The liquid iron core of the Earth undergoes vigorous convection driven by thermal and compositional buoyancy. The dynamics of convective fluid motions and heat transfer in such conditions are determined by background rotation, geometrical symmetry, and thermal interactions across the boundaries. In this study, rotating thermal convection in a horizontal fluid layer is considered to understand the fluid flow characteristics in the Earth's outer core focusing on the regions close to the rotational axis. The effects of a partial stable stratification on fluid flow and heat transfer are investigated to ascertain the physical significance of thermal core–mantle interaction on geomagnetic field generation driven by core fluid motion. It is found that even with non-linear evolution, convective instabilities retain the fundamental characteristics of linear onset modes. Mildly supercritical regimes lead to near laminar flows with the transition to turbulent convection occurring for strongly driven convection around 50–100 times enhanced buoyancy. Axial symmetry breaking and preferential damping of small-scale vortical structures are the hallmark of penetrative convection. Rapid rotation sustains small-scale helical flows in stable regions, a necessary ingredient for the sustenance of Earthlike dipolar magnetic fields. Coherent flow structures for strongly turbulent convection are obtained using reduced-order modeling. The overall total heat transfer is suppressed (up to 25%) due to the stable stratification although convective efficiency is enhanced (up to 30%) in the unstable regions favored by rapid rotation. Flow suppression is overcome under strong buoyancy forces, a relevant dynamical regime for deep-seated dynamo action in the Earth's core.
REFERENCES
1.
Ahlers
,
G.
,
Bodenschatz
,
E.
,
Hartmann
,
R.
,
He
,
X.
,
Lohse
,
D.
,
Reiter
,
P.
,
Stevens
,
R. J.
,
Verzicco
,
R.
,
Wedi
,
M.
,
Weiss
,
S.
et al, “
Aspect ratio dependence of heat transfer in a cylindrical Rayleigh–Bénard cell
,” Phys. Rev. Lett.
128
(8
), 084501
(2022
).2.
Aujogue
,
K.
,
Pothérat
,
A.
, and
Sreenivasan
,
B.
, “
Onset of plane layer magnetoconvection at low Ekman number
,” Phys. Fluids
27
(10
), 106602
(2015
).3.
Aujogue
,
K.
,
Pothérat.
A.
,
Sreenivasan
,
B.
, and
Debray
,
F.
, “
Experimental study of the convection in a rotating tangent cylinder
,” J. Fluid Mech.
843
, 355
–381
(2018
).4.
Aurnou
,
J. M.
and
Olson
,
P. L.
, “
Strong zonal winds from thermal convection in a rotating spherical shell
,” Geophys. Res. Lett.
28
(13
), 2557
–2559
, https://doi.org/10.1029/2000GL012474 (2001
).5.
Begiashvili
,
B.
,
Groun
,
N.
,
Garicano-Mena
,
J.
,
Le Clainche
,
S.
, and
Valero
,
E.
, “
Data-driven modal decomposition methods as feature detection techniques for flow problems: A critical assessment
,” Phys. Fluids
35
(4
), 041301
(2023
).6.
Bhattacharya
,
S.
,
Verma
,
M. K.
, and
Bhattacharya
,
A.
, “
Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models
,” Phys. Fluids
34
(2
), 025102
(2022
).7.
Bhattacharya
,
S.
,
Verma
,
M. K.
, and
Samtaney
,
R.
, “
Revisiting Reynolds and Nusselt numbers in turbulent thermal convection
,” Phys. Fluids
33
(1
), 015113
(2021
).8.
Brunton
,
S. L.
and
Kutz
,
J. N.
, Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control
(
Cambridge University Press
, 2022
).9.
Buffett
,
B.
, “
Geomagnetic fluctuations reveal stable stratification at the top of the earth's core
,” Nature
507
(7493
), 484
–487
(2014
).10.
Buffett
,
B. A.
and
Seagle
,
C. T.
, “
Stratification of the top of the core due to chemical interactions with the mantle
,” J. Geophys. Res.
115
(B4
), B04407
, https://doi.org/10.1029/2009JB006751 (2010
).11.
Burns
,
K.
,
Vasil
,
G.
