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Bursting and critical layer frequencies in minimal turbulent dynamics and connections to exact coherent states

Jae Sung Park

Ashwin Shekar and Michael D. Graham*

  • Department of Mechanical and Materials Engineering, University of Nebraska–Lincoln, Lincoln, Nebraska 68588-0526, USA

  • Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706-1691, USA

  • *Corresponding author: mdgraham@wisc.edu
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Phys. Rev. Fluids 3, 014611 – Published 25 January, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.014611

Abstract

The dynamics of the turbulent near-wall region is known to be dominated by coherent structures. These near-wall coherent structures are observed to burst in a very intermittent fashion, exporting turbulent kinetic energy to the rest of the flow. In addition, they are closely related to invariant solutions known as exact coherent states (ECS), some of which display nonlinear critical layer dynamics (motions that are highly localized around the surface on which the streamwise velocity matches the wave speed of ECS). The present work aims to investigate temporal coherence in minimal channel flow relevant to turbulent bursting and critical layer dynamics and its connection to the instability of ECS. It is seen that the minimal channel turbulence displays frequencies very close to those displayed by an ECS family recently identified in the channel flow geometry. The frequencies of these ECS are determined by critical layer structures and thus might be described as “critical layer frequencies.” While the bursting frequency is predominant near the wall, the ECS frequencies (critical layer frequencies) become predominant over the bursting frequency at larger distances from the wall, and increasingly so as Reynolds number increases. Turbulent bursts are classified into strong and relatively weak classes with respect to an intermittent approach to a lower branch ECS. This temporally intermittent approach is closely related to an intermittent low drag event, called hibernating turbulence, found in minimal and large domains. The relationship between the strong burst and the instability of the lower branch ECS is further discussed in state space. The state-space dynamics of strong bursts is very similar to that of the unstable manifolds of the lower branch ECS. In particular, strong bursting processes are always preceded by hibernation events. This precursor dynamics to strong turbulence may aid in development of more effective control schemes by a way of anticipating dynamics such as intermittent hibernating dynamics.

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Phys. Rev. Fluids 3, 014611– Published 25 January, 2018
  • Received 29 August 2016
Article part of CHORUS
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