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Self-similar decay and mixing of a high-Schmidt-number passive scalar in an oscillating boundary layer in the intermittently turbulent regime

Published online by Cambridge University Press:  05 June 2013

Carlo Scalo ,
Ugo Piomelli  and
Leon Boegman
Carlo Scalo
Affiliation:
Department of Mechanical and Materials Engineering, Queen’s University, 130 Stuart Street, Kingston, Ontario K7L 3N6, Canada
Ugo Piomelli
Affiliation:
Department of Mechanical and Materials Engineering, Queen’s University, 130 Stuart Street, Kingston, Ontario K7L 3N6, Canada
Leon Boegman
Affiliation:
Department of Civil Engineering, Queen’s University, 58 University Avenue, Kingston, Ontario K7L 3N6, Canada
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Abstract

We performed numerical simulations of dissolved oxygen (DO) transfer from a turbulent flow, driven by periodic boundary-layer turbulence in the intermittent regime, to underlying DO-absorbing organic sediment layers. A uniform initial distribution of oxygen is left to decay (with no re-aeration) as the turbulent transport supplies the sediment with oxygen from the outer layers to be absorbed. A very thin diffusive sublayer at the sediment–water interface (SWI), caused by the high Schmidt number of DO in water, limits the overall decay rate. A decomposition of the instantaneous decaying turbulent scalar field is proposed, which results in the development of similarity solutions that collapse the data in time. The decomposition is then tested against the governing equations, leading to a rigorous procedure for the extraction of an ergodic turbulent scalar field. The latter is composed of a statistically periodic and a steady non-decaying field. Temporal averaging is used in lieu of ensemble averaging to evaluate flow statistics, allowing the investigation of turbulent mixing dynamics from a single flow realization. In spite of the highly unsteady state of turbulence, the monotonically decaying component is surprisingly consistent with experimental and numerical correlations valid for steady high-Schmidt-number turbulent mass transfer. Linearly superimposed onto it is the statistically periodic component, which incorporates all the features of the non-equilibrium state of turbulence. It is modulated by the evolution of the turbulent coherent structures driven by the oscillating boundary layer in the intermittent regime, which are responsible for the violent turbulent production mechanisms. These cause, in turn, a rapid increase of the turbulent mass flux at the edge of the diffusive sublayer. This outer-layer forcing mechanism drives a periodic accumulation of high scalar concentration levels in the near-wall region. The resulting modulated scalar flux across the SWI is delayed by a quarter of a cycle with respect to the wall-shear stress, consistently with the non-equilibrium state of the turbulent mixing.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , pp. 338 - 370
Copyright
©2013 Cambridge University Press 

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