,
Oishi
,
J.
,
Lecoanet
,
D.
, and
Brown
,
B.
, “
Dedalus: A flexible framework for numerical simulations with spectral methods
,” (2019
).12.
Busse
,
F. H.
, “
Generation of planetary magnetism by convection
,” Phys. Earth Planet. Inter.
12
(4
), 350
–358
(1976
).13.
Busse
,
F. H.
and
Carrigan
,
C.
, “
Convection induced by centrifugal buoyancy
,” J. Fluid Mech.
62
(3
), 579
–592
(1974
).14.
Calkins
,
M. A.
, “
Quasi-geostrophic dynamo theory
,” Phys. Earth Planet. Inter.
276
, 182
–189
(2018
).15.
Chandrasekhar
,
S.
, Hydrodynamic and Hydromagnetic Stability
(
Courier Corporation
, 2013
).16.
Chatterjee
,
A.
, “
An introduction to the proper orthogonal decomposition
,” Curr. Sci.
78
, 808
–817
(2000
).17.
Chi-Durán
,
R.
and
Buffett
,
B. A.
, “
Extracting spatial–temporal coherent patterns in geomagnetic secular variation using dynamic mode decomposition
,” Geophys. Res. Lett.
50
(5
), e2022GL101288
, https://doi.org/10.1029/2022GL101288 (2023
).18.
Christensen
,
U. R.
,
Aubert
,
J.
,
Cardin
,
P.
,
Dormy
,
E.
,
Gibbons
,
S.
,
Glatzmaier
,
G.
,
Grote
,
E.
,
Honkura
,
Y.
,
Jones
,
C.
,
Kono
,
M.
et al, “
A numerical dynamo benchmark
,” Phys. Earth Planet. Inter.
128
(1–4
), 25
–34
(2001
).19.
Couston
,
L.-A.
,
Lecoanet
,
D.
,
Favier
,
B.
, and
Le Bars
,
M.
, “
Dynamics of mixed convective–stably-stratified fluids
,” Phys. Rev. Fluids
2
(9
), 094804
(2017
).20.
Davidson
,
P.
and
Ranjan
,
A.
, “
On the spatial segregation of helicity by inertial waves in dynamo simulations and planetary cores
,” J. Fluid Mech.
851
, 268
–287
(2018
).21.
Davies
,
C.
and
Gubbins
,
D.
, “
A buoyancy profile for the earth's core
,” Geophys. J. Int.
187
(2
), 549
–563
(2011
).22.
Dormy
,
E.
,
Soward
,
A.
,
Jones
,
C.
,
Jault
,
D.
, and
Cardin
,
P.
, “
The onset of thermal convection in rotating spherical shells
,” J. Fluid Mech.
501
, 43
–70
(2004
).23.
Garai
,
S.
and
Sahoo
,
S.
, “
On convective instabilities in a rotating fluid with stably stratified layer and thermally heterogeneous boundary
,” Phys. Fluids
34
(12
), 124101
(2022
).24.
Gastine
,
T.
and
Wicht
,
J.
, “
Stable stratification promotes multiple zonal jets in a turbulent Jovian dynamo model
,” Icarus
368
, 114514
(2021
).25.
Gilman
,
P. A.
, “
The solar dynamo: Observations and theories of solar convection, global circulation, and magnetic fields
,” in Physics of the Sun: The Solar Interior
(
Springer
, 1986
), pp. 95
–160
.26.
Glatzmaier
,
G.
, Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation
(
Princeton University Press
, 2013
).27.
Gubbins
,
D.
, “
Geomagnetic constraints on stratification at the top of earth's core
,” Earth, Planets, Space
59
, 661
–664
(2007
).28.
Guervilly
,
C.
, “
Fingering convection in the stably stratified layers of planetary cores
,” J. Geophys. Res.
127
(11
), e2022JE007350
, https://doi.org/10.1029/2022JE007350 (2022
).29.
Guzmán
,
A. J. A.
,
Madonia
,
M.
,
Cheng
,
J. S.
,
Ostilla-Mónico
,
R.
,
Clercx
,
H. J.
, and
Kunnen
,
R. P.
, “
Force balance in rapidly rotating Rayleigh–Bénard convection
,” J. Fluid Mech.
