Data-driven low-dimensional modelling of solar tachocline dynamics

Abstract:

Periodicity in the Sun's magnetic activity does not only occur in its 11-year cycle, it is also present on shorter “space-weather” timescales, where the
intensity of extreme events such as solar flares follows a quasi-periodic pattern [1], with quiet periods and periods of enhanced bursts lasting several
months. Using a shallow-water model for the solar tachocline [2], these quasi-periodic patterns have been explained as arising from oscillatory
interactions between Rossby waves and latitudinal differential rotation [3], termed Tachocline Nonlinear Oscillations (TNOs). As a first step towards a
data-driven prediction of bursty periods in solar dynamics, we use Dynamic Mode Decomposition (DMD) [2] to construct a low-dimensional data-driven
representation of TNO-dynamics based on the data of Ref.[3]. DMD detects spatio-temporal coherence, with each dynamic mode corresponding to a
characteristic frequency of the dynamics, and does not require any knowledge of the governing equations of a given system. As such it is very well suited to
extract periodic patterns from observational, experimental or numerically generated data. Here, we reconstruct the main features of the shallow-water
tachocline dynamics for different values of the rotation rate.

[1] S. W. McIntosh et al., The solar magnetic activity band interaction and instabilities that shape quasi-periodic variability, Nat. Comm. 6, 6491 (2015)
[2] M. Dikpati, Nonlinear evolution of global hydrodynamic shallow-water instability in the solar tachocline, Astrophys. Journal, 745 (128) 1-20 (2012)
[3] M. Dikpati, P. S. Cally, S. W. McIntosh, E. Heifetz, The Origin of the “Seasons” in Space Weather, Sci. Rep. 7, 14750 (2017)
[4] P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech. 656, 5-28 (2010).