Onset criteria for freely decaying isotropic turbulence

TL;DR

This paper investigates the criteria for onset of freely decaying isotropic turbulence using DNS, revealing how measurement choices affect observed dissipation-Reynolds relationships and analyzing decay exponents across different Reynolds numbers.

Contribution

It introduces a new onset criterion based on peak values in dissipation and inertial transfer, linking decay behavior to initial conditions and measurement timing.

Findings

The dissipation-Reynolds curve shape depends on measurement time.

Decay exponent varies between 1.35 and 2.60 with Reynolds number.

Energy cascade time is approximately half an initial eddy turnover time.

Abstract

From DNS of turbulence decaying from specified initial conditions for the range of initial Taylor-Reynolds numbers 2.58 < R{\lambda}(0) < 358.6, it was found that the shape of the iconic curve of dimensionless dissipation versus Reynolds number depended strongly on the choice of measurement time. For our preferred time, a composite based on peak values in the dissipation and inertial transfer curves, the result was virtually identical to the forced, stationary case. In the course of studying onset criteria, we found that the exponent for the power-law decay of the energy decreased with increasing Reynolds number and lay in the range 1.35 < n < 2.60. An additional run was performed, using the data from a stationary, forced simulation with R{\lambda} = 335 for the initial condition. The results of this suggested that the time taken for energy to pass through the cascade was about one half of an initial eddy turnover time.