928
, A16
(2021
).30.
Guzmán
,
A. J. A.
,
Madonia
,
M.
,
Cheng
,
J. S.
,
Ostilla-Mónico
,
R.
,
Clercx
,
H. J.
, and
Kunnen
,
R. P.
, “
Flow-and temperature-based statistics characterizing the regimes in rapidly rotating turbulent convection in simulations employing no-slip boundary conditions
,” Phys. Rev. Fluids
7
(1
), 013501
(2022
).31.
Heimpel
,
M.
,
Aurnou
,
J.
,
Al-Shamali
,
F.
, and
Perez
,
N. G.
, “
A numerical study of dynamo action as a function of spherical shell geometry
,” Earth Planet. Sci. Lett.
236
(1–2
), 542
–557
(2005
).32.
Hori
,
K.
,
Wicht
,
J.
, and
Christensen
,
U. R.
, “
The effect of thermal boundary conditions on dynamos driven by internal heating
,” Phys. Earth Planet. Inter.
182
(1–2
), 85
–97
(2010
).33.
Julien
,
K.
,
Knobloch
,
E.
,
Rubio
,
A. M.
, and
Vasil
,
G. M.
, “
Heat transport in low-Rossby-number Rayleigh–Bénard convection
,” Phys. Rev. Lett.
109
(25
), 254503
(2012
).34.
Julien
,
K.
,
Legg
,
S.
,
McWilliams
,
J.
, and
Werne
,
J.
, “
Rapidly rotating turbulent Rayleigh–Bénard convection
,” J. Fluid Mech.
322
, 243
–273
(1996
).35.
Kaneshima
,
S.
, “
Array analyses of SmKS waves and the stratification of earth's outermost core
,” Phys. Earth Planet. Inter.
276
, 234
–246
(2018
).36.
King
,
E. M.
,
Stellmach
,
S.
, and
Aurnou
,
J. M.
, “
Heat transfer by rapidly rotating Rayleigh–Bénard convection
,” J. Fluid Mech.
691
, 568
–582
(2012
).37.
Kolhey
,
P.
,
Stellmach
,
S.
, and
Heyner
,
D.
, “
Influence of boundary conditions on rapidly rotating convection and its dynamo action in a plane fluid layer
,” Phys. Rev. Fluids
7
(4
), 043502
(2022
).38.
Kundu
,
P. K.
,
Cohen
,
I. M.
, and
Dowling
,
D. R.
, Fluid Mechanics
(
Academic Press
, 2015
).39.
R.
Kunnen
,
B. J.
Geurts
, and
Clercx
,
H.
, “
Turbulence statistics and energy budget in rotating Rayleigh–Bénard convection
,” Eur. J. Mech.-B/Fluids
28
(4
), 578
–589
(2009
).40.
Larmor
,
J.
, “
How could a rotating body such as the sun become a magnet
?,” in A Source Book in Astronomy and Astrophysics, 1900–1975
(
Harvard University Press
, 1979
), pp. 106
–107
.41.
Lay
,
T.
and
Young
C. J.
, “
The stably-stratified outermost core revisited
,” Geophys. Res. Lett.
17
(11
), 2001
–2004
, https://doi.org/10.1029/GL017i011p02001 (1990
).42.
Li
,
J.
,
Lin
,
Y.
, and
Zhang
,
K.
, “
Dynamic mode decomposition of the core surface flow inverted from geomagnetic field models
,” Geophys. Res. Lett.
51
(1
), e2023GL106362
, https://doi.org/10.1029/2023GL106362 (2024
).43.
Malkus
,
W.
, “
Energy sources for planetary dynamos
,” in Lectures on Solar and Planetary Dynamos
(
Cambridge University Press
, 1994
), p. 161
.44.
Moeng
,
C.-H.
and
Rotunno
,
R.
, “
Vertical-velocity skewness in the buoyancy-driven boundary layer
,” J. Atmos. Sci.
47
(9
), 1149
–1162
(1990
).45.
Moffatt
,
H.
, “
Helicity and celestial magnetism
,” Proc. R. Soc. A
472
(2190
), 20160183
(2016
).46.
