Direct Statistical Simulation of the Sun and Stars (D5S)

Grant Agreement ID

786780

The ERC, D5S project addresses a key problem of astrophysics – the origin of magnetic activity in the sun and solar-type stars. This is a problem not only of outstanding theoretical importance but also significant practical impact – solar activity has major terrestrial consequences. An increase in activity can lead to an increase in the number and violence of solar flares and coronal mass ejections, with profound consequences for our terrestrial environment, causing disruption to satellites and power. Predictions of magnetic activity are highly desired by government and industry groups alike. A deep understanding of the mechanisms leading to solar magnetic activity is required. The variable magnetic field is generated by a dynamo in the solar interior. Though this mechanism is known to involve the interaction of magnetohydrodynamic (MHD) turbulence with rotation, no realistic model for dynamo action currently exists. D5S utilises two recent significant breakthroughs to construct new models for magnetic field generation in the sun and other solar-type stars. The first of these involves an entirely new approach termed Direct Statistical Simulation (DSS) (developed by the PI), where the statistics of the astrophysical flows are solved directly (enabling the construction of more realistic models). This approach is coupled to a breakthrough  in our understanding of the physics of MHD turbulence at the extreme parameters relevant to solar interiors. D5S also uses the methodology of DSS to provide statistical subgrid models for Direct Numerical Simulation (DNS). This will increase the utility, fidelity and predictability of such models for solar magnetic activity. Either of these new approaches, taken in isolation, would lead to significant progress in our understanding of magnetic field generation in stars. Taken together, as in this proposal, they will provide a paradigm shift in our theories for solar magnetic activity.

Objective

This proposal (D5S) addresses a key problem of astrophysics – the origin of magnetic activity in the sun and solar-type stars. This is a problem not only of outstanding theoretical importance but also significant practical impact – solar activity has major terrestrial consequences. An increase in activity can lead to an increase in the number and violence of solar flares and coronal mass ejections, with profound consequences for our terrestrial environment, causing disruption to satellites and power. Predictions of magnetic activity are highly desired by government and industry groups alike. A deep understanding of the mechanisms leading to solar magnetic activity is required. The variable magnetic field is generated by a dynamo in the solar interior. Though this mechanism is known to involve the interaction of magnetohydrodynamic (MHD) turbulence with rotation, no realistic model for dynamo action currently exists. D5S utilises two recent significant breakthroughs to construct new models for magnetic field generation in the sun and other solar-type stars. The first of these involves an entirely new approach termed Direct Statistical Simulation (DSS) (developed by the PI), where the statistics of the astrophysical flows are solved directly (enabling the construction of more realistic models). This approach is coupled to a breakthrough in our understanding of the physics of MHD turbulence at the extreme parameters relevant to solar interiors. D5S also uses the methodology of DSS to provide statistical subgrid models for Direct Numerical Simulation (DNS). This will increase the utility, fidelity and predictability of such models for solar magnetic activity. Either of these new approaches, taken in isolation, would lead to significant progress in our understanding of magnetic field generation in stars.
Taken together, as in this proposal, they will provide a paradigm shift in our theories for solar magnetic activity.

 

