Parameterization of Mean Residence Times in Idealized Rectangular Dead Zones Representative of Natural Streams
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 8
Abstract
Three-dimensional Reynolds averaged Navier-Stokes modeling, validated against experimental data, is used to parameterize the flow features and time scales in idealized rectangular cavities for a wide range of width-to-length ratios, , and Reynolds number based on the depth, , representative of isolated dead zones in small natural streams. The flow features for this parameter range are similar to open cavity flows and consist of a mixing layer spanning the entire length of the dead zone together with a single main recirculation region. The Langmuir time scale (ratio of dead-zone volume to discharge) based on the assumption of a well-mixed dead zone is found to be a function of the mean rotation time scale (inverse of average rotation rate) within the dead zone, the momentum thickness of the upstream boundary layer, and the dead-zone width. The entrainment coefficient, used to relate the exchange velocity to the average free- stream velocity, is shown to be directly related to the upstream boundary layer momentum thickness nondimensionalized by the width of the dead zone. Using passive tracer to quantify the mean residence time showed that the dead zone can be characterized by two perfectly mixed regions including a core or secondary region around the center of the eddy and a surrounding primary region that interacts directly with the free-stream through the mixing layer. A two-region model is developed to obtain time scales associated with the primary and secondary regions within the dead zone using an optimization procedure based on the computational data. The time scale associated with the primary region is representative of the Langmuir time scale and is found to be a strong function of the aspect ratio and the Reynolds number. The secondary region time scale represents the long-time asymptotic behavior of the tracer concentration and is found to be a strong function of the dead- zone geometric parameters only.
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Acknowledgments
This work was supported by the National Science Foundation, EAR 0943570. We also thank all the reviewers for their critical comments that helped improve the quality of the work.
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Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 8 • August 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Oct 19, 2012
Accepted: Jan 27, 2014
Published online: Apr 21, 2014
Published in print: Aug 1, 2014
Discussion open until: Sep 21, 2014
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