magnetohydrodynamics

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Earth is not the only planet in our solar system with auroras. As the solar wind–a stream of rarefied plasma from our sun–blows through the solar system, it interacts with the magnetic fields of other planets as well as our own. Saturn’s magnetic field second only to Jupiter’s in strength. This strong magnetosphere deflects many of the solar wind’s energetic particles, but, as on Earth, some of the particles get drawn in along Saturn’s magnetic field lines. These lines converge at the poles, where the high-energy particles interact with the gases in the upper reaches of Saturn’s atmosphere. As a result, Saturn, like Earth, has impressive and colorful light displays around its poles. (Image credit: ESA/Hubble, M. Kornmesser & L. Calçada, source video; via spaceplasma)

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Solar magnetohydrodynamics

The sun is a magnetohydrodynamics (MHD) system that is not well understood. It is thought that the energy necessary to heat the corona is provided by turbulent motion in the convection zone below the photosphere, and two main mechanisms have been proposed to explain coronal heating:

The first is wave heating, in which sound, gravitational or magnetohydrodynamic waves are produced by turbulence in the convection zone. These waves travel upward and dissipate in the corona, depositing their energy in the ambient gas in the form of heat. The other is magnetic heating, in which magnetic energy is continuously built up by photospheric motion and released through magnetic reconnection in the form of large solar flares and myriad similar but smaller events—nanoflares. Currently, it is unclear whether waves are an efficient heating mechanism.

The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970. He described the class of MHD waves now known as Alfvén waves. Observations show that all waves except Alfvén waves have been found to dissipate or refract before reaching the corona. Current research focus has therefore shifted towards flare heating mechanisms.

The magnetic filament above erupted on April 19, 2010. The black “hair-like object” is a speck of dust on the CCD camera.

Credit: SDO/AIA

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FIGURE 1: A 3D snapshot of the Earth’s magetic field; lines in blue are directed inward and lines in yellow are directed outward

FIGURE 2: 500 years after a field reversal

At the heart of our planet lies a solid iron ball, about as hot as the surface of the sun. Researchers call it “the inner core.” It’s really a world within a world. The inner core is 70% as wide as the moon. It spins at its own rate, as much as 0.2o of longitude per year faster than the Earth above it, and it has its own ocean: a very deep layer of liquid iron known as “the outer core.”

Earth’s magnetic field comes from this ocean of iron, which is an electrically conducting fluid in constant motion. Sitting atop the hot inner core, the liquid outer core seethes and roils like water in a pan on a hot stove. The outer core also has “hurricanes”–whirlpools powered by the Coriolis forces of Earth’s rotation. These complex motions generate our planet’s magnetism through a process called the dynamo effect.

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Sometimes fluids are slow-moving enough that it takes timelapse techniques to reveal the flow. Fog is one example, and, as seen above, magnetic silly putty is another. The putty is an unusual fluid in a couple of ways. First, having been impregnated with ferromagnetic nanoparticles, it is sensitive to magnetic fields, making it a sort of ferrofluid. And secondly, being silly putty, it’s a non-Newtonian fluid, meaning that it has a nonlinear response to deformation - a fact that will be familiar to anyone who has tried to knead putty versus striking it. With a strong enough magnet, the putty makes for an impressively tenacious creeping flow. (Video credit: I. Parks; via io9; submitted by Chad W.)

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Accretion Disks

Accretion flows are ubiquitous in astrophysics: they occur around protostars, accreting compact objects in binary systems, and supermassive black holes at the cores of galaxies. Much of professor James M. Stone’s work has concerned studies of the local hydrodynamic and magnetohydrodynamics (MHD) processes that can lead to outward angular momentum transport in accretion disks. As computers become more powerful, previous studies of local patches of an accretion flow are being expanded into global studies that encompass the entire disk.

