Two-dimensional and quasi-two-dimensional turbulence

5 problems

• Are inverse-cascade vorticity isolines exactly conformally invariant?

  Open

  In flat turbulence, the curves where the local spin of the fluid changes sign look statistically identical to the boundaries of random clusters in a classic model of percolation, a symmetry known from equilibrium critical points. Why a driven, dissipative flow should have this symmetry is unexplained.

• Logarithmic correction in the two-dimensional direct enstrophy cascade

  Open

  Flat turbulence also sends enstrophy (the mean squared spin of the fluid) to small scales, and theory predicts the energy spectrum there with a small logarithmic correction. That correction has not been confirmed.

• Why is the two-dimensional inverse energy cascade non-intermittent?

  Open

  In three-dimensional turbulence rare violent events dominate high-order statistics, but the energy flow to large scales in flat turbulence shows no growth of such events with decreasing scale. The reason for this difference is not known.

• When does decaying 2D turbulence reach its statistical-mechanics equilibrium?

  Open

  Freely decaying flat turbulence organizes itself into a few large vortices or jets, and a theory from statistical mechanics predicts the final pattern by maximizing a mixing entropy. The prediction works in some cases and fails in others, and no rule says when.

• Decay exponent of vortex number in freely decaying 2D turbulence

  Contested

  In freely decaying flat turbulence, small vortices merge into fewer, larger ones. The rate at which the number of vortices falls with time has been measured, and a scaling theory exists, but whether the exponent is universal is not settled.