Magnetised turbulent-laminar dynamics in shear flows

Turbulence is ubiquitous in nature, however, the characterisation of the transition that gives rise to turbulence in shear flows is yet to be accomplished. Intermittency is a defining feature of the initial onset of turbulence in wall-bounded flows, in which chaotic regions, often in the form of bands or spots, coexist and compete with laminar motion. Connections between the behaviour of this laminar-turbulence transition have been made with both the dynamics of excitable media in addition to predator-prey dynamics, although it is hard to differentiate between these two models since there is only one control parameter, namely the Reynolds number. In this study, we attempt to unfold this problem by adding a magnetic field, the presence of which suppresses the excitability of the medium, making the turbulence less intermittent and modifying the form of the bands. By considering the low magnetic Reynolds number approximation, we introduce a second control parameter, the Hartmann number, thereby enabling this transition to be explored in a systematic manner. Specifically, we study the idealised shear between stress-free boundaries driven by a sinusoidal body force. This system, known as Waleffe flow, is further reduced by constructing a model that uses only four Fourier modes in the wall-normal direction, thus substantially reducing the computational cost of simulations whilst retaining the fidelity of the essential physics. Conclusions are drawn based on a series of carefully designed numerical simulations.