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Parametric resonance in unsteady watertable flow

Published online by Cambridge University Press:  12 March 2015

Carlo Camporeale  and
Peter J. Schmid
Carlo Camporeale*
Affiliation:
Department of Environment, Land and Infrastructure Engineering, Politecnico di Torino, 10129 Torino, Italy
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

The stability of unsteady open-channel flow down an inclined plane is studied using an iterative approach based on the direct and adjoint stability equations combined with a physically justified energy measure. An efficient parametric resonance mechanism has been identified between the exogenous base-flow oscillations and the intrinsic frequencies of streamwise disturbance vortices. This resonance results in strong amplification over a substantial range of the governing parameters, favouring streamwise elongated structures. The optimal frequency for a maximal disturbance response can be efficiently approximated from simpler steady calculations; two frequency-selection criteria are given for this purpose. The analysis generalizes earlier work on steady watertable flow and provides an effective framework and starting point for further work on pattern formation in harmonically forced open-channel flows.

JFM classification

Mathematical Foundations: Computational methods Instability: Parametric instability Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 524 - 548
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Copyright
© 2015 Cambridge University Press 

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Camporeale and Schmid supplementary movie

Movie reporting the entire transient growth period showed from Fig.8 in the manuscript and discussed in section 5 for the WP with optimal initial condions. Upper left panel: lateral view; Upper right panel free surface; Lower left panel: frontal view; Lower right panel: depth perturbation in arbitrary scale (red) and growth function (blue)

Download Camporeale and Schmid supplementary movie(Video)
Video 13.1 MB