Charney equation

E542052

The Charney equation is a fundamental quasi-geostrophic equation in atmospheric dynamics that describes large-scale Rossby waves and mid-latitude weather patterns on a rotating planet.

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Charney equation canonical 1

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Predicate Object
instanceOf equation in atmospheric dynamics
partial differential equation
quasi-geostrophic equation
appliesTo Earth atmosphere NERFINISHED
rotating planets
assumes Boussinesq or shallow-atmosphere approximation
hydrostatic atmosphere
small Froude number
small Rossby number
basedOn geostrophic balance
hydrostatic balance
quasi-geostrophic approximation
canBe linearized for small-amplitude Rossby waves
captures dispersion of large-scale atmospheric waves
westward phase propagation of Rossby waves
describes large-scale Rossby waves
mid-latitude weather patterns
domain synoptic and planetary scales
expressedIn isobaric coordinates
pressure coordinates
field atmospheric science
geophysical fluid dynamics
meteorology
formulatedFor mid-latitude beta-plane
governs evolution of quasi-geostrophic potential vorticity
historicalContext developed in mid-20th century
includesTerm beta effect
planetary vorticity gradient
relative vorticity
influenced development of modern numerical weather prediction
mathematicalForm nonlinear partial differential equation
namedAfter Jule Gregory Charney NERFINISHED
neglects ageostrophic inertia-gravity waves
friction at leading order
relatedTo Rossby wave dispersion relation NERFINISHED
barotropic vorticity equation
beta-plane approximation
quasi-geostrophic potential vorticity equation
requires background zonal flow specification
usedFor analysis of large-scale atmospheric waves
simplified numerical weather prediction models
theoretical study of baroclinic instability
usedIn idealized climate and circulation models
large-scale atmospheric dynamics
synoptic-scale meteorology
theory of Rossby waves

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Jule Gregory Charney knownFor Charney equation