. 1997)
level coordinates, free surface
finite differences, C−grid
5 km horizontal resolution (Ld = 10 km)
12 levels in the vertical
1000 m deep, flat bottom
500 km diameter basin
−4
f−plane, f = 10
−1
s
2
Laplacian viscosity, diffusivity
(50 m / s)
no−slip lateral boundary conditions
linear EOS with temperature only
Consider a simple analytic model governed by
linear voricity dynamics in a 2 layer fluid:
f w = −A v xxx
H
one can derive a solution for the pressure
anomaly (or upper layer thickness)
−α y
P = P0
i k1 x
i k2 x
e ( e − k1/k2 e )
For a lateral diffusion of density,
the boundary current width is
½
δ = Ld σ
and the along boundary decay scale is
−1
3/2
−1
α = Ld σ E
where σ = A / Κ is the Prandtl number
Ld is the deformation radius
2
E = A/f0Ld is the horizontal Ekman number
An example case with Q=200 W/m^2
600
5.4
5.3
500
5.2
400
5.1
5
300
4.9
200
4.8
4.7
100
4.6
50
100
150
200
250
300
350
400
450
4.5
Mean temperature at level 1 (years 7−10)
O
cooling is applied within circle
O
takes ~ 5 years to spin−up basin ave temp
O
cold interior, warm inflow along boundary
(note temperature gradient along bdy)
O
densest water is offset from center
of cooling region
Restratification (not main focus today)
potential vorticity
temperature
5.5
600
5.5
600
5
4.5
500
500
4
400
3.5
400
5
3
300
2.5
300
2
200
200
1.5
4.5
1
100
100
0.5
0
0
0
100
200
300
400
temperature
O
0
100
200
300
400
500
500
potential vorticity
10 days after cooling has ceased, year 8
O eddies spreading dense water laterally
away from cooling region
O inflowing boundary current is also unstable
O dense water in eddies stays near the surface
pv constrants limit sinking in the interior
O high pv caps overlay recently formed eddies
high stratification is not advected from the
open ocean − generated internally via
"pv sheet" boundary condition (Bretherton, 1967)
Where does the downwelling take place ?
0
depth (m)
100
200
−5
300
−10
400
−15
500
−20
600
−25
700
−30
800
−35
900
−40
1000
50
100
150
200
250
radius (km)
center of
marginal sea
outer
boundary
2
Azimuthally integrated vertical velocity (m /s)
O Essentially all of the downwelling takes
place near the lateral boundary
O width of downwelling ~ 20 km
O maximum at mid−depths
O total downwelling transport at 460 m
6
3
is 0.5 x10 m / s
Comparison between PE model and theory
3.5
16
log(Ld σ1.5 E−1)
14
Ld σ1/2
12
10
3
2.5
8
6
4
2
2
0
0
10
20
30
40
1.5
1.5
50
model bdylayer width (km)
2
2.5
3
3.5
model log(decay scale(km) )
O region of downwelling in the PE model
1/2
scales well with Ld σ
varies between 10 − 40 km
O along boundary decay scale diagnosed
from the model compares well with 1/α
varies between 100 − 1000 km
O submesoscale parameterizations influence
characteristics of the THC
−4
−1
2
A =150, 250 m / s (squares)
Κ = 150, 250 m / s (triangles) half stratification (+)
500 m, 2000 m depth (diamonds)
f=0.5, 2x10
s
(asterisks)
Example with large decay scale
600
5.4
5.3
500
5.2
400
5.1
5
300
4.9
200
4.8
4.7
100
4.6
50
−1
100
150
200
250
300
350
400
4.5
450
2
α = 1100 km (increased A to 150 m / s)
O warm water extends farther around the
marginal sea
O temperature is more symmetric around
basin, larger horizontal gradient
Example with small decay scale
600
5.4
5.3
500
5.2
400
5.1
5
300
4.9
200
4.8
4.7
100
4.6
50
100
150
200
250
300
350
400
4.5
450
−1
2
α = 125 km (increased Κ to 150 m / s)
O warm water is eroded very quickly
O basin−averaged temperature is
colder than standard case
Summary and conclusions
O Interior cooling is balanced by mean
and low frequency (1−10 years)
oscillations of barotropic gyres and
mesoscale eddies
O Dense water Interacting with the
boundaries develops a baroclinic
boundary current that advects warm
water into the basin to balance
cooling
O downwelling limb of THC is
concentrated in this boundary current
1/2
width
Ld σ
3/2
length
Ld σ / E
O characteristics of the THC are
strongly influenced by lateral
processes at the smallest scales