Moffatt
,
H. K.
, Field Generation in Electrically Conducting Fluids
(
Cambridge University Press
,
Cambridge, London, New York, Melbourne
, 1978
).47.
Moffatt
,
H. K.
, “
Helicity and singular structures in fluid dynamics
,” Proc. Natl. Acad. Sci. U. S. A.
111
(10
), 3663
–3670
(2014
).48.
Moffatt
,
H. K.
and
Tsinober
,
A.
, “
Helicity in laminar and turbulent flow
,” Annu. Rev. Fluid Mech.
24
(1
), 281
–312
(1992
).49.
Mukherjee
,
P.
and
Sahoo
,
S.
, “
Thermal convection and dynamo action with stable stratification at the top of the earth's outer core
,” Phys. Earth Planet. Inter.
345
, 107111
(2023
).50.
Oliver
,
T. G.
,
Jacobi
,
A. S.
,
Julien
,
K.
, and
Calkins
,
M. A.
, “
Small scale quasigeostrophic convective turbulence at large Rayleigh number
,” Phys. Rev. Fluids
8
(9
), 093502
(2023
).51.
Olson
,
P.
, “
Gravitational dynamos and the low-frequency geomagnetic secular variation
,” Proc. Natl. Acad. Sci. U. S. A.
104
(51
), 20159
–20166
(2007
).52.
Olson
,
P.
, “
Core dynamics: An introduction and overview
,” in Treatise of Geophysics
(
Elsevier
, 2015
).53.
Olson
,
P.
,
Christensen
,
U.
, and
Glatzmaier
,
G. A.
, “
Numerical modeling of the geodynamo: Mechanisms of field generation and equilibration
,” J. Geophys. Res.
104
(B5
), 10383
–10404
, https://doi.org/10.1029/1999JB900013 (1999
).54.
Olson
,
P. L.
,
Coe
,
R. S.
,
Driscoll
,
P. E.
,
Glatzmaier
,
G. A.
, and
Roberts
,
P. H.
, “
Geodynamo reversal frequency and heterogeneous core–mantle boundary heat flow
,” Phys. Earth Planet. Inter.
180
(1–2
), 66
–79
(2010
).55.
Pan
,
X.
and
Choi
,
J.-I.
, “
Non-Oberbeck–Boussinesq effects in two-dimensional Rayleigh–Bénard convection of different fluids
,” Phys. Fluids
35
(9
), 095108
(2023
).56.
Rajaei
,
H.
,
Kunnen
,
R. P.
, and
Clercx
,
H. J.
, “
Exploring the geostrophic regime of rapidly rotating convection with experiments
,” Phys. Fluids
29
(4
), 045105
(2017
).57.
Ranjan
,
A.
, “
Segregation of helicity in inertial wave packets
,” Phys. Rev. Fluids
2
(3
), 033801
(2017
).58.
Ranjan
,
A.
and
Davidson
,
P.
, “
The spatial segregation of kinetic helicity in geodynamo simulations
,” in Helicities in Geophysics, Astrophysics and Beyond
, Geophysical Monograph Series (
John Wiley and Sons
, 2024
), p. 241
.59.
Ranjan
,
A.
,
Davidson
,
P.
,
Christensen
,
U. R.
, and
Wicht
,
J.
, “
On the generation and segregation of helicity in geodynamo simulations
,” Geophys. J. Int.
221
(2
), 741
–757
(2020
).60.
Reshetnyak
,
M. Y.
, “
Evolution of helicities in dynamo problems
,” in Doklady Physics
(
Springer
, 2015
), Vol.
60
, pp. 283
–287
.61.
Roberts
,
P. H.
, “
Dynamics of the core, geodynamo
,” Rev. Geophys.
33
(S1
), 443
–450
, https://doi.org/10.1029/95RG00735 (1995
).62.
Sahoo
,
S.
and
Sethulakshmy
,
E. S.
, “
Onset of oscillatory magnetoconvection under rapid rotation and spatially varying magnetic field
,” Phys. Fluids
35
(2
), 024113
(2023
).63.
Sahoo
,
S.
and
Sreenivasan
,
B.
