$$J(\psi,\zeta)$$

Equation 4 · Mathematics

From Origins to Frontier: A History of Mathematics, Proof, and Scientific Computation

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

where $\psi$ is the stream function describing the horizontal flow, $\zeta$ is the relative vorticity, and J($\psi$,$\zeta$) 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, high-volume calculation electronic computation was built for and hand computation was not.

Meanings in this article

• $J$: the Jacobian term expressing advection of vorticity by the flow itself.
• $\psi$: the stream function describing the horizontal flow.
• $\zeta$: the relative vorticity.

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