saltfingers - awi · modeltime of 21 2 d–simulation saltfingers. introduction simulation of...
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IntroductionSimulation Of Saltfingers
Conclusions
Saltfingers
Alfred Wegener Institute, Bremerhaven
18. Juni 2009
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
IntroductionMotivation
Simulation Of SaltfingersPreliminary WorkDifferent Lewis NumbersPresent WorkResults
Conclusions
Saltfingers
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IntroductionSimulation Of Saltfingers
ConclusionsMotivation
Short Introduction to Saltfingers
I warm and saline water lies over cold and less saline water withdensity ratio Rρ
1 ≤ Rρ =|α|∂zTβ∂zS
≤ κT
κS
with α = thermal expansion coefficient
β = saline contraction coefficientT , S = temperature and salinity
Rρ < 1 stratification is unstable(not get confused with Semiconvection)
Saltfingers
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IntroductionSimulation Of Saltfingers
ConclusionsMotivation
Definitions
Reynolds Average: X = X + X ′
Density ratio: Rρ =α∂zTβ∂zS
Lewis Number: τ =κS
κT
Flux Ratio: γ =αw ′T ′
βw ′S ′
Turbulent Fluxes: w ′X ′
Saltfingers
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IntroductionSimulation Of Saltfingers
ConclusionsMotivation
Why We Do Saltfinger Simulations
I Thermohaline staircases are a possible result from saltfingers(William Merryfield „Origin of thermohaline staircases“ (2000), Timour Radko (2005))
I Saltfingers play an important role in mixing processes wheredouble–diffusion occur
I Study the structure of saltfingers there are high resolved3D–simulations necessary
I Resolve the Lewis Number τ = 0.01
Saltfingers
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IntroductionSimulation Of Saltfingers
ConclusionsMotivation
I Today there are a lot of different systems known wheredouble–diffusion occur (e.g. massive He3 stars, earth core,compositions of metals, coffee and milk, ... )[Turner 1985]
I These systems are compareable (e.g eddy size of turbulences inthe ocean and stars both ≈ 1cm but convective scales arequiet different)
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
3D and 212D Saltfinger Simulations
Simulations with 5123 and with 512x8x512 gridpoints in a regulargridInitial conditions:Gridspace: ∆x = ∆y = ∆z = 160µmLewis Number: τ =
κSκT
= 0.01Density Ratio: Rρ ≈ 1.3We have ≈ 170 sec modeltime of 3D–simulation and over 1400 secmodeltime of 21
2D–simulation
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Mean Turbulent Fluxes, w ′T ′ and w ′S ′
Abbildung: 3D and 2 12D
simulation, tubulent flux oftemperature
Abbildung: 3D and 2 12D
simulation, turbulent flux ofsalinity
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Fluxratio γ = αw ′T ′
βw ′S ′
Abbildung: Flux Ratio of 3D and2 1
2D simulationAbbildung: Density Ratio, 3Dand 2 1
2D
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Lewis Numbers τ = 0.01 and τ = 0.1?
Differences resulting from varied Lewis Numbers
τ−11 = 100 and τ−1
2 = 10
other initial conditions are identically (Rρ = 1.32, ...)
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Snapshot of Saltfingers with different Lewis Numbers
Abbildung: τ = 0.01, t = 500sec Abbildung: τ = 0.1, t = 500sec
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Turbulent Fluxes w ′T ′ and w ′S ′
Abbildung: Turbulent fluxes oftemperature
Abbildung: Turbulent fluxes ofsalinity
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Flux Ratio γ = α∂zw ′T ′
β∂zw ′S ′ and Density Ratio Rρ
Abbildung: Flux Ratio Abbildung: Density Ratio
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Mean Values of Temperature and Salinity
Abbildung: Mean temperature Abbildung: Mean salinity
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Conclusions For Further Work
I 3D simulations are expensiveI Mean values between 3D– and 21
2D simulations do not differsignifficant
I For our case (estimate vertical fluxes) we can use 212D
simulations for further work
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Aims
I get an estimate of the vertical fluxes of heat and salinityI find good initial coditions for simulationsI find the effective vertical diffusivity of heat and salinityI e.g Merryfield found a parametrisation for the case of
saltfingers like
K fS = 0.17× 1− τRρ
Rρ − γ
where K fS is the effecitve diffusivity of salinity
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Initial Conditions for 212D–Simulations
Initial conditions of simulationsI
1Rρ ≈ 1.7
2Rρ ≈ 1.07
I1/2
σ = νκT
= 7 Prandtl NumberI τ = κS
κT= 0.01 Lewis Number
I use a stretched coordinate system in vertical direction with∆z = 200µ m (∆z = 600µ m upper and lower 100 gridpoints)
I use a damping layer to absorb vertical fluxes at the upper andlower boundaries
512× 16× 512 gridpoints
0.1024× 0.0032× 0.1824 m3
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Saltfingersimulation Rρ = 1.7
salinity and contour oftemperature
I Rρ = 1.7I fingerwidth about
d ≈ 0.005m
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Saltfingers with Rρ = 1.7 and Rρ = 1.07
Abbildung: snapshot of salinityat modeltime t = 400
Abbildung: snapshot of salinityat modeltime t = 400
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Mean Values of Temperature and Salinity
Abbildung: mean values of temperature and salinity with Rρ = 1.7 (leftside) and Rρ = 1.07 (right side)
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Mean Values of Temperature and Salinity
Abbildung: mean values of temperature and salinity with Rρ = 1.7 (leftside) and Rρ = 1.07 (right side)
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Density Ratio of Saltfingers
Abbildung: densityratio Rρ = α∂zTβ∂zS
left side Rρ = 1.7, right side Rρ = 1.07
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Turbulent Fluxes
Abbildung: turbulent fluxes w ′T∂zT
(w ′S′
∂zS)
Rρ = 1.7 (left side) and Rρ = 1.07 (right side)
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Buoyancy
Abbildung: buoyancy N2 = − gρ ∂zρ
Rρ = 1.7 (left side) and Rρ = 1.07 (right side)
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Fingerwidth
Abbildung: Fingerwidth d4 =νκT
gα∂zTRρ = 1.7 (left side) and Rρ = 1.07 (right side)
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Simulation of Saltfingers
salinity and contour oftemperature
I Rρ = 1.07I 512x16x512
GridpointsI fingerwidth about
d ≈ 0.004− 0.005m
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Preliminary WorkDifferent Lewis NumbersPresent WorkResults
Unstable Case
salinity and contour oftemperature
I Rρ = 0.6I 512× 16× 512
Gridpoints
salinity and contour of temperature
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Conclusions
I stability is allways preserved (except in Rρ = 0.6 simulation)
I flux ratio γ = αw ′T ′
βw ′S ′ ≈ 0.5I ...
If we compare our data with the work from Shen (1997):I similar fingerwidth: ≈ 0.5 cmI τ−1
shen = 80 where τ−1awi = 100
I higher grid resolution as ShenI 3–dimensional not 2–dimensionalI Shen‘s simulation end before mixing begins and diffusive
Saltfingers occur
Saltfingers
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IntroductionSimulation Of Saltfingers
Conclusions
Critical Points
I is our vertical domain wide enough?I
Saltfingers