Extreme vorticity growth in Navier-Stokes turbulence

Details Extreme vorticity growth in Navier-Stokes turbulence Extreme vorticity growth in Navier-Stokes turbulence

2009-11-27

arxiv.org/abs/0911.5215v1

Phys. Lett. A, 374 (2010) 861

Physics

Fluid Dynamics

12 pages, 5 Postscript figures, accepted for publication in Physics Letters A

Scientific paper

10.1016/j.physleta.2009.11.078

According to statistical turbulence theory, the ensemble averaged squared vorticity rho_E is expected to grow not faster than drho_E/dt ~ rho_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 dE/dt ~ 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 dE/dt ~ 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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