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

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.

14 pages, 9 figures, Accepted in Eur. Phys. J. B

References in corpus (4)

• The large deviation approach to statistical mechanics
• The lift-up effect: the linear mechanism behind transition and turbulence in shear flows
• Ginzburg--Landau description of laminar-turbulent oblique band formation in transitional plane Couette flow
• Pattern fluctuations in transitional plane Couette flow