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Lagrangian mixing in straight compound channels

Published online by Cambridge University Press:  29 March 2011

ALESSANDRO STOCCHINO ,
GIOVANNI BESIO ,
SONIA ANGIOLANI  and
MAURIZIO BROCCHINI
ALESSANDRO STOCCHINO*
Affiliation:
Dipartimento di Ingegneria delle Costruzioni, dell'Ambiente e del Territorio, University of Genova, Genova 16145, Italy
GIOVANNI BESIO
Affiliation:
Dipartimento di Ingegneria delle Costruzioni, dell'Ambiente e del Territorio, University of Genova, Genova 16145, Italy
SONIA ANGIOLANI
Affiliation:
Dipartimento di Ingegneria delle Costruzioni, dell'Ambiente e del Territorio, University of Genova, Genova 16145, Italy
MAURIZIO BROCCHINI
Affiliation:
Department ISAC, Polytechnic University of Marche, Via Brecce Bianche, 12, 60131 Ancona, Italy
*
†Email address for correspondence: jorma@dicat.unige.it
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Abstract

Recently Stocchino & Brocchini (J. Fluid Mech., vol. 643, 2010, p. 425 have studied the dynamics of two-dimensional (2D) large-scale vortices with vertical axis evolving in a straight compound channel under quasi-uniform flow conditions. The mixing processes associated with such vortical structures are here analysed through the results of a dedicated experimental campaign. Time-resolved Eulerian surface velocity fields, measured using a 2D particle-image velocimetry system, form the basis for a Lagrangian analysis of the dispersive processes that occur in compound channels when the controlling physical parameters, i.e. the flow depth ratio (rh) and the Froude number (Fr) are changed. Lagrangian mixing is studied by means of various approaches based either on single-particle or multiple-particle statistics (relative and absolute statistics, probability density functions (p.d.f.s) of relative displacements and finite-scale Lyapunov exponents). Absolute statistics reveal that transitional macrovortices, typical of shallow flow conditions, strongly influence the growth in time of the total absolute dispersion, after the initial ballistic regime, leading to a non-monotonic behaviour. In deep flow conditions, on the contrary, the absolute dispersion displays a monotonic growth because the generation of transitional macrovortices does not take place. In all cases an asymptotic diffusive regime is reached.

Multiple-particle dynamics is controlled by rh and Fr. Different growth regimes of the relative diffusivity have been found depending on the flow conditions. This behaviour can be associated with different energy transfer processes and it is further confirmed by the p.d.f.s of relative displacements, which show a different asymptotical shape depending on the separation scales and the Froude number. Finally, an equilibrium regime is observed for all the experiments by analysing the decay of the finite-scale Lyapunov exponents with the particle separations.

JFM classification

Geophysical and Geological Flows: River dynamics Geophysical and Geological Flows: Shallow water flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 168 - 198
Copyright
Copyright © Cambridge University Press 2011

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