Hydrodynamic Fluctuations in Laminar Fluid Flow. II. Fluctuating Squire Equation

TL;DR

This paper investigates how thermal fluctuations in laminar plane Couette flow are amplified, revealing that wall-normal vorticity fluctuations dominate and generate spontaneous streaks without external disturbances.

Contribution

It derives the energy amplification from wall-normal vorticity fluctuations using the fluctuating Squire equation, extending previous work on wall-normal fluctuations.

Findings

Wall-normal vorticity fluctuations dominate energy amplification.

Thermally excited streaks occur spontaneously in laminar flow.

Vorticity fluctuations significantly influence flow stability.

Abstract

We use fluctuating hydrodynamics to evaluate the enhancement of thermally excited fluctuations in laminar fluid flow using plane Couette flow as a representative example. In a previous publication [J. Stat. Phys. vol. 144 (2011) p. 774] we derived the energy amplification arising from thermally excited wall-normal fluctuations by solving a fluctuating Orr-Sommerfeld equation. In the present paper we derive the energy amplification arising from wall-normal vorticity fluctuation by solving a fluctuating Squire equation. The thermally excited wall-normal vorticity fluctuations turn out to yield the dominant contribution to the energy amplification. In addition, we show that thermally excited streaks, even in the absence of any externally imposed perturbations, are present in laminar fluid flow.