, “
On the effect of laterally varying boundary heat flux on rapidly rotating spherical shell convection
,” Phys. Fluids
29
(8
), 086602
(2017
).64.
Saunders
,
P. M.
, “
Penetrative convection in stably stratified fluids 1, 2
,” Tellus A
14
(2
), 177
–194
(1962
).65.
Schaeffer
,
N.
,
Jault
,
D.
,
Nataf
,
H.-C.
, and
Fournier
,
A.
, “
Turbulent geodynamo simulations: A leap towards earth's core
,” Geophys. J. Int.
211
(1
), 1
–29
(2017
).66.
Schmid
,
P. J.
, “
Dynamic mode decomposition of numerical and experimental data
,” J. Fluid Mech.
656
, 5
–28
(2010
).67.
Sreenivasan
,
B.
and
Gopinath
,
V.
, “
Confinement of rotating convection by a laterally varying magnetic field
,” J. Fluid Mech.
822
, 590
–616
(2017
).68.
Sreenivasan
,
B.
and
Gubbins
,
D.
, “
Dynamos with weakly convecting outer layers: Implications for core-mantle boundary interaction
,” Geophys. Astrophys. Fluid Dyn.
102
(4
), 395
–407
(2008
).69.
Sreenivasan
,
B.
and
Jones
,
C. A.
, “
Structure and dynamics of the polar vortex in the earth's core
,” Geophys. Res. Lett.
32
(20
), L20301
, https://doi.org/10.1029/2005GL023841 (2005
).70.
Sreenivasan
,
B.
and
Jones
,
C. A.
, “
Helicity generation and subcritical behaviour in rapidly rotating dynamos
,” J. Fluid Mech.
688
, 5
(2011
).71.
Stellmach
,
S.
,
Lischper
,
M.
,
Julien
,
K.
,
Vasil
,
G.
,
Cheng
,
J. S.
,
Ribeiro
,
A.
,
King
,
E. M.
, and
Aurnou
,
J. M.
, “
Approaching the asymptotic regime of rapidly rotating convection: Boundary layers versus interior dynamics
,” Phys. Rev. Lett.
113
(25
), 254501
(2014
).72.
Stevenson
,
D.
, “
Planetary magnetic fields
,” Rep. Prog. Phys.
46
(5
), 555
(1983
).73.
Takehiro
,
S.-i.
and
Lister
,
J. R.
, “
Penetration of columnar convection into an outer stably stratified layer in rapidly rotating spherical fluid shells
,” Earth Planet. Sci. Lett.
187
(3–4
), 357
–366
(2001
).74.
Toppaladoddi
,
S.
and
Wettlaufer
,
J. S.
, “
Penetrative convection at high Rayleigh numbers
,” Phys. Rev. Fluids
3
(4
), 043501
(2018
).75.
Tu
,
J. H.
, “
Dynamic mode decomposition: Theory and applications
,” Ph.D. thesis (
Princeton University
, 2013
).76.
Veronis
,
G.
, “
Penetrative convection
,” Astrophys. J.
137
, 641
(1963
).77.
Wang
,
Q.
,
Reiter
,
P.
,
Lohse
,
D.
, and
Shishkina
,
O.
, “
Universal properties of penetrative turbulent Rayleigh–Bénard convection
,” Phys. Rev. Fluids
6
(6
), 063502
(2021
).78.
Wang
,
Q.
,
Zhou
,
Q.
,
Wan
,
Z.-H.
, and
Sun
,
D.-J.
, “
Penetrative turbulent Rayleigh–Bénard convection in two and three dimensions
,” J. Fluid Mech.
870
, 718
–734
(2019
).79.
Willis
,
A. P.
,
Sreenivasan
,
B.
, and
Gubbins
,
D.
, “
Thermal core–mantle interaction: Exploring regimes for ‘locked’ dynamo action
,” Phys. Earth Planet. Inter.
165
(1–2
), 83
–92
(2007
).80.
Xu
,
J.
and
Lin
,
Y.
, “
Dynamic mode decomposition of the geomagnetic field over the last two decades
,” Earth Planet. Phys.
7
(1
), 32
–38
(2023
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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