Abstract
According to statistical turbulence theory, the ensemble averaged squared vorticity ρ E is expected to grow not faster than d ρ E / d t ∼ ρ E 3 / 2 . Solving a variational problem for maximal bulk enstrophy ( E) growth, velocity fields were found for which the growth rate is as large as d E / d t ∼ E 3 . Using numerical simulations with well resolved small scales and a quasi-Lagrangian advection to track fluid subvolumes with rapidly growing vorticity, we study spatially resolved statistics of vorticity growth. We find that the volume ensemble averaged growth bound is satisfied locally to a remarkable degree of accuracy. Elements with d E / d t ∼ E 3 can also be identified, but their growth tends to be replaced by the ensemble-averaged law when the intensities become too large.
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