Accretion flows that cannot cool via emission of radiation become vertically thick and nearly spherical. Thus, they are intrinsically multidimensional. To study the structure and evolution of non-radiative accretion flows, 2D (axisymmetric) hydrodynamical simulations were performed using a non-uniform grid that spanned more than two decades in radius.

The most striking property of the flow is the large fluctuations produced by strong convection. Convective eddies transport a lot of mass both inwards and outwards, but the net mass accretion rate is very small and set by the properties of the flow near the inner boundary. A vanishingly small accretion rate may help to explain the deficit of high energy emission observed from accreting compact sources.

While understanding the properties of hydrodynamical accretion flows is important, it is generally agreed that angular momentum transport is in fact mediated by magnetic stresses. Thus, repeating the global simulations of non-radiative accretion flows with MHD calculations is vital.

Credit: James M. Stone

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For those of us who are Earthbound, it’s easy to think of liquids and gases as being the most common fluids. But plasma–the fourth state of matter–is a fluid as well. Plasmas are essentially ionized gases, which, thanks to their freely flowing electrons, are electrically conductive and sensitive to magnetic fields. Their motions are described by a combination of the Navier-Stokes equations–the usual equations of motion for a fluid–and Maxwell’s equations–the equations governing electricity and magnetism. Studies of plasma motion often fall under the subject of magnetohydrodynamics and can include topics like planetary auroras, sunspots, and solar flares. (Video credit: SciShow)

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Solar ‘Tadpoles’ a.k.a. Supra-Arcade Downflows

These dark, elongated plasma structures, known as supra-arcade downflows (SADs) – also called “tadpoles”(because of their sinuous shape), are sunward/downward-moving features observed in low-density region above post-eruption flare arcades. They were originally thought of as flux tubes contracting under tension after reconnection, but later it was argued that SADs are not flux tubes, rather wakes behind shrinking loops or jet-flows caused by the Rayleigh-Taylor instability. The exact mechanism of the formation of SADs is still not fully understood, despite various MHD models and observational studies.

Further Reading:

Credit & source: NASA/GSFC

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NASA’s Solar Dynamics Observatory (SDO) is our premiere source for data on the sun. In honor of its five-year anniversary, NASA released this beautiful video compiling some of the highlights among the 2600 terabytes of data the spacecraft has recorded. SDO has captured some truly stunning footage over the years of sunspots, prominences, and eruptions. The latter two are examples of plasma flows and visible magnetohydrodynamics. SDO’s observations are also helping researchers determine what goes on just beneath the sun’s surface, where convection and buoyancy are major forces in the transport of heat generated from fusion in the star’s core. Incidentally, SDO’s launch featured some uncommonly stunning fluid dynamics as well. (Video credit: NASA Goddard)

A droplet of glycerol coalescing in silicone oil while subjected to strong electric fields exhibits a whip-like instability reminiscent of fireworks. Check out videos of the phenomenon or see the paper for more information. Happy Independence Day to our American readers!

For more fun, holiday-themed high-speed video, check out PopSci’s fireworks videos.

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The auroras at Earth’s poles are much more than pretty lights. This video explains their formation; fluid mechanics (specifically magnetohydrodynamics) play a major role in the convective transport of heat inside the sun as well as the movement of the plasma that makes up a solar storm that interacts with Earth’s magnetic field and produces the auroras.

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In early June, NASA’s Solar Dynamics Observatory recorded a stunning coronal mass ejection, in which larger than usual quantities of cool (relatively speaking) plasma erupted from the surface of the sun and rained back down along magnetic field lines. Plasma is an ionized gas-like state of matter subject to the same laws that govern more familiar fluids like water or air, with the additional caveat that, being electrically conductive, plasmas also obey Maxwell’s equations. #

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NASA’s Solar Dynamics Observatory has found evidence of Kelvin-Helmholtz waves in the sun’s corona. These waves, which occur between two fluids of different densities or moving at different speeds, are similar to the iconic waves surfers ride. Researchers suspect that this turbulent motion may help explain why the corona is 1,000 times hotter than the surface of the sun. #