Periodic Reporting for period 4 - D5S (Direct Statistical Simulation of the Sun and Stars)
Reporting period: 2023-04-01 to 2024-09-30
Turbulence in the Sun and Stars:
Astrophysical objects such as planets, stars and galaxies exhibit complicated dynamics that it is not currently possible to simulate even using the most sophisticated methods on
current high performance computers. One such example of this is the eleven year solar activity cycle, wherein the Sun's magnetic activity waxes and wanes over the timescale
of eleven years. It is believed that the magnetic field that is responsible for the solar cycle is generated by a dynamo deep within the Sun and this "ordered activity" is the result of the interactions of
turbulence with magnetic fields. The project addresses the development of theoretical and computational tools for the understanding of this interaction. The development of such tools
will lead to breakthroughs not only in our understanding of the Sun, but also for many other astrophysical problems.
Importance for Society:
In addition to the usual importance of understanding the physical processes that lead to the dynamics of our natural universe, which is clearly key for us as a society, the project has a more
pragmatic role. The solar magnetic field is responsible for many of the solar phenomena that have such an impact on our terrestrial environment. These include solar flare, coronal mass ejections and the solar wind.
It is also responsible for heating the corona to such high temperatures. This "space weather" may have a significant role, it can damage satellites, increase their orbital drags and interfere with power generation.
Hence an understanding of the mechanisms that lead to the field generation is of great importance.
Summary of Global Objectives:
D5S has scientific objectives both to answer critically important science questions and develop radical new techniques for explaining a wide range of astrophysical phenomena.
1. What is the origin of Solar Magnetic Activity?
a. What drives large-scale differential rotation and meridional flows in solar-type stars?
b. What is the role of the tachocline in solar and stellar dynamos?
c. How does the dynamo mechanism change for rapidly rotating stars – what leads to the formation of strong polar spots?
d. How does turbulence interact with large-scale fields at high magnetic Reynolds number?
2. Can the radical new technique DSS be utilised successfully for astrophysical flows?
a. How can DSS be used to calculate the statistics of flows and fields in stellar interiors?
b. Can DSS provide subgrid models for DNS that increase the predictability of these models?
c. Can DSS be brought to the astrophysical community via the open-source framework Dedalus?
Astrophysical objects such as planets, stars and galaxies exhibit complicated dynamics that it is not currently possible to simulate even using the most sophisticated methods on
current high performance computers. One such example of this is the eleven year solar activity cycle, wherein the Sun's magnetic activity waxes and wanes over the timescale
of eleven years. It is believed that the magnetic field that is responsible for the solar cycle is generated by a dynamo deep within the Sun and this "ordered activity" is the result of the interactions of
turbulence with magnetic fields. The project addresses the development of theoretical and computational tools for the understanding of this interaction. The development of such tools
will lead to breakthroughs not only in our understanding of the Sun, but also for many other astrophysical problems.
Importance for Society:
In addition to the usual importance of understanding the physical processes that lead to the dynamics of our natural universe, which is clearly key for us as a society, the project has a more
pragmatic role. The solar magnetic field is responsible for many of the solar phenomena that have such an impact on our terrestrial environment. These include solar flare, coronal mass ejections and the solar wind.
It is also responsible for heating the corona to such high temperatures. This "space weather" may have a significant role, it can damage satellites, increase their orbital drags and interfere with power generation.
Hence an understanding of the mechanisms that lead to the field generation is of great importance.
Summary of Global Objectives:
D5S has scientific objectives both to answer critically important science questions and develop radical new techniques for explaining a wide range of astrophysical phenomena.
1. What is the origin of Solar Magnetic Activity?
a. What drives large-scale differential rotation and meridional flows in solar-type stars?
b. What is the role of the tachocline in solar and stellar dynamos?
c. How does the dynamo mechanism change for rapidly rotating stars – what leads to the formation of strong polar spots?
d. How does turbulence interact with large-scale fields at high magnetic Reynolds number?
