Concept

Numerical error — where it appears

The difference between what a scheme computes and what the equations it approximates would give. It has an order in the step size, so halving the step says which part of a discrepancy is the method and which part is the model.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

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

There and back again. A blob of a hundred and twenty tracer particles at the start, after four time units of stirring, and after the same four run backwards. The third set is drawn over the first and the worst particle is 1.4·10⁻⁹ from where it began.

Reversible, and unusable

Ideal flow has no arrow of time in it. Run a stirring backwards and the dye comes back — here to 1.4 parts in a thousand million. Nudge the state by a hundred-millionth first and the same reversal returns a blob almost five hundred times further from home than the nudge was large.

inviscid · Vortex dynamics

Each collapsed form of the plate's heat transfer reaches its limit decades away from air. The exact local Nusselt number of a vertical isothermal plate in its two collapsed forms against the Prandtl number: over (Gr·Pr²)^¼, which tends to Le Fevre's 0.600 as Pr → 0, and over (Gr·Pr)^¼, which tends to 0.503 as Pr → ∞. At Pr = 10⁻⁵ the first reads 0.5994; at 10⁵ the second reads 0.5023. The two limit laws cross at Pr = 0.494, where the exact value is 0.736 of either; air, at 0.72, reads 0.421 and 0.387.

Over a plate in mercury the warm layer flows as if inviscid

The exact solution for a warm vertical plate has been tabulated since 1953 and is usually shot from the wall, which fails in a liquid metal unless the shot starts within a thousandth of the answer. Posed instead as one algebraic system, it solves from a Prandtl number of a hundred-thousandth to a hundred thousand — and shows that in mercury the layer's speed is set without viscosity, that the integral method runs low there rather than high, and that air sits where neither limiting law is within a fifth.

regimes · Grashof

Named alongside it

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

Conserved quantity Measurement Memory kernel Model validity Asymptotics Boundary layer Buoyancy Circulation Convergence Entrainment Flow map Heat transfer

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