‘Horizontal convection’ 3 Coriolis effects adjustment to changing bc’s, thermohaline effects

‘Horizontal convection’ 3 Coriolis effects

adjustment to changing bc’s, thermohaline effects

Ross Griffiths

Research School of Earth Sciences The Australian National University

Outline (#3)

• Effects of rotation

• Adjustment processes and timescales

• full-depth or partial-depth overturning?

• Effects of salt or freshwater fluxes (B.C.s and DDC)?

• simplified condition for ‘shut-down’ of deep sinking?

Effects of Rotation

Geostrophic flow, PV dynamics, horizontal gyres, boundary currents along meridional (N-S) boundaries, baroclinic instability and eddies, convective instability in eddies (‘open ocean’ sinking?), Northern/Southern boundary sinking.

Ekman transport, Ekman pumping

Boundary layer scaling - geostrophic case

Steady state balances when h>>hE:

• continuity & vertical advection-diffusion

vh ~ wL ~ L/h• thermal wind (geostrophic constraint)

gTh/L ~ fuu ~ v• conservation of heat

FL ~ ocpTvh

=>

u, v h

Ta

Tc

Nu ~ (RaE)1/3

h/L ~ (RaE)–1/3

uL/ ~ (RaE)2/3

(Bryan & Cox, 1967; Park & Bryan 2000)

bl/L ~ (RaE)1/3

(indept. of viscosity)

Simple GCMs(Bryan 1987, Park & Bryan 2000, Winton 1995,96)

Dependence on sometimes weaker than scaling result 2/3

owing to different B.C.s (with restoring B.C.s use internal T)

Rotating annulus geometry, bottom forced

Annular geometry

Strong zonal flow

Meridional overturning

1990

Rotating annulus geometry, bottom forced(photo from Miller & Reynolds, JFM, 1990)

Rotating HC with meridional boundaries

movie shows Ω = 0.3 rad/s anticlockwise

QuickTime™ and aH.264 decompressor

are needed to see this picture.

Parameters (and flow regimes)?

Ocean:Ra ~ 1025, Pr ≈ 1, hT/hv ~ 10-20, Rd/L = (g’D)1/2/fL ≈ 10-3, N/f ~ 30, Ni/f ~ 3

Horizontal convection in lab:Ra ≈ 1014, Pr ≈ 4, hT/hv ~ 10-20, Rd/L = (g’D)1/2/fL ≈ 5x10-

2, N/f ≈ 2, Ni/f ~ 0.02

Rotating ‘horizontal convection’

Applied heating flux 140 WΩ = 0.2 rad/s

Viewed after thermal equilibration - steady state

3D, unsteady flowBoundary currents and gyresB.L. convective instabilityBaroclinic instability3D endwall plumeinterior vortex plume convection

Local/mesoscale processes in deep-convection

A small patch of surface buoyancy flux above a density stratification

(eg. a polynya of 12km diameter).

Fernando & Smith, Eur. J. Mech. 2001

Rotating ‘horizontal convection’Applied heating flux 140 W, Ω = 0.2 rad/s

Viewed after thermal equilibration, at 8x speedup

QuickTime™ and aDV - PAL decompressor


Rotating ‘horizontal convection’Applied heating flux 140 W, Ω = 0.2 rad/s

Viewed after thermal equilibration, at 16x speedup

QuickTime™ and aDV - PAL decompressor


Temporal adjustmentsto a sensitive balance

Ocean circulation:• How would a convective MOC respond to perturbations

in the surface B.C.s.• would the response be different for changes at high or

low latitudes? • What B.C. changes will shut-down deep overturning,

and will it return to full-depth? • timescales for adjustment and equilibration?

Horizontal convection:• mechanisms for adjustment to changed B.C.s?• switch to shallow convection?• can a shallow circulation persist?

• timescales of response? • Role of interior diffusion? Sensitivity to type of B.C.s?

