Horizontal wavenumber spectra of winds, temperature, and ...
Behind the scenes: Benchmarking sub-grid scales models in ... · Wavenumber L Numerical and...
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Behind the scenes: Benchmarking sub-grid scales models in global simulations of stellar convective dynamo 1. Introduction 2. Implicit vs Explicit dissipation: modeling subgrid-scales effects 3. Numerical simulations of stellar dynamos: a new take on cyclicality 4. Conclusions With P. Beaudoin, P. Charbonneau, A.S. Brun, S. Mathis, P. Smolarkiewicz Antoine Strugarek
Transcript of Behind the scenes: Benchmarking sub-grid scales models in ... · Wavenumber L Numerical and...
Behind the scenes: Benchmarking sub-grid scales models in global
simulations of stellar convective dynamo
1. Introduction
2. Implicit vs Explicit dissipation:modeling subgrid-scales effects
3. Numerical simulations of stellar dynamos: a new take on cyclicality
4. Conclusions
With P. Beaudoin, P. Charbonneau, A.S. Brun, S. Mathis, P. Smolarkiewicz
Antoine Strugarek
2Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
The many scales of solar magnetism
SunSize ~ 700 Mm
Rotation ~ monthCycle ~ 11 years
GranulesSize ~ 1 Mm
Life ~ 10 minutes
SpotsSize ~ 10 MmLife ~ days
3Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Challenge: ab-initio models of convective dynamos
[cred. A.S. Brun]
Tremendously high Reynolds (flow), Taylor (rotation), and Rayleigh (buoyancy,heat) numbers
4Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Variety of ‘stellar’ convective dynamos today
[Fan+14]
FSAM
[Kapyla+12,Warnecke+14]
PENCIL
[Augustson+15][Nelson+13]
[Brown+11]
ASH[Racine+11]
EULAG’s millenium simulation
[Masada+ 13]
Yin-Yang
5
Benchmarking convective dynamo simulations: a first take on convection
Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Strugarek+ 2016, Advances in Space Research
6Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
A set of anelastic MHD equations
τ ~ 20 rotationsDissipation
+Sub-grid scales effects
☛ Background state based on the anelastic benchmark of Jones+ 2011
7Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
ASH
Enhanced diffusion(& dynamic Smagorinsky, SLD)Pseudo-Spectral
Implicit dissipation(& explicit diffusion)
Finite volumes
EULAG-MHD
7Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
ASH
Enhanced diffusion(& dynamic Smagorinsky, SLD)Pseudo-Spectral
Implicit dissipation(& explicit diffusion)
Finite volumes
EULAG-MHD
Decomposition on spherical harmonicsRadial direction: Chebyshev poly. or FD
Linear parts integration: Crank-NicholsonNon-linear parts: Adams-Bashforth
Pressure is handled by taking the horizontal divergence of the mom. equation
Vectors: solenoidal decomposition
⇢u = r⇥ [Aer +r⇥ (Cer)]
8Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
A simple convection simulation with EULAG (I)
E1Vr
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0.98
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1.02
⌦/⌦
?
