Extreme vorticity growth in Navier-Stokes turbulence

TL;DR

This paper investigates extreme vorticity growth in Navier-Stokes turbulence, combining theoretical bounds, variational solutions, and high-resolution simulations to understand localized vorticity amplification and its statistical properties.

Contribution

It provides a detailed analysis of the maximum vorticity growth rates, combining theoretical bounds with numerical simulations to explore localized extreme events in turbulence.

Findings

Local growth rates can reach the theoretical maximum of dE/dt ~ E^3.

The ensemble-averaged growth bound is maintained with high accuracy in simulations.

Extreme vorticity growth events are identified but are statistically suppressed at high intensities.

Abstract

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.