2. Can the radical new technique DSS be utilised successfully for astrophysical flows?
a. How can DSS be used to calculate the statistics of flows and fields in stellar interiors?
b. Can DSS provide subgrid models for DNS that increase the predictability of these models?
c. Can DSS be brought to the astrophysical community via the open-source framework Dedalus?
We have made progress on the following:
1) We have been investigating convection in geometries relevant to rapidly rotating planets and stars. My team member Sandeep Kanuganti has managed to formulate the problem in both a three-dimensional annulus and in a geometry relevant to experiments to be performed at UCLA by Professor Jon Aurnou.
2) Together with team members Kuan Li and Girish Nivarti, I have been investigating Direct Statistical Simulation in both ODE and PDE models. Excellent progress has been made leading to many publications and some that are to appear in the next couple of years.
3) We have been developing timestepping methods for slow-fast dynamics relevant to rapidly rotating astrophysical objects. In addition we have been investigating rotating magnetoconvection.
4) Together with team member Pallavi Bhat, I have been investigating the role of magnetic helicity in computational models of dynamo action. This has led to a publication in preparation.
5) Together with team member Curtis Saxton, I have been investigating the effectiveness of the quasilinear and generalised quasilinear approximations for models of convection. This has led to a couple of publications and significant theoretical developments.
6) Together with team member Curtis Saxton, I have been investigating theoretically and mathematically the interactions involved in the generalised quasilinear approximation.
7) Together with team member Curtis Saxton, I have been investigating, the use of logarithmic lattices in problems of astrophysical flows.
8) Together with team member Anna Guseva, we have examined the use of data-driven methods for producing reduced order models of astrophysical flows.
9) Ankan Banerjee, Calum Skene and I have been looking at utilising Fourier Neural Operators (a form of machine learning) to solve the relevant equations for the generation of zonal flows in planets and stars. This promises some significant success.
The project has been extremely successful, leading to (so far) over 30 research papers and development of the field and of numerical techniques that can be utilised by the whole community. Many thanks have been given at international conferences and workshops.
1) We have been investigating convection in geometries relevant to rapidly rotating planets and stars. My team member Sandeep Kanuganti has managed to formulate the problem in both a three-dimensional annulus and in a geometry relevant to experiments to be performed at UCLA by Professor Jon Aurnou.
2) Together with team members Kuan Li and Girish Nivarti, I have been investigating Direct Statistical Simulation in both ODE and PDE models. Excellent progress has been made leading to many publications and some that are to appear in the next couple of years.
3) We have been developing timestepping methods for slow-fast dynamics relevant to rapidly rotating astrophysical objects. In addition we have been investigating rotating magnetoconvection.
4) Together with team member Pallavi Bhat, I have been investigating the role of magnetic helicity in computational models of dynamo action. This has led to a publication in preparation.
5) Together with team member Curtis Saxton, I have been investigating the effectiveness of the quasilinear and generalised quasilinear approximations for models of convection. This has led to a couple of publications and significant theoretical developments.
6) Together with team member Curtis Saxton, I have been investigating theoretically and mathematically the interactions involved in the generalised quasilinear approximation.
7) Together with team member Curtis Saxton, I have been investigating, the use of logarithmic lattices in problems of astrophysical flows.
8) Together with team member Anna Guseva, we have examined the use of data-driven methods for producing reduced order models of astrophysical flows.
9) Ankan Banerjee, Calum Skene and I have been looking at utilising Fourier Neural Operators (a form of machine learning) to solve the relevant equations for the generation of zonal flows in planets and stars. This promises some significant success.
The project has been extremely successful, leading to (so far) over 30 research papers and development of the field and of numerical techniques that can be utilised by the whole community. Many thanks have been given at international conferences and workshops.
The developments described above are significantly beyond the state-of-the-art. They are the beginnings of a framework that is a completely different way of investigating
solar and stellar dynamos.
solar and stellar dynamos.