A ‘benchmark’ simulation of a turbulent convection zone generating cylindrical %-contours
[cf Jones+ 2011, Icarus]
Ro ~ 0.06 Nρ = 1.5∆S = 2 103 erg/K/g
10Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Kinetic energy balance: scale-by-scale budget
Coriolis
Pressure Gradient
Buoyancy Reynolds stress
Viscous& subgrid model
Statistical steady-state:
[cf Strugarek+13]
The same procedure can be repeated for the heat equation
Clebsch-Gordan coefficients
11Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Spectral energy transfer in EULAG simulation
0 10 20 30 40 50 60
L
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KE balance @ r/R = 0.850
0 10 20 30 40 50 60 70 80
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KE balance @ r/R = 0.844
CoriolisrP
BuoyancyAdvecTotal
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L
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KE balance @ r/R = 0.844
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Entropy balance @ r/R = 0.850
0 10 20 30 40 50 60 70 80
L
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Entropy balance @ r/R = 0.844
Amb. Advec.Newt. cool.AdvectionTotal
0 10 20 30 40 50 60
L
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Entropy balance @ r/R = 0.850
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Entropy balance @ r/R = 0.844
Amb. Advec.Newt. cool.AdvectionTotal
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Wavenumber L Wavenumber L
Wavenumber L12Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Spectral energy transfer in EULAG simulation
0 10 20 30 40 50 60
L
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KE balance @ r/R = 0.850
0 10 20 30 40 50 60 70 80
L
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KE balance @ r/R = 0.844
CoriolisrP
BuoyancyAdvecTotal
0 10 20 30 40 50 60
L
�100
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KE balance @ r/R = 0.850
0 10 20 30 40 50 60 70 80
L
E2
KE balance @ r/R = 0.844
CoriolisrP
BuoyancyAdvecTotal
0 10 20 30 40 50 60
L
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KE balance @ r/R = 0.844
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L
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KE balance @ r/R = 0.844
CoriolisrP
BuoyancyAdvecTotal
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13Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Spectral energy transfer in EULAG simulation
0 10 20 30 40 50 60
L
�100
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0 10 20 30 40 50 60 70 80
L
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KE balance @ r/R = 0.844
CoriolisrP
BuoyancyAdvecTotal
0 10 20 30 40 50 60
L
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0 10 20 30 40 50 60 70 80
L
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KE balance @ r/R = 0.844
CoriolisrP
BuoyancyAdvecTotal
0 10 20 30 40 50 60
L
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Entropy balance @ r/R = 0.850
0 10 20 30 40 50 60 70 80
L
E2
Entropy balance @ r/R = 0.844
Amb. Advec.Newt. cool.AdvectionTotal
0 10 20 30 40 50 60
L
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0 10 20 30 40 50 60 70 80
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Entropy balance @ r/R = 0.844
Amb. Advec.Newt. cool.AdvectionTotal
E1Vr
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1000
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[cm
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50
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1000
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m/s
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[cm
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[cm
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Wavenumber L Wavenumber L
[Strugarek+ 2016]
14Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Effective dissipation coefficients in EULAG
0.75 0.80 0.85 0.90 0.95r/R?
10
20
30
40
50
60
L
⌫e↵
11.0
11.2
11.4
11.6
11.8
12.0
12.2
12.4
log 1
0⌫
e↵[c
m2/s
]0.75 0.80 0.85 0.90 0.95
r/R?
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
[cm
2/s
]
⇥1012 ⌫e↵(r)
Averaged smoothed ⌫e↵
⌫fit
Standard Deviation along L
0 10 20 30 40 50 60
L
⌫e↵(L)
Averaged smoothed ⌫e↵
⌫fit(Lcut = 14,17,20)Standard Deviation along r
Effective viscosity
0.75 0.80 0.85 0.90 0.95r/R?
10
20
30
40
50
60
L
e↵
11.0
11.2
11.4
11.6
11.8
12.0
12.2
12.4
log 1
0
e↵[c
m2/s
]
0.75 0.80 0.85 0.90 0.95r/R?
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
[cm
2/s
]⇥1012 e↵(r)
Averaged smoothed e↵
fit
Standard Deviation along L
0 10 20 30 40 50 60
L
e↵(L)
Averaged smoothed e↵
fit(Lcut = 14,17,20)Standard Deviation along r
Effective heat diffusivity
15Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Effective dissipation coefficients in EULAG
0.75 0.80 0.85 0.90 0.95r/R?
10
20
30
40
50
60
L
Pre↵
�1.0
�0.8
�0.6
�0.4
�0.2
0.0
0.2
0.4
0.6
0.8
1.0
log 1
0P
r e↵
0.75 0.80 0.85 0.90 0.95r/R?
