Invariants of free turbulent decay

TL;DR

This paper derives new turbulence decay laws for homogeneous isotropic turbulence based on angular momentum invariance, providing insights into decay behavior and practical modeling strategies for turbulent dissipation.

Contribution

It introduces a novel theoretical approach using angular momentum invariance to predict turbulence decay in various configurations, expanding beyond traditional cascade models.

Findings

Decay laws derived from angular momentum invariance.

Prediction of turbulence decay in layer, tube, and spot zones.

Implications for improved turbulence modeling in simulations.

Abstract

In practically all turbulent flows, turbulent energy decay is present and competes with numerous other phenomena. In Kolmogorov's theory, decay proceeds by transfer from large energy-containing scales towards small viscous scales through the "inertial cascade." Yet, this description cannot predict an actual decay rate, even in the simplest case of homogeneous isotropic turbulence (HIT). As empirically observed over 50 years, the steepness of the "infrared" spectrum - at scales larger than energy-containing eddies - determines decay, but theoretical understanding is still missing. Here, HIT decay laws are derived from angular momentum invariance at large scales - an approach first mentioned by Landau in 1944, but unduly dismissed later. This invariance also predicts the so-far unexplored turbulence decay in layer, tube, and spot zones in a fluid at rest. Beyond expanded and simplified theoretical descriptions, these findings suggest new practical modeling strategies for turbulent dissipation, often deficient in applied simulations.