Concept

Time reversal — where it appears

Running a motion backwards from a stated moment. An inviscid flow's equations allow it exactly, so a reversed solution is also a solution; viscosity does not allow it. Whether a reversal can be carried out in practice is a separate question, set by how fast small errors grow.

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

The second law is the only thing that forbids the other half of this curve. Entropy change across a normal shock, against the Mach number in front of it. The solid branch is the compression shock that exists. The dashed branch below Mach one is the expansion shock, and it satisfies mass, momentum and energy exactly — the residuals are zero to machine precision. It is refused by the second law alone, the one statement in the problem that no conservation residual can show.

The only law that forbids it

The jump conditions permit a discontinuity in either direction. An expansion shock conserves mass, momentum and energy exactly — the residuals are zero to machine precision — and it does not exist. Nothing that can be drawn rules it out.

compressible · Shock

Each side squared falls in a straight line, so the meeting is at a stated time and not at infinity. The squares of the triangle's three sides against time, from sides 1, 0.748 and 1.2. All three are straight and reach zero together at t = 7.719. A shape nearer equilateral takes longer; the equilateral triangle itself only turns.

Three vortices can meet at a point in a finite time, and one per cent stops them

Two vortices can only circle or travel. Three can do something the equations of an ideal fluid look as if they forbid: choose strengths of 1, 1 and −1/2, set them on a triangle the invariants allow, and all three reach one point together at a stated moment, after turning about each other infinitely many times along paths of finite length. The energy allows it because a scale change costs nothing at exactly these strengths. Change the third strength by one part in a hundred and the same triangle stops at a third of its size and comes back out.

inviscid · Vortex dynamics

Named alongside it

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

Conservation Discontinuity Entropy Hamiltonian Irreversibility Model limit Point vortex Rankine–Hugoniot conditions The second law of thermodynamics Shock wave Singularity Total pressure

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