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Magnetic Reynolds number

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In magnetohydrodynamics, the magnetic Reynolds number (Rm) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion.

MagnetohydrodynamicsMagnetohydrodynamicsModel of electrically conducting fluids The plasma making up the Sun can be modeled as an MHD system Simulation of the Orszag–Tang MHD vortex problem, a well-known model problem for testing the transition to supersonic 2D MHD turbulence Magnetohydrodynamics (MHD; also called magnetofluid dynamics or hydro­magnetics) is a model of electrically conducting fluids that treats all types of charged particles together as a single continuous fluid.Reynolds numberReynolds numberIn fluid dynamics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent.Dynamo theoryDynamo theoryIn physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales. A dynamo is thought to be the source of the Earth's magnetic field and the magnetic fields of Mercury and the Jovian planets.Magnetic diffusionMagnetic diffusion refers to the motion of magnetic fields, typically in the presence of a conducting solid or fluid such as a plasma. The motion of magnetic fields is described by the magnetic diffusion equation and is due primarily to induction and diffusion of magnetic fields through the material. The magnetic diffusion equation is a partial differential equation commonly used in physics.Electromagnetic inductionElectromagnetic inductionElectromagnetic induction or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction of the induced field.Magnetic diffusivityMagnetic diffusivityThe magnetic diffusivity controls the rate of magnetic field diffusion. Since its role in the evolution equation for the magnetic field is analogous to that of the viscosity for the velocity field, some authors refer to it as the 'magnetic viscosity'. The magnetic diffusivity appears in the definition of the magnetic Reynolds number. A finite value of the magnetic Reynolds number (i.e. a nonzero magnetic diffusivity) is associated with violation of Alfvén's theorem.Magnetic fieldMagnetic fieldProperty of space that quantifies the magnetic influence at a given locationIn magnetism and electromagnetism, magnetic field is a physical property of space that quantifies the magnetic influence at a given location.Induction equationIn magnetohydrodynamics, the induction equation is a partial differential equation that relates the magnetic field and velocity of an electrically conductive fluid such as a plasma. It can be derived from Maxwell's equations and Ohm's law, and plays a major role in plasma physics and astrophysics, especially in dynamo theory.AdvectionIn the fields of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is also a fluid. The properties that are carried with the advected substance are conserved properties such as energy. An example of advection is the transport of pollutants or silt in a river by bulk water flow downstream.Fluid mechanicsFluid mechanicsBranch of physics Part of a series onContinuum mechanics J = − D d φ d x {\displaystyle J=-D{\frac {d\varphi }{dx}}} Fick's laws of diffusion Laws Conservations Mass Momentum Energy Inequalities Clausius–Duhem (entropy) Solid mechanics Deformation Elasticity linear Plasticity Hooke's law Stress Strain Finite strain Infinitesimal strain Compatibility Bending Contact mechanics frictional Material failure theory Fracture mechanics Fluid mechanics Fluids Statics · Dynamics Archimedes' principle · Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids Adhesion Capillary action Chromatography Cohesion (chemistry) Surface tension Gases Atmosphere Boyle's law Charles's law Combined gas law Fick's law Gay-Lussac's law Graham's law Plasma Magnetohydrodynamics Rheology Viscoelasticity Rheometry Rheometer Smart fluids Electrorheological Magnetorheological Ferrofluids Scientists Bernoulli Boyle Cauchy Charles Euler Fick Gay-Lussac Graham Hooke Newton Navier Noll Pascal Stokes Truesdell vte Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.Solar SystemSolar SystemThe Solar System is the gravitationally bound system of the Sun and the masses that orbit it, most prominently its eight planets, of which Earth is one. The Solar System is an isolated single-star planetary system (not part of a larger star system) within the Milky Way Galaxy. The system formed about 4.6 billion years ago when a dense region of a molecular cloud collapsed, creating the Sun and a protoplanetary disc from which the orbiting bodies assembled.Dimensionless quantityDimensionless quantityDimensionless quantities, or quantities of dimension one, are quantities with no associated units of measurement. These may be ratios of quantities with the same physical units or ratios of dimensionally equal products with identical units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific units of volume used, such as in milliliters per milliliter (mL/mL).

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