Turbulent bands in a planar shear flow without walls

etc15 Tracking Number 339

The banded structure of turbulence is observed immediately beyond transition in shear flows with two unconstrained directions (e.g. TCF, PCF, PPF). Yet despite its ubiquitous nature, the mechanisms underpinning bands are not understood to the level of localized turbulence in pipe flow. To this aim we investigate turbulent bands in Waleffe flow, a sinusoidal shear flow, U(y)=sin(pi/2 * y), with stress-free boundary conditions at y=+-1. The existence of turbulent bands in this system demonstrates that walls are not necessary to induce the phenomenon. The sinusoidal nature of the base forcing means the dominant features of bands can be viewed through a small number of Fourier modes in y. Utilizing this simple dependence we examine the emergence of turbulent bands from uniform turbulence.