Turbulent spot growth in plane Couette flow: statistical study and formation of spanwise vorticity

Abstract

This article presents direct numerical simulations of the growth of turbulent spots in the transitional regime of plane Couette flow. A quantitative description of the growth process and of the detail of the quadrupolar flow around the spot is given. Focus is put on formation of spanwise vorticity in the velocity streaks that resembles a secondary shear instability. The main features of the instability (coherence lengths, advection velocity) are studied in the context of the turbulent spot, below and above the threshold Reynolds number of appearance of the oblique turbulent bands of plane Couette flow.