Magneto-Rossby waves arise due to the inhomogeneity of the Coriolis force depending on latitude on a sphere in rotating astrophysical plasma by analogy with a neutral fluid (Petviashvili & Pokhotelov 1992; Onishchenko et al. 2004; Vallis 2006; Onishchenko, Pokhotelov & Astafieva 2008; Zeitlin 2018). It should be noted that owing to the presence of Lorentz force full vorticity is no longer conserved and in the case of a strong magnetic field magneto-Rossby waves tend to Alfvén wave solutions almost on all wavenumber range (Zaqarashvili et al. 2021). Magneto-Rossby waves are basic mechanism in variability of various objects in plasma astrophysics. Magneto-Rossby waves determine the large-scale dynamics of the Sun and stars (Hughes et al. 2007; Zaqarashvili et al. 2007, 2011; Dikpati et al. 2020; Mandal & Hanasoge 2020; Raphaldini et al. 2020), dynamics of magnetoactive atmospheres of exoplanets captured by tides from the host star (Cho 2008), flows in accretion discs of neutron stars (Inogamov & Sunyaev 2010). Despite the difficulty of observing Rossby waves in astrophysical plasma, they have recently been detected on the Sun (McIntosh et al. 2017; Zaqarashvili & Gurgenashvili 2018; Loeptien et al. 2018; Liang et al. 2019). We also note a number of important studies on the effect of Magneto-Rossby waves on solar seasons (Lou 2000; Dikpati et al. 2017, 2018) and space weather (Dikpati & McIntosh 2020; Dikpati, McIntosh & Wing 2021). In addition, magneto-Rossby waves play a key role in the occurrence of zonal flows in two-dimensional magnetohydrodynamic turbulence (Tobias, Diamond & Hughes 2007; Zinyakov & Petrosyan 2018, 2020). The weakly non-linear theory of magneto-Rossby waves in the quasi-two-dimensional MHD single-layer model has been developed in Klimachkov & Petrosyan (2017a) and in the presence of large-scale compressibility in Klimachkov & Petrosyan (2018). In Fedotova et al. (2020), MHD shallow water approximation has been extended to the case of external vertical magnetic field and stratified flows. Linear and weakly non-linear theory of magneto-Rossby waves in a rotating stratified plasma in the quasi-two-dimensional MHD approximation in two-layer model has been developed. In Klimachkov & Petrosyan (2017a, 2018) and Fedotova et al. (2020), the phase matching conditions have been investigated and non-linear interactions of three magneto-Rossby waves have been found. In Raphaldini & Raupp (2015), Raphaldini et al. (2019, 2020) influence of non-linear dynamics of magneto-Rossby waves on cyclic nature of solar magnetic activity is studied. Non-linear interactions of magneto-Rossby waves are associated with the duration of the solar cycle. In Raphaldini et al. (2020) is shown that irregular transitions in wave amplitudes resemble the observed time series of solar activity. In Klimachkov & Petrosyan (2017a, 2018), Fedotova et al. (2020) magneto-Rossby waves have been investigated in the β-plane approximation for the Coriolis force. The β-plane approximation describes rotating spherical plasma flows in a local Cartesian coordinate system. In this case, the Coriolis parameter changes little with small changes in latitude and expands in a series up to the first order in latitude.
Citation: Dikpati et al. 2020
Citation function: Background