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Modal energy flow analysis of a highly modulated wake behind a wall-mounted pyramid

Published online by Cambridge University Press:  09 June 2016

Zahra Hosseini ,
Robert J. Martinuzzi  and
Bernd R. Noack
Zahra Hosseini
Affiliation:
Department of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, T2N 1N4, Canada
Robert J. Martinuzzi*
Affiliation:
Department of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, T2N 1N4, Canada
Bernd R. Noack
Affiliation:
LIMSI-CNRS, UPR 3251, Rue John von Neumann, Campus Universitaire d’Orsay, Bât. 508, 91405 Orsay CEDEX, France Institut für Strömungsmechanik, Technische Universität Brauschweig, Hermann-Blenk-Str. 37, 38108 Braunschweig, Germany
*
†Email address for correspondence: rmartinu@ucalgary.ca
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Abstract

We experimentally investigate the highly modulated turbulent wake behind a wall-mounted square-base pyramid protruding through the boundary layer. We present the first modal energy flow analysis of a time-resolved three-dimensional velocity field from experimental particle image velocimetry data. The underlying low-order representation is optimized for resolving the base-flow variation as well as the first and second harmonics associated with vortex shedding – generalizing the triple decomposition of Reynolds & Hussain (J. Fluid Mech., vol. 54, 1972, pp. 263–288). This analysis comprises not only a detailed modal balance of turbulent kinetic energy as pioneered by Rempfer & Fasel (J. Fluid Mech., vol. 275, 1994, pp. 257–283) for proper orthogonal decomposition (POD) models, but also the companion energy balance of the mean flow. The experimental results vividly demonstrate how constitutive elements of mean-field theory (Stuart, J. Fluid Mech., vol. 4, 1958, pp. 1–21) near laminar Hopf bifurcations remain strongly pronounced in a turbulent wake characterized by highly modulated, quasi-periodic shedding. The study emphasizes, for instance, the stabilizing role of mean-field manifolds, as explored in the pioneering POD model of Aubry et al. (J. Fluid Mech., vol. 192, 1988, pp. 115–173). The presented low-order representation of the flow and modal energy flow analyses may provide important insights and reference data for computational turbulence modelling, e.g. unsteady Reynolds-averaged Navier–Stokes simulations.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , pp. 717 - 750
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Copyright
© 2016 Cambridge University Press 

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