Dynamics and decay of a spherical region of turbulence in free space

TL;DR

This paper uses advanced numerical simulations to study how a spherical region of turbulence evolves and decays in free space, revealing insights into turbulence spectrum, decay rates, and vortex ring ejections.

Contribution

It introduces a novel simulation approach for turbulence in free space and compares decay behaviors for different initial spectral conditions.

Findings

Decay rates follow Saffman predictions for up to 400 eddy turnover times.

The turbulent sphere expands with similar growth exponents for radius and integral scale.

Vortex ring ejections occur at the initial turbulence scale, linked to local impulse imbalances.

Abstract

We perform direct numerical simulation (DNS) and large eddy simulation (LES) of an initially spherical region of turbulence evolving in free space. The computations are performed with a lattice Green's function method, which allows the exact free-space boundary conditions to be imposed on a compact vortical region. LES simulations are conducted with the stretched vortex sub-grid stress model. The initial condition is spherically windowed, isotropic homogeneous incompressible turbulence. We study the spectrum and statistics of the decaying turbulence and compare the results with decaying isotropic turbulence, including cases representing different low wavenumber behavior of the energy spectrum (i.e. k^2 versus k^4). At late times the turbulent sphere expands with both mean radius and integral scale showing similar time-wise growth exponents. The low wavenumber behavior has little effect on the inertial scales, and we find that decay rates follow Saffman (1967) predictions in both cases, at least until about 400 initial eddy turnover times. The boundary of the spherical region develops intermittency and features ejections of vortex rings. These are shown to occur at the integral scale of the initial turbulence field and are hypothesized to occur due to a local imbalance of impulse on this scale.