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Equation 1 · Part 4 · From Origins to Frontier: A History of Mathematics, Proof, and Scientific Computation

Symbol psi

∂ζ∂t+J(ψ,ζ)=0,ζ=∇2ψ,\frac{\partial \zeta}{\partial t} + J(\psi, \zeta) = 0, \qquad \zeta = \nabla^2 \psi,
ψ\psi

What this part means

the stream function describing the horizontal flow.

Its job in the formula

psi is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Where the article explains it

where ψ\psi is the stream function describing the horizontal flow, ζ\zeta is the relative vorticity, and J(ψ\psi,ζ\zeta) is the Jacobian term expressing advection of vorticity by the flow itself.

The passage around this formula

A model of the barotropic vorticity equation used in that 1950 work can be written, in simplified form, as ∂ζ∂t+J(ψ,ζ)=0,ζ=∇2ψ\frac{\partial \zeta}{\partial t} + J(\psi, \zeta) = 0, \qquad \zeta = \nabla^2 \psi. where ψ\psi is the stream function describing the horizontal flow, ζ\zeta is the relative vorticity, and J(ψ\psi,ζ\zeta) is the Jacobian term expressing advection of vorticity by the flow itself. This is stated here not to reproduce the numerics of the original run but because the equation exposes exactly…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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