Transition to Turbulence from Spatially Localised States

Lead Research Organisation: University of Leeds
Department Name: Applied Mathematics

Abstract

Many flows encountered in industrial processes are turbulent and in most applications, turbulence is detrimental. Undesired effects include wall friction and drag increase, mixing enhancement and unsteadiness. Controlling these flows to delay transition to turbulence and preserve as much laminar unidirectional flow as possible represents a promising strategy but its implementation lacks fundamental knowledge on the underpinning mechanisms of transition.

We consider one of the simplest flows that exhibits transition to turbulence: plane Couette flow, i.e., a three-dimensional viscous incompressible fluid placed between two parallel plates moving in opposite directions. This flow, like most shear flows, is characterised by the coexistence between the laminar unidirectional and the turbulent flows. As both flows are observable in the same configuration, transition is reached when a perturbation crosses the boundary between the basin of attraction of the laminar state and that of turbulence. This boundary is called the edge of chaos and its structure is critical to the understanding of transition and to its control: it determines which perturbations transition and which ones do not. In large domains, the edge of chaos is populated by turbulent spots: spatially localized patches of turbulence sharply connected to a laminar background by fronts. The laminar flow being stable, the only way for turbulence to spread is through the diverging motion of the fronts. The proposed research aims at providing a description of the various stages of transition from these localized states. The fundamental findings on this project will advance our knowledge on the mechanisms at play in transition and provide new ideas for the control of these flows.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509681/1 01/10/2016 30/09/2021
1886935 Studentship EP/N509681/1 01/01/2017 30/06/2020 Anton Pershin
 
Description We analysed how spatially localised perturbations decay or transition to turbulence in a model of typical fluid flows. We found that, depending on the size of the localised perturbation and the Reynolds number, the perturbations exhibit several well-defined dynamical regimes. We provided a comprehensive study of these regimes.
Exploitation Route These results could be helpful when designing a control strategy to prevent transition to turbulence and its undesirable effects in industry. The location of the various regimes in parameter space might act as a benchmark for various control strategies allowing for quantitative comparisons.
Sectors Aerospace, Defence and Marine,Energy,Manufacturing, including Industrial Biotechology

URL https://arxiv.org/abs/1806.10097