Equatorial Magnetohydrodynamic Shallow Water Waves in the Solar Tachocline

Abstract

The influence of a toroidal magnetic field on the dynamics of shallow water waves in the solar tachocline is studied. A sub-adiabatic temperature gradient in the upper overshoot layer of the tachocline causes significant reduction of surface gravity speed, which leads to trapping of the waves near the equator and to an increase of the Rossby wave period up to the timescale of solar cycles. Dispersion relations of all equatorial magnetohydrodynamic (MHD) shallow water waves are obtained in the upper tachocline conditions and solved analytically and numerically. It is found that the toroidal magnetic field splits equatorial Rossby and Rossby-gravity waves into fast and slow modes. For a reasonable value of reduced gravity, global equatorial fast magneto-Rossby waves (with the spatial scale of equatorial extent) have a periodicity of 11 years, matching the timescale of activity cycles. The solutions are confined around the equator between latitudes ±20 0 − 40 0 , coinciding with sunspot activity belts. Equatorial slow magneto-Rossby waves have a periodicity of 90-100 yr, resembling the observed long-term modulation of cycle strength, i.e., the Gleissberg cycle. Equatorial magneto-Kelvin and slow magneto-Rossby-gravity waves have the periodicity of 1-2 years and may correspond to observed annual and quasi-biennial oscillations. Equatorial fast magneto-Rossby-gravity and magnetoinertia-gravity waves have periods of hundreds of days and might be responsible for observed Rieger-type periodicity. Consequently, the equatorial MHD shallow water waves in the upper overshoot tachocline may capture all timescales of observed variations in solar activity, but detailed analytical and numerical studies are necessary to make a firm conclusion toward the connection of the waves to the solar dynamo.

Magneto-Rossby Waves in the Solar Tachocline and the Annual Variations in Solar Activity

“…For m = 1, one may get ∼ 1 yr periodicity for n = 5 or n = 6. If ǫ ≫ 1 then the period of Rossby waves increases up to the length of solar cycle (Zaqarashvili 2018). Consequently, the Rossby wave might give 1 yr periodicity in the lower part of tachocline with ǫ ≪ 1.…”

“…The sub-adiabatic temperature gradient leads to the significant decrease of the effective gravity in the upper part of the tachocline (Gilman 2000;Dikpati & Gilman 2005), which then causes the trapping of shallow water waves around the equator (Zaqarashvili 2018).…”

Shallow-water Magnetohydrodynamics for Westward Hotspots on Hot Jupiters

“…Perturbations to the background state are separated using the plane wave ansatz, {u 1 , h 1 , B 1 } = {û(y),ĥ(y),B(y)}e i(kx−ωt) . The resulting ordinary differential equation, (with terms up to y 2 only 1 ) is then solved using the boundary conditions, |v| → 0 as |y| → ∞, yielding bounded solutions of the form (Zaqarashvili 2018) v n (y) = H n ( √ µy)e −(µ+d)y 2 /2 ,…”

Systematic regularity of solar coronal rotation during the time interval 1939–2019

“…The dashed red lines are the 95% confidence level lines for the statistical significant test. Zaqarashvili et al (2010), McIntosh et al (2015, and Zaqarashvili (2018) concluded that the solar QBO of magnetic activities should be caused by the magnetic Rossby wave instabilities. Therefore, it is an evidence that the rotational behavior of the solar corona shows the similar temporal variation as the lower atmospheric layers, and both of them might be connected with dynamical process at the base of the solar convection zone.…”