0
1
2
3
4
5
6
7
8Pre↵(r)
Averaged smoothed Pre↵Standard Deviation along L
0 10 20 30 40 50 60
L
Pre↵(L)
Averaged smoothed Pre↵Standard Deviation along r
16Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Comparison with an ‘equivalent’ ASH simulation
In the ASH simulation, we have degrees of liberty as to what amount of dissipation to put at large and small scales
Encouraging results: qualitatively similar DR profile obtained with an ASH simulation with fitted κ,ν
Next: comparing dynamo cases with the same formalism…
100
101
102
103
104
105
106
107
108
EK L[e
rgcm
�3]
A14A17A20E1
100 101 102
L
10�1
100
101
102
103
ES L[e
rg2
g�2
K�
2]
A14A17A20E1
A14 A17 A20 E1
0.98
1.00
1.02
⌦/⌦
?
0.75 0.80 0.85 0.90 0.95r/R?
10
20
30
40
50
60
L
⌫e↵
11.0
11.2
11.4
11.6
11.8
12.0
12.2
12.4
log 1
0⌫
e↵[c
m2/s
]
0.75 0.80 0.85 0.90 0.95r/R?
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
[cm
2/s
]
⇥1012 ⌫e↵(r)
Averaged smoothed ⌫e↵
⌫fit
Standard Deviation along L
0 10 20 30 40 50 60
L
⌫e↵(L)
Averaged smoothed ⌫e↵
⌫fit(Lcut = 14,17,20)Standard Deviation along r
[Strugarek+ ASR 2016]
17
A new take on stellar magnetic cycles
Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
18Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Prototype cyclic dynamo in a convective enveloppe
Ro ~ 0.34 Nρ = 3.2 ΔS = 104 erg/K/g
0 100 200 300 400 500
Time [years]
�50
0
50
Latit
ude
[�]
B' at r = 0.75R�
�0.16
0.00
0.16
[T]
19Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Cycle period is inversely proportional to the Rossby number
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0log10 (Rossby number)
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
log 1
0(P
cyc)
[yea
rs]
R�1.1±0.15o
Basic ingredients of stellar dynamos
- Differential rotation - Cyclonic turbulence
‘Go to’ parameter is the Rossby number
0.8 1.0 1.2 1.4 1.6 1.8log10 (Prot) [days]
-0.5
0.0
0.5
1.0
1.5lo
g 10
Pcy
c
⇣ Lbc
L�
⌘ 0.78� [y
ears
]⌦�1.06
?
BV07L11Simulations
�
20Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Magnetic cycles in a stellar context
0.8 1.0 1.2 1.4 1.6 1.8log10 (Prot) [days]
-0.5
0.0
0.5
1.0
1.5lo
g 10
Pcy
c
⇣ Lbc
L�
⌘ 0.78� [y
ears
]
BV07L11
�
A new take on observational data
0.8 1.0 1.2 1.4 1.6 1.8log10 (Prot) [days]
-0.5
0.0
0.5
1.0
1.5lo
g 10
Pcy
c
⇣ Lbc
L�
⌘ 0.78� [y
ears
]⌦�1.06
?
BV07L11Simulations
�
20Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Magnetic cycles in a stellar context
A new take on observational data
21Numerical and computational methods for simulation of all-scale geophysical flows, Reading, 05/10/2016 A. Strugarek
Conclusions & perspectives
A convective dynamo benchmark has been successfully developed to specifically study the impact of sub-grid scales modelling (dynamo comparison to be achieved soon)
A powerful method based on spectral transfers analysis is proposed to relate implicit and explicit sub-grid scales models
For the first time we are able to simulate cycles in 3D turbulent convection zone that vary systematically with the large scale parameters of the star (rotation, luminosity)
Very promising first comparisons with observational data
Future prospects: vary the convection zone aspect ratio, and explore states with higher degree of turbulence (closer to real stars)