Impact

The D5S project has had a large number of significant research achievements over the course of the grant.
D5S was proposed with specific scientific objectives - both to answer critically important science questions and develop radical new techniques for explaining a wide range of astrophysical phenomena. The major achievements are listed with reference to those objectives.
1.    What is the origin of Solar Magnetic Activity?
a.    What drives large-scale differential rotation and meridional flows in solar-type stars? 
There has been a number of papers that have increased our understanding of the interaction of turbulent convection and rotation in astrophysical objects [2, 10, 11, 13, 22, 27, 32]. Specifically, we have examined the scalings for heat transport as a function of rotation, how stratification and rotation can combine to yield zonal flows and large-scale vortices and the importance of boundary layers in controlling the transport in convection. Moreover, we have proposed an exciting new theory for the variability of differential rotation in Giant Planets such as Jupiter – the theory for which can be related to that for stars.
b. What is the role of the tachocline in solar and stellar dynamos?
Here we have made significant progress for our understanding of a range of issues. In particular, we have characterised the linear and nonlinear development of the Goldreich-Schubert-Fricke instability [1, 9, 33]. This is important as it is a double diffusive instability that may play a significant role in transport in the solar tachocline. Furthermore, we have elucidated the role of the solar magnetic field in modifying this transport. Once turbulence is driven, its transport propertied depend on the subtle interplay between conservation laws that exist for hydrodynamic turbulence and the magnetic field [16, 31]. This interaction is best studied within the framework of a new set of derived equations that describe tachocline dynamics [26]
The magnetic field can also contribute to driving instabilities in the solar tachocline. Such current-driven instabilities may lead to turbulence and provide one crucial piece of the dynamo loop [5]. 
c.    How does the dynamo mechanism change for rapidly rotating stars – what leads to the formation of strong polar spots?
The generation of magnetic field, and its interaction with convection has been elucidated in four critical papers for the project [3, 14, 15, 19]. These examine scaling laws for dynamos driven by convection and how the presence of field can lead to the formation and detection of waves in rotating stars and planets. Finally a new timestepping scheme has been developed for the solution of the equations of rapidly rotating dynamos – making use of the fast/slow dynamics. This will have significant consequences for our future understanding of this field.
d.    How does turbulence interact with large-scale fields at high magnetic Reynolds number?
Dynamo action at high magnetic Reynolds number is one of the great unsolved problems of astrophysics. This problem was examined and related to Lagrangian chaos in papers [6,7, 23, 30], which also provide a seminal and highly cited  review of the field.
2.    Can the radical new technique DSS be utilised successfully for astrophysical flows?
How can DSS be used to calculate the statistics of flows and fields in stellar interiors?
Direct Statistical Simulation (DSS) has been developed as an alternative paradigm to direct numerical simulation (DNS). We have applied this novel approach to a range of problems at various hierarchy truncations, including the Lorenz systems, dynamo systems, and convection systems [22, 24, 25, 29]. The approach is extremely promising for future astrophysical applications. 
b.    Can DSS provide subgrid models for DNS that increase the predictability of these models? 
Progress has been made in this area in papers [17, 20, 21], which also explore the role of machine learning.
c.    Can DSS be brought to the astrophysical community via the open-source framework Dedalus?

We are continuing to work with the Dedalus developers. Dedalus was used for DSS in paper [22].
In addition, the project has been involved in the career development of the following Postdoctoral Research Associates who have worked as part of the D5S Team: Kuan Li; Girish Nivarti; Curtis Saxton; Calum Skene; Pallavi Bhat; Sandeep Kanuganti; Krasymyr Tretia; Anna Guseva; Chris Wareing; and, Ankan Banerjee
 

Publications and outputs

The project has the produced following publications and outputs:

Generation of shear flows and vortices in rotating anelastic convection 
Author(s): Laura K. Currie, Steven M. Tobias
Published in: Physical Review Fluids, Issue 5/7, 2020, ISSN 2469-990X
Publisher: American Physical Society
DOI: 10.1103/physrevfluids.5.073501

Scaling behaviour of small-scale dynamos driven by Rayleigh–Bénard convection 
Author(s): M. Yan, S.M. Tobias, M.A. Calkins
Published in: Journal of Fluid Mechanics, 2021, ISSN 1469-7645
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2021.61

Thermal boundary layer structure in convection with and without rotation 
Author(s): Robert S. Long, Jon E. Mound, Christopher J. Davies, Steven M. Tobias
Published in: Physical Review Fluids, Issue 5/11, 2020, ISSN 2469-990X
Publisher: American Physical Society
DOI: 10.1103/physrevfluids.5.113502

Floquet stability and Lagrangian statistics of a nonlinear time-dependent ABC dynamo 
Author(s): Calum S. Skene, Steven M. Tobias
Published in: Physical Review Fluids, Issue 8, 2023, ISSN 2469-990X
Publisher: American Physical Society
DOI: 10.1103/physrevfluids.8.083701

The magnetic non-hydrostatic shallow-water model 
Author(s): David G. Dritschel, Steven M. Tobias
Published in: Journal of Fluid Mechanics, Issue 973, 2023, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2023.746

Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence 
Author(s): J.B. Marston, S.M. Tobias
Published in: Annual Review of Fluid Mechanics, Issue 55, 2024, Page(s) 351-375, ISSN 0066-4189
Publisher: Annual Reviews, Inc.
DOI: 10.1146/annurev-fluid-120720-031006

