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The prediction of a supersonic solar wind was first confirmed by spacecraft near Earth and later by spacecraft at heliocentric distances as small as 62 solar radii . These missions showed that plasma accelerates as it emerges from the corona, aided by unidentified processes that transport energy outwards from the Sun before depositing it in the wind. Alfvénic fluctuations are a promising candidate for such a process because they are seen in the corona and solar wind and contain considerable energy . Magnetic tension forces the corona to co-rotate with the Sun, but any residual rotation far from the Sun reported until now has been much smaller than the amplitude of waves and deflections from interacting wind streams . Here we report observations of solar-wind plasma at heliocentric distances of about 35 solar radii , well within the distance at which stream interactions become important. We find that Alfvén waves organize into structured velocity spikes with duration of up to minutes, which are associated with propagating S-like bends in the magnetic-field lines. We detect an increasing rotational component to the flow velocity of the solar wind around the Sun, peaking at 35 to 50 kilometres per second-considerably above the amplitude of the waves. These flows exceed classical velocity predictions of a few kilometres per second, challenging models of circulation in the corona and calling into question our understanding of how stars lose angular momentum and spin down as they age .

In this review we will focus on a topic of fundamental importance for both astrophysics and plasma physics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Helios inner heliosphere and Ulysses’ high latitude observations, recent multi-spacecrafts measurements in the solar wind (Cluster four satellites) and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD) turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.

We present novel numerical schemes for ideal magnetohydrodynamic (MHD) simulations aimed at enhancing stability against numerical shock instability and improving the accuracy of low-speed flows in multidimensions. Stringent benchmark tests confirm that our scheme is more robust against numerical shock instability and is more accurate for low-speed, nearly incompressible flows than conventional shock-capturing schemes. Our scheme is a promising tool for tackling MHD systems, including both high and low Mach number flows.

The present study is related to the analytical investigation of the magnetohydrodynamic flow of Ag - MgO/ water hybrid nanoliquid with slip conditions via an extending surface. The thermal radiation and Joule heating effects are incorporated within the existing hybrid nanofluid model. The system of higher-order partial differential equations is converted to the nonlinear system of ordinary differential equations by interpreting the similarity transformations. With the implementation of a strong analytical method called HAM, the solution of resulting higher-order ordinary differential equations is obtained. The results of the skin friction coefficient, Nusselt number, velocity profile, and temperature profile of the hybrid nanofluid for varying different flow parameters are attained in the form of graphs and tables. Some important outcomes showed that the Nusselt number and skin friction are increased with the enhancement in Eckert number, stretching parameter, heat generation parameter and radiation parameter for both slip and no-slip conditions. The thermal profile of the hybrid nanofluid is higher for suction effect but lower for Eckert number, stretching parameter, magnetic field, heat generation and radiation parameter. For both slip and no-slip conditions, the hybrid nanofluid velocity shows an upward trend for both the stretching and mixed convection parameters.

In this work, we describe a new flux splitting method for an ideal MHD in the 3D curvilinear coordinate system. The method is designed to create a dissipation term by zero flux term of flux split and create a new central difference scheme for ideal MHD. Numerical tests are performed to demonstrate the accuracy and capability of the new scheme to capture complex waves of ideal MHD.

We have studied the nature of the magnetohydrodynamic (MHD) kink waves in magnetically twisted flux tubes in the presence of plasma flow. To do this, the eigenfunctions of the kink oscillations have been determined using the dispersion relation and the boundary conditions of the tube. Then the components of the magnetic-tension force and the gradient of the pressure force have been obtained to determine the nature of the waves. For the waves with positive azimuthal wavenumber, the magnetic twist and plasma flow have opposite effects on the ratio of restoring forces and the wave has a mixed nature. However, for the waves with negative azimuthal wavenumber the magnetic twist and plasma flow strengthen the effects of each other in increasing the ratio of the magnetic-tension force to the gradient of the pressure force, and they make the nature of the wave more Alfvénic. In the presence of both plasma flow and magnetic twist, in the case of the waves with negative azimuthal wavenumber, for some specific values of the tube parameters, the magnetic-tension force becomes the dominant restoring force both in the radial and azimuthal directions, and the wave can be considered as an Alfvén wave in the internal region of the tube. However, in the case of the waves with positive azimuthal wavenumber, the nature of the wave remains mixed under all circumstances.