Box 1.25m long x 0.2m high x 0.3m wide



792h:42min

+ 13 min

+ 33 minT2=34˚CT1=10˚C

The steady stateNon-rotating,applied T

Adjustment to perturbed BCs

Perturbations:

Warm up the hot plate

Cool down hot plate

Warm up cold plate

Cool down cold plate

Conditions:

Applied F or T

Rotating or non-rotating

Effects of ambient temperature

+

Warm up case

Example #1:

non-rotating, applied T

Warm up hot plate (34˚ to 38˚C),

applied cooling T1= 10˚C

Warm up hot plateie. increase destablizing

buoyancy(showing heated end of box)



Warm up hot plate(showing whole box)



Simplest model: full-depth circulation and applied heat

input

• Hold Tc fixed, increase heat input from F0 to Fo+∆F

• plume carries base heat input to top - assume well-mixed interior

• Flux imbalance: cpDLTt = ∆F - F’(t)

• Boundary layer conduction: F0 + F’(t) = cp(T - Tc)L/h, h ~ 2.65LRa-1/6

=> T = T0 + ∆T(1- e-t/hD), ∆T = Tf - T0 = h∆F/(cpL)

or (T-Tf)/(T0-Tf) = e-t/hD

Dh

L

Tc F0+F’(t)

~uniformT(t) F0+∆F

Warm up case(ie. increase destabilizing buoyancy input or decrease stablizing

flux)

T(t) at mid-depth (above hot plate, thermistor #8)

T* = (T(t) - Tf)/(T0 - Tf)

Example #2: Constant applied heating flux (1556 Wm-2), hot lab (Tlab=31.15˚, T0=31.16˚, Tf=34.94˚C)

Warm up cold plate (10˚–>15˚C)

Cool down case (ie. decrease de-stabilizing buoy. input or increase stablizing

flux)Example #3:

Cool down cold plate (from 15˚ to 10˚C), constant hot plate temperature (34˚C)



Note long timescale of re-adjustment to full-depth ~ 20 hours

Cool down case

T(t) at mid-depthabove hot plate, thermistor #8

T* = (T(t) - Tf)/(T0 - Tf)

Example #4:Constant applied heating flux (1556 Wm-2), hot lab (Tlab=31.15˚, T0=34.94˚, Tf=31.13˚C)

Cool down cold plate (15˚–>10˚C)

timescalese-

fold

ing

time

interior Top outflow at 175/150 mm above CP(#3, #19)

0.0

0.1

0.2

0.3

Heat upcold plate

Heat uphot plate

Cool downhot plate

Cool downcold plate

__e\D

2

Boundary layer at 15/20mm, mid tank (#4, #15)

0.0

0.1

0.2

0.3

Heat upcold plate

Heat uphot plate

Cool downhot plate

Cool downcold plate

__e\D

2

TExp Flux-Hot lab

TExp Flux

TExpTemperature

-Texpdouble

,flux hotlabTexp

,Temprotating

= hD/

Top outflow at 175/150 mm above CP(#3, #19)

0.0

0.2

0.4

0.6

0.8

1.0

Heat upcold plate

Heat uphot plate

Cool downhot plate

Cool downcold plate

__95\D

2

Boundary layer at 15/20mm, mid tank (#4, #15)

0.0

0.2

0.4

0.6

0.8

1.0

Heat upcold plate

Heat uphot plate

Cool downhot plate

Cool downcold plate

__95\D

2

95 -T FluxHot lab

95-T Flux

95-TTemperature95 ,T Temp

rotating

= hD/

95%

of

chan

ge

boundary layer

Time development - infinite Pr initial T = lowest T applied at top

(ie. box starts at T = 0, colder than final equilib.T)

T=0 T=1

Response to changed B.C.s Implications for a convective

MOC• An increased sea surface cooling at high latitudes, or decreased

heat input at low latitudes

––> enhanced full-depth overturning

––> exponential adjustment (hD/ ~ 500 - 8000 yrs

• A decreased surface cooling (or freshwater input), or increased heat input

––> temporary partial-depth circulation

––> return to full depth with oscillations in fountain penetration (entrainment?)