New applications for the Boris Spectral Deferred Correction algorithm for plasma simulations 
Author(s): Kris Smedt, Daniel Ruprecht, Jitse Niesen, Steven Tobias, Joonas Nättilä
Published in: Applied Mathematics and Computation, Issue 442, 2024, Page(s) 127706, ISSN 0096-3003
Publisher: Elsevier BV
DOI: 10.1016/j.amc.2022.127706

Direct statistical simulation of low-order dynamosystems 
Author(s): Kuan Li, J. B. Marston, Steven M. Tobias
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Issue 477/2254, 2021, ISSN 1364-5021
Publisher: Royal Society of London
DOI: 10.1098/rspa.2021.0427

Dimensional reduction of direct statistical simulation 
Author(s): Altan Allawala, S. M. Tobias, J. B. Marston
Published in: Journal of Fluid Mechanics, Issue 898, 2021, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2020.382

Topological Gaseous Plasmon Polariton in Realistic Plasma 
Author(s): Jeffrey B. Parker, J. B. Marston, Steven M. Tobias, Ziyan Zhu
Published in: Physical Review Letters, Issue 124/19, 2020, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.124.195001

Linear and non-linear properties of the Goldreich–Schubert–Fricke instability in stellar interiors with arbitrary local radial and latitudinal differential rotation 
Author(s): R W Dymott, A J Barker, C A Jones, S M Tobias
Published in: Monthly Notices of the Royal Astronomical Society, Issue 524, 2023, Page(s) 2857-2882, ISSN 0035-8711
Publisher: Blackwell Publishing Inc.
DOI: 10.1093/mnras/stad1982

The turbulent dynamo 
Author(s): S.M. Tobias
Published in: Journal of Fluid Mechanics, Issue 912, 2021, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2020.1055

Waves in planetary dynamos 
Author(s): K. Hori, A. Nilsson, S. M. Tobias
Published in: Reviews of Modern Plasma Physics, Issue 7, 2024, ISSN 2367-3192
Publisher: Springer Science
DOI: 10.1007/s41614-022-00104-1

Direct statistical simulation of the Lorenz63 system 
Author(s): Kuan Li, J. B. Marston, Saloni Saxena, Steven M. Tobias
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, Issue 32, 2023, ISSN 1054-1500
Publisher: American Institute of Physics
DOI: 10.1063/5.0075580

Solitary magnetostrophic Rossby waves in spherical shells 
Author(s): K. Hori, S.M. Tobias, C.A. Jones
Published in: Journal of Fluid Mechanics, 2020, ISSN 1469-7645
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2020.743

Nontrivial topology in the continuous spectrum of a magnetized plasma 
Author(s): Jeffrey B. Parker, J. W. Burby, J. B. Marston, Steven M. Tobias
Published in: Physical Review Research, Issue 2/3, 2020, ISSN 2643-1564
Publisher: American Physical Society
DOI: 10.1103/physrevresearch.2.033425

Jupiter’s cloud-level variability triggered by torsional oscillations in the interior 
Author(s): Kumiko Hori, Chris A. Jones, Arrate Antuñano, Leigh N. Fletcher, Steven M. Tobias
Published in: Nature Astronomy, Issue 7, 2023, Page(s) 825-835, ISSN 2397-3366
Publisher: Nature
DOI: 10.1038/s41550-023-01967-1

Direct statistical simulation of the Busse annulus 
Author(s): Jeffrey S. Oishi, Keaton J. Burns, J.B. Marston, Steven M. Tobias
Published in: Journal of Fluid Mechanics, Issue 949, 2022, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2022.798

Angular momentum transport by the GSF instability: non-linear simulations at the equator 
Author(s): A J Barker, C A Jones, S M Tobias
Published in: Monthly Notices of the Royal Astronomical Society, Issue 487/2, 2019, Page(s) 1777-1794, ISSN 0035-8711
Publisher: Blackwell Publishing Inc.
DOI: 10.1093/mnras/stz1386

Scaling behaviour in spherical shell rotating convection with fixed-flux thermal boundary conditions 
Author(s): R. S. Long, J. E. Mound, C. J. Davies, S. M. Tobias
Published in: Journal of Fluid Mechanics, Issue 889, 2020, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2020.67

Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field 
Author(s): Ming Yan, Michael A. Calkins, Stefano Maffei, Keith Julien, Steven M. Tobias, Philippe Marti
Published in: Journal of Fluid Mechanics, Issue 877, 2019, Page(s) 1186-1206, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2019.615

Generalized quasilinear approximation of the interaction of convection and mean flows in a thermal annulus 
Author(s): S. M. Tobias, J. S. Oishi, J. B. Marston
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Issue 474/2219, 2018, Page(s) 20180422, ISSN 1364-5021
Publisher: Royal Society of London
DOI: 10.1098/rspa.2018.0422

Joint instability and abrupt nonlinear transitions in a differentially rotating plasma 
Author(s): A. Plummer, J. B. Marston, S. M. Tobias
Published in: Journal of Plasma Physics, Issue 85/1, 2019, ISSN 0022-3778
Publisher: Cambridge University Press
DOI: 10.1017/s0022377819000060

Parallel-in-time integration of kinematic dynamos 
Author(s): Andrew T. Clarke, Christopher J. Davies, Daniel Ruprecht, Steven M. Tobias
Published in: Journal of Computational Physics: X, Issue 7, 2020, Page(s) 100057, ISSN 2590-0552
Publisher: Elsevier
DOI: 10.1016/j.jcpx.2020.100057

Performance of parallel-in-time integration for Rayleigh Bénard convection 
Author(s): Andrew Clarke, Chris Davies, Daniel Ruprecht, Steven Tobias, Jeffrey S. Oishi
Published in: Computing and Visualization in Science, Issue 23/1-4, 2020, ISSN 1432-9360
Publisher: Springer Verlag
DOI: 10.1007/s00791-020-00332-3

Training a neural network to predict dynamics it has never seen 
Author(s): Anton Pershin; Cédric Beaume; Kuan Li; Steven M. Tobias
Published in: Physical Review E, Issue 5, 2023, ISSN 2470-0045
Publisher: American Physical Society
DOI: 10.1103/physreve.107.014304

Potential vorticity transport in weakly and strongly magnetized plasmas 
Author(s): Chang-Chun Chen, Patrick H. Diamond, Rameswar Singh, Steven M. Tobias
Published in: Physics of Plasmas, Issue 28/4, 2021, Page(s) 042301, ISSN 1070-664X
Publisher: American Institute of Physics
DOI: 10.1063/5.0041072

Optimizing the control of transition to turbulence using a Bayesian method 
Author(s): Anton Pershin; Cédric Beaume; Tom S. Eaves; Steven M. Tobias
Published in: Journal of Fluid Mechanics, Issue 5, 2022, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2022.298

Angular momentum transport, layering, and zonal jet formation by the GSF instability: non-linear simulations at a general latitude 
Author(s): A J Barker, C A Jones, S M Tobias
Published in: Monthly Notices of the Royal Astronomical Society, Issue 495/1, 2020, Page(s) 1468-1490, ISSN 0035-8711
Publisher: Blackwell Publishing Inc.
DOI: 10.1093/mnras/staa1327

Saturation of large-scale dynamo in anisotropically forced turbulence 
Author(s): Pallavi Bhat; Pallavi Bhat
Published in: Monthly Notices of the Royal Astronomical Society, Issue 1, 2022, ISSN 1365-2966
Publisher: Oxford University Press
DOI: 10.1093/mnras/stab3138

Efficiency gains of a multi-scale integration method applied to a scale-separated model for rapidly rotating dynamos 
Author(s): Krasymyr Tretiak; Meredith Plumley; Michael Calkins; Steven Tobias
Published in: Computer Physics Communications, Issue 1, 2021, ISSN 0010-4655
Publisher: Elsevier BV
DOI: 10.1016/j.cpc.2021.108253

Ion heat and parallel momentum transport by stochastic magnetic fields and turbulence 
Author(s): Chang-Chun Chen, P H Diamond, S M Tobias
Published in: Plasma Physics and Controlled Fusion, Issue 64, 2021, Page(s) 015006, ISSN 0741-3335
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6587/ac38b2

Turbulent times for the Sun’s magnetic field 
Author(s): Steven Tobias
Published in: Nature Astronomy, Issue 7, 2023, Page(s) 644-645, ISSN 2397-3366
Publisher: Nature Publishing
DOI: 10.1038/s41550-023-01971-5
 

Project website

https://cordis.europa.eu/programme/id/H2020-EU.1.1.