Mechanical and statistical study of the laminar hole formation in transitional plane Couette flow

TL;DR

This study investigates the formation of laminar holes in transitional plane Couette flow through numerical simulations, analyzing both forced quenches and natural hole formation, revealing mechanisms behind turbulence decay and band fragmentation.

Contribution

It provides a detailed numerical and statistical analysis of laminar hole formation, introducing a kinetic energy budget approach and applying Large Deviations theory to turbulence decay.

Findings

Kinetic energy decreases during quenches due to viscosity effects.

Laminar holes contribute to band fragmentation and orientation changes.

Disappearance of turbulence can be modeled with Large Deviations.

Abstract

This article is concerned with the numerical study and modelling of two aspects the formation of laminar holes in transitional turbulence of plane Couette flow (PCF). On the one hand, we consider quenches: sudden decreases of the Reynolds number R which force the formation of holes. The Reynolds number is decreased from featureless turbulence to the range of existence of the oblique laminar-turbulent bands [Rg;Rt]. The successive stages of the quench are studied by means of visualisations and measurements of kinetic energy and turbulent fraction. The behaviour of the kinetic energy is explained using a kinetic energy budget: it shows that viscosity causes quasi modal decay until lift-up equals it and creates a new balance. Moreover, the budget confirms that the physical mechanisms at play are independent of the way the quench is performed. On the other hand we consider the natural formation of laminar holes in the bands, near Rg. The Direct Numerical simulations (DNS) show that holes in the turbulent bands provide a mechanism for the fragmented bands regime and orientation fluctuations near Rg. Moreover the analysis of the fluctuations of kinetic energy toward low values demonstrates that the disappearance of turbulence in the bands can be described within the framework of Large Deviations. A Large Deviation function is extracted from the Probability Density Function of the kinetic energy.