Pattern Formation Mechanisms in Planar Shear Flows

The continuing increase in energy consumption and the need to cope with the resulting climate crisis is the most challenging endeavour for modern society. Although turbulent flow is beneficial for certain engineering applications involving fluid mixing, for fluid transport laminar flows are widely preferred for reducing frictional losses and hence transport costs are far lower. Therefore, comprehending the origin of turbulence is a crucial first step towards its effective control. More specifically, the study of the transition from a laminar to a turbulent flow in simple geometries provides extremely valuable knowledge of the involved mechanisms, which later can be used to understand the transition in more complex geometries and industrial applications. Transition to turbulence in shear flows is usually characterised by intermittency, which is the coexistence of laminar and turbulent flow regions. Moreover, this intermittency first appears as localised patches of turbulence that later on grow and develop into elongated oblique stripe bands surrounded by laminar flow. Finally, when increasing the flow rate, these stripes begin to proliferate and form visible stripe patterns with a well defined spacing between individual stripes. As this is a general phenomena in many fluid problems, we focus this project on the study of stripe pattern formation mechanisms in the transitional regime of planar shear flows. While this phenomenon has been known for long time, two key questions such as the angle of the stripe patterns and their formation process remain open. These questions will be addressed using novel approaches that are distinctly different from earlier studies. Basically, the project will explore two possible routes that could explain the aforementioned questions. The first is based in a top-down view, starting from a fully turbulent flow and then decreasing the flow rate allowing laminar gaps to nucleate. The second is a bottom-up approach based on the concept of directed percolation, which basically consists in explaining the pattern formation as local interactions and spreading of turbulence from small initial seeds. These structures will be mainly studied by means of direct numerical simulations using a particular computational domain, which is tilted with the main direction of the flow. This special choice is made to avoid effects and instabilities on the flow that could give rise to a mix of effects that might complicate the interpretation of the results.