We analyse quasi-periodic pulsations (QPP) detected in the microwave and decimetre radio emission of the 5 September 2017 7:04 UT (SOL2017-09-05T07:04) solar flare, using simultaneous observations by the Siberian Radioheliograph 48 (SRH-48, 4 – 8 GHz) and Mingantu Spectral Radioheliograph (MUSER-I, 0.4 – 2 GHz). The microwave emission was broadband with a typical gyrosynchrotron spectrum, while a quasi-periodic enhancement of the decimetric emission appeared in a narrow spectral band (500 – 700 MHz), consistent with the coherent-plasma-emission mechanism. The periodicity that we found in microwaves is about 30 seconds, coming from a compact loop-like source with a typical height of about 31 Mm. The decimetric emission exhibited a periodicity of about 6 seconds. We suggest a qualitative scenario linking the QPPs observed in both incoherent and coherent spectral bands and their generation mechanisms. The properties of the QPPs found in the microwave signal are typical for perturbations of the flare loop by the standing sausage mode of a fast magnetohydrodynamic (MHD) wave. Our analysis indicated that this sausage-oscillating flare loop was the primary source of oscillations in the discussed event. The suggested scenario is that a fundamental sausage harmonic is the dominant cause for the observed QPPs in the microwave emission. The initiation of oscillations in the decimetric emission is caused by the third sausage harmonic via periodic and nonlinear triggering of the acceleration processes in the current sheets, formed at the interface between the sausage-oscillating flare loop and the external coronal loop that extended to higher altitudes. Our results demonstrate the possible role of MHD wave processes in the release and transport of energy during solar flares, linking coherent and incoherent radio emission mechanisms.

The heating of the solar chromosphere and corona to the observed high temperatures, imply the presence of ongoing heating that balances the strong radiative and thermal conduction losses expected in the solar atmosphere. It has been theorized for decades that the required heating mechanisms of the chromospheric and coronal parts of the active regions, quiet-Sun, and coronal holes are associated with the solar magnetic fields. However, the exact physical process that transport and dissipate the magnetic energy which ultimately leads to the solar plasma heating are not yet fully understood. The current understanding of coronal heating relies on two main mechanism: reconnection and MHD waves that may have various degrees of importance in different coronal regions. In this review we focus on recent advances in our understanding of MHD wave heating mechanisms. First, we focus on giving an overview of observational results, where we show that different wave modes have been discovered in the corona in the last decade, many of which are associated with a significant energy flux, either generated in situ or pumped from the lower solar atmosphere. Afterwards, we summarise the recent findings of numerical modelling of waves, motivated by the observational results. Despite the advances, only 3D MHD models with Alfvén wave heating in an unstructured corona can explain the observed coronal temperatures compatible with the quiet Sun, while 3D MHD wave heating models including cross-field density structuring are not yet able to account for the heating of coronal loops in active regions to their observed temperature.

The current article aims to present a numerical analysis of MHD Williamson nanofluid flow maintained to flow through porous medium bounded by a non-linearly stretching flat surface. The second law of thermodynamics was applied to analyze the fluid flow, heat and mass transport as well as the aspects of entropy generation using Buongiorno model. Thermophoresis and Brownian diffusion is considered which appears due to the concentration and random motion of nanoparticles in base fluid, respectively. Uniform magnetic effect is induced but the assumption of tiny magnetic Reynolds number results in zero magnetic induction. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations. The numerical method is used for solving the so-formulated highly nonlinear problem. The graphical presentation of results highlights that the heat flux receives enhancement for augmented Brownian diffusion. The Bejan number is found to be increasing with a larger Weissenberg number. The tabulated results for skin-friction, Nusselt number and Sherwood number are given. A decent agreement is noted in the results when compared with previously published literature on Williamson nanofluids.

Kink oscillations of coronal loops, i.e., standing kink waves, is one of the most studied dynamic phenomena in the solar corona. The oscillations are excited by impulsive energy releases, such as low coronal eruptions. Typical periods of the oscillations are from a few to several minutes, and are found to increase linearly with the increase in the major radius of the oscillating loops. It clearly demonstrates that kink oscillations are natural modes of the loops, and can be described as standing fast magnetoacoustic waves with the wavelength determined by the length of the loop. Kink oscillations are observed in two different regimes. In the rapidly decaying regime, the apparent displacement amplitude reaches several minor radii of the loop. The damping time which is about several oscillation periods decreases with the increase in the oscillation amplitude, suggesting a nonlinear nature of the damping. In the decayless regime, the amplitudes are smaller than a minor radius, and the driver is still debated. The review summarises major findings obtained during the last decade, and covers both observational and theoretical results. Observational results include creation and analysis of comprehensive catalogues of the oscillation events, and detection of kink oscillations with imaging and spectral instruments in the EUV and microwave bands. Theoretical results include various approaches to modelling in terms of the magnetohydrodynamic wave theory. Properties of kink oscillations are found to depend on parameters of the oscillating loop, such as the magnetic twist, stratification, steady flows, temperature variations and so on, which make kink oscillations a natural probe of these parameters by the method of magnetohydrodynamic seismology.