Concept

Quadrature — where it appears

The numerical evaluation of an integral from samples of the integrand. Its error is a property of the scheme and the spacing rather than of the physics, which makes it the first thing to rule out when a computed quantity fails to conserve something.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The excess energy is the energy of the difference, exactly. Add any admissible perturbation to the potential flow and its kinetic energy rises by precisely the energy of the perturbation itself — not approximately, and not to leading order. The measured excess and the perturbation's own energy lie on one another to two parts in 10¹¹ across a sixty-fold range of amplitude.

How much more than the least

Of all the flows that conserve mass and stay inside the walls, the ideal one carries the least energy. That is a theorem, and the useful half of it is the part nobody quotes: it says by exactly how much every other flow misses, and the answer is the square of how wrong it looks.

inviscid · Least energy

One material loop, at five stages of being drawn out. A circle of fluid particles carried by four point vortices, drawn at equal intervals over fourteen time units. Its length grows by a factor of six and its shape becomes unrecognisable; the circulation round it does not move at all.

The drift was the instrument

Kelvin's theorem was checked on this site by carrying a loop and watching its circulation move by eight parts in a hundred thousand. That drift is not the flow forgetting. The exact number is a count of what is inside the loop, it does not move by anything at all, and the drift belongs entirely to the two instruments used to measure it.

inviscid · Kelvin

Named alongside it

The objects these essays reach for when they reach for this one.

Circulation Measurement Boundary condition Conservation Conserved quantity Convergence Irrotational Kelvin's circulation theorem Kinetic energy Laplace's equation Material line Memory kernel

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