Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves

Abstract

We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low-β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, and also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, thenonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, i.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.

Two-fluid Numerical Simulations of the Origin of the Fast Solar Wind

“…The presence of Alfvén waves is essential in the model, as in the nonlinear regime they are capable of driving vertical flow (e.g. Hollweg 1986;Murawski 1992;Shestov et al 2017).…”

“…Along this line of investigation, Yang et al (2016) found that Alfvén waves are able to form fast plasma outflows. See also Ofman et al (1995) and Shestov et al (2017) for a similar analysis. However, Alfvén waves are difficult for detection, particularly when high-frequency waves are concerned (Srivastava et al 2017); in an inhomogeneous and structured medium, these waves can experience reflection, mode coupling, phase-mixing and resonant absorption (Ofman et al 1995;Nakariakov et al 1997;Zaqarashvili & Roberts 2006;Goossens et al 2012).…”

Large-scale magnetic fields and anomalies of chemical composition of stellar coronae

“…The mechanism suggested by L15 was never applied to estimate the FIP bias for the Sun as a star. Also, the linear estimations of the ponderomotive force profiles given by Laming (2015) can be inconsistent as we have to take into account the nonlinear effects (see, Shestov et al, 2017). Laming (2004) and Wood et al (2012) argued that the inverse FIP bias on M-dwarfs can be related with strong reflections of alfvenic waves from the upper boundary of the transition region.…”

Could Switchbacks Originate in the Lower Solar Atmosphere? I. Formation Mechanisms of Switchbacks

“…4, we can notice that initially the driven torsional waves are weakly nonlinear, but subsequent wavefronts are strongly affected by nonlinear wave steepening (see, e.g. Verwichte et al 1999;Shestov et al 2017). This leads to strong bends in the magnetic field, which can be identified as switchbacks.…”