Intermittency at Fine Scales and Complex Singularities of Turbulent Couette Flow

TL;DR

This paper introduces a numerical method to analyze the complex plane singularities of turbulent velocity fields, revealing their connection to fine-scale intermittency in turbulent Couette flow.

Contribution

It presents a novel technique for analytically continuing turbulent velocity fields into the complex plane to locate singularities linked to intermittency.

Findings

Singularities are closely related to intermittent bursts in turbulence.

The method effectively visualizes complex singularities near the real axis.

A robust connection between singularities and intermittency is demonstrated.

Abstract

Fine scales of turbulent velocity fields, beyond the inertial range and well into the dissipative range, are highly intermittent. It has been hypothesized that complex plane singularities are the principal mechanism behind fine scale intermittency. In this article, we view the velocity field of a turbulent flow as an analytic function of time. Although the function is only available for real values of time, we present a numerical technique to analytically continue the function to complex values of time, and with sufficient fidelity to locate and visualize the singularity closest to the real axis. Using this technique, we demonstrate a robust connection between temporal intermittency and the location of singularities in the complex plane.