––> equilibration times may approach D2/ (~ 5000 - 50000 yrs)

––> timescale is longest for applied flux

• Coriolis accelerations have little effect on equilibration times

• Need to examine magnitude of changes required to shut down the deep sinking (see thermohaline effects)

Questions:

• interaction of thermally-driven circulation and surface freshwater fluxes at high latitudes? (opposing buoyancy fluxes)

• or with brine rejection on seasonal timescales? (reinforcing thermal buoyancy flux)

• steady or fluctuating behaviour?• does double-diffusive convection play

significant roles? (salt-fingering at low latitude, ‘diffusive’ layering at high latitudes)

Thermohaline effects

Modelling a surface freshwater input

Parameters:

RaF = gFL4/(ocpT2

Pr = /T

= S /T

A = D/L

R = S/T

BS/BT = 2cpSQ/(FLW

Thermal convection

‘Synthetic schlieren’ image / heated end

imposed heat flux

20cm

x=0 L/2=60cm

Small salinity buoyancy flux

steady flow

Large salt buoyancy flux

flooding of forcing surface

S = 2.0%

Q = 2.7x10-7 m3s-1

BS/BT = 0.5

2 0

2 5

3 0

3 5

4 0

4 5

5 0

0 2 0 4 0 6 0 8 0 1 0 0

T i m e ( 1 0

3

s )

Temp (

o

C)

1

2

3

4

5

6 7

8

S = 2.0%

Q = 2.7x10-7 m3s-1

BS/BT = 0.5

Large salt buoyancy flux

flooding of forcing surface

Intermediate salt buoyancy flux

oscillatory flow

3 0

3 2

3 4

3 6

3 8

4 0

4 2

4 4

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0

T i m e ( 1 0

3

s )

Temp (

o

C)

1

2

3

4

78

Small-intermediate salt flux

oscillatory flow

S = 1.0% Q = 0.99x10-7 m3s-1 BS/BT = 0.1

1

Intermediate salt flux

Thermistorpositions

Large-intermediate salt fluxintrusions above b.l.

S = 0.51% Q = 3.6x10-7 m3s-1 BS/BT = 1.04

Flow regimesand ratio of buoyancy fluxes

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5

( %)S wt

1/Q(10 6 s m-3)

1. steady

2. oscillations & flooding

3. flooding

4. oscillations

0.12

0.47

BS/BT = 0.07

Timescales

• flushing by the volume input

tf ~ V/Q ~ 105 s

• convective ventilation time

tc ~ V/uW ~ 2000 - 5000 s

• internal wave travel time along the thermocline

tw ~ L/N* ~ 45 s

• observed fluctuation time scales ~ tc

Summary

A stabilising salinity flux adds:

• a mostly stable halocline (in the ‘sinking’ region)

• steady, oscillatory or surface-flooding regimes

• regime depends primarily on the ratio of buoyancy fluxes (BS/BT).

Conclusions• ‘horizontal convection’ shows a wide range of behaviour and poses many fascinating questions that remain unexplored.

• ocean MOC and THC has buoyancy as one important motive force (with wind also very important) and studies of horizontal convection can contribute to the understanding of the ocean circulation.

• there is argument about the extent to which the overturning circulation relies on diffusion and the extent to which the sub-surface flow is adiabatic.

• in a diffusive circulation (with energy for mixing provided by tides and winds), the flow is governed equally by both mixing rate and buoyancy supply.

Further questions

• scaling of T-H fluctuation times to the oceans

• effects of time-varying heat and salinity fluxes

• effects of marginal seas and hydraulic controls

• rotation and thermohaline effects

• -effects

• non-Boussinesq effects (eg. nonlinear density equation)

Documents

‘Horizontal convection’ 3 Coriolis effects adjustment to changing bc’s, thermohaline effects