Random Vortex-Street Model for a Self-Similar Plane Turbulent Jet

TL;DR

This paper introduces a vortex-street model for self-similar plane turbulent jets that accurately reproduces experimental velocity profiles and structure positions, revealing the small jet angle results from a balance between vortex sweeping and randomness.

Contribution

The paper develops a deterministic vortex-street model that captures large-scale jet structures without adjustable parameters, explaining the origin of the small jet angle.

Findings

Model reproduces mean velocity profiles and structure positions quantitatively.

Exact self-similar vortex arrangements lead to jet angle collapse.

Randomness in vortex structure causes weak jet spreading.

Abstract

We ask what determines the (small) angle of turbulent jets. To answer this question we first construct a deterministic vortex-street model representing the large scale structure in a self-similar plane turbulent jet. Without adjustable parameters the model reproduces the mean velocity profiles and the transverse positions of the large scale structures, including their mean sweeping velocities, in a quantitative agreement with experiments. Nevertheless the exact self similar arrangement of the vortices (or any other deterministic model) necessarily leads to a collapse of the jet angle. The observed (small) angle results from a competition between vortex sweeping tending to strongly collapse the jet and randomness in the vortex structure, with the latter resulting in a weak spreading of the jet.