The optical analogy for vector fields

Journal Article · Sun Sep 01 04:00:00 EDT 1991 · Physics of Fluids B; (United States)

DOI:https://doi.org/10.1063/1.859977· OSTI ID:5310015

Parker, E N ^[1]

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1. University of Chicago, Chicago, IL (USA). Department of Physics University of Chicago, Chicago, IL (USA). Department of Astronomy

This paper develops the {ital optical} {ital analogy} for a general vector field {bold F}({bold r}), noting that the projection {bold F}{sub {ital s}} of {bold F} onto any surface locus {ital S} of {del}{times}{bold F} can be expressed as the gradient of a scalar, {bold F}{sub {ital s}}={minus}{del}{phi}. It follows that the field lines of {bold F}{sub {ital s}} pass across {ital S} as if refracted by an index of refraction {vert bar}{bold F}{sub {ital s}}{vert bar}. A sufficiently localized maximum in {vert bar}{bold F}{sub {ital s}}{vert bar} refracts the field so as to produce a gap in the field pattern in {ital S}, with the field bifurcating and passing around the sides, rather than across, the maximum. Such a disruption of the field pattern produces a discontinuity in {bold F}. The optical analogy allows the examination of certain aspects of a vector field that are not otherwise readily accessible. In particular, in the cases of a stationary Eulerian flow {bold v} of an ideal fluid and a magnetostatic field {bold B}, the vectors {bold v} and {bold B} have surface loci in common with their curls. The intrinsic discontinuities around local maxima in {vert bar}{bold v}{vert bar} and {vert bar}{bold B}{vert bar} take the form of vortex sheets and current sheets, respectively, the former playing a fundamental role in the development of hydrodynamic turbulence and the latter playing a major role in heating the x-ray coronas of stars and galaxies.

• OSTI ID: 5310015
• Journal Information: Physics of Fluids B; (United States), Journal Name: Physics of Fluids B; (United States) Vol. 3:9; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

Related Subjects

640430* -- Fluid Physics-- Magnetohydrodynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
FLUID FLOW
FLUID MECHANICS
FLUIDS
GALAXIES
HYDRODYNAMICS
IDEAL FLOW
INCOMPRESSIBLE FLOW
MAGNETOHYDRODYNAMICS
MECHANICS
STARS
TURBULENCE
VECTOR FIELDS