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Equation 1 · Part 11 · From Origins to Frontier: A History of Mathematics, Proof, and Scientific Computation

Denominator: partial t

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

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

partial t occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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 what made the problem hard to do by hand and tractable by machine: it is a single nonlinear evolution equation, and marching it forward requires repeating the same arithmetic over many small time steps across many grid points — precisely the kind of repetitive, exact,…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.