We use nearly two decades of helioseismic data obtained from the GONG (2002–2020) and HMI (2010–2020) ring-diagram pipelines to examine the temporal variations of the properties of individual equatorial Rossby modes with azimuthal orders in the range 6 ≤ m ≤ 10. We find that the mode parameters obtained from GONG and HMI are consistent during the data overlapping period of 2010–2020. The power and the frequency of each mode exhibit significant temporal variations over the full observing period. Using the GONG data during solar cycles 23 and 24, we find that the mode power averaged over 6 ≤ m ≤ 10 shows a positive correlation with the sunspot number (0.42), while the averaged frequency shift is anti-correlated (–0.91). The anti-correlation between the average mode power and frequency shift is –0.44.

The grand minimum in the Sun’s activity is a distinctive mode characterized by a magnetic lull that almost completely lacks the emergence of sunspots on the solar surface for an extended duration. The factors driving this transition of an otherwise magnetically active star into a quiescent phase, the processes occurring within the solar interior and across the heliosphere during this period, and the mechanisms leading to the eventual resurgence of surface magnetic activity remain enigmatic. However, there have been sustained efforts in the past few decades to unravel these mysteries by employing a combination of observation, reconstruction and simulation of solar magnetic variability. Here, we summarize recent research on the solar grand minimum and highlight some outstanding challenges – both intellectual and practical – that necessitate further investigations.

We show that on-off intermittency in solar and stellar cycles is a result of amplitude-phase synchronization in multiscale interactions in solar/stellar dynamos or magnetorotational instability which leads to the formation of kinematic and magnetic coherent structures, and the novel techniques of Lagrangian coherent structures can detect transport barriers and vortices such as magnetic flux tubes/ropes in solar and stellar turbulence with high accuracy.

Glaciated alpine landscapes are sensitive to changes in climate. Shifts in temperature and precipitation can cause significant changes to glacier size and terminus position, the production and delivery of organic mass, and in the hydrologic energy related to the transport of water and sediment through proglacial environments. A sediment core representing a 12,900-yr record collected from Swiftcurrent Lake, located on the eastern side of Glacier National Park, Montana, was analyzed to assess variability in Holocene and latest Pleistocene environment. The spectral signature of total organic carbon content (%TOC) since ~ 7.6 ka matches that of solar forcing over 70–500 yr timescales. Periodic inputs of dolomite to the lake reflect an increased footprint of Grinnell Glacier, and occur during periods when sediment sinks are reduced, glacial erosion is increased, and hydrologic energy is increased. Grain size, carbon/nitrogen (C/N) ratios, and %TOC broadly define the termination of the Younger Dryas chronozone at Swiftcurrent Lake, as well as major Holocene climate transitions. Variability in core parameters is linked to other records of temperature and aridity in the northern Rocky Mountains over the late Pleistocene and Holocene.

Assuming that the torsional oscillation is driven by the Lorentz force of the magnetic field associated with the sunspot cycle, we use a flux transport dynamo to model it and explain its initiation at a high latitude before the beginning of the sunspot cycle.