Equation 4 · Part 1 · From Origins to Frontier: A History of Mathematics, Proof, and Scientific Computation
Symbol J
What this part means
the Jacobian term expressing advection of vorticity by the flow itself.
Its job in the formula
J is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol J→Article meaning
Where the article explains it
where is the stream function describing the horizontal flow, is the relative vorticity, and J(,) is the Jacobian term expressing advection of vorticity by the flow itself.
The passage around this formula
where is the stream function describing the horizontal flow, is the relative vorticity, and J(,) 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.
Learn the underlying idea
A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.
Open the illustrated functions: inputs become outputs guide →
See this notation across published equations →
Sources cited in the article section
- [3] Penn's ENIAC, the world's first electronic computer, turns 80 ↗
- [2] Numerical Integration of the Barotropic Vorticity Equation ↗
These citations provide research context; check each source for the exact claim it supports.