Concept

Condensate — where it appears

The accumulation of energy at the largest scale a two-dimensional flow allows, once an inverse cascade has carried it there and nothing removes it. It appears as a pair of counter-rotating vortices filling the domain, and it is an equilibrium rather than a remainder.

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

The condensate, and the limit of no friction which does not exist. In a steady state the friction must remove everything the forcing puts in, so the energy is eps/(2 alpha) and the coherent velocity is sqrt(eps/alpha) — exactly a minus one half power, checked to 10⁻¹². As the friction is weakened the condensate grows without bound: the limit alpha to zero is not a flow with a weak condensate, it is a flow with no steady state at all.

Where the inverse cascade stops

Two-dimensional turbulence sends its energy upward in scale, and the upward direction has an end: the box. Without something to remove the energy before it arrives, it accumulates there in a pair of vortices filling the domain, and the limit of no friction has no steady state at all.

turbulence · Two-dimensional

A count of states that has a maximum in it. How many configurations of thirty point vortices have each energy, sampled from the measure their own Hamiltonian defines — which is the area measure, because a vortex's coordinates are its own conjugate pair. The count peaks at an energy of -0.054 and falls away on both sides, which no ordinary system's does. Above the peak, adding energy reduces the number of ways of arranging the fluid.

An equilibrium a three-dimensional flow cannot have

The condensate an inverse cascade ends in is treated as what is left over when the energy has nowhere further to go. It is not a remainder. A two-dimensional fluid's phase space is its own region and therefore has finite volume, so its entropy has a maximum, its temperature changes sign, and the clustered state above that point is an equilibrium.

turbulence · Two-dimensional

Named alongside it

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

Inverse cascade Model limit Two-dimensional turbulence Box scale Conservation Energy flux Enstrophy Entropy Friction Hamiltonian Kraichnan Logarithmic correction

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