Unique Laminar‐Flow Stability Limit Based on Shallow‐Water Theory
Publication: Journal of Hydraulic Engineering
Volume 119, Issue 7
Abstract
Two approaches are generally taken in deriving the stability limit for the Froude number for laminar sheet flow: The first approach uses the Orr‐Sommerfeld equation, while the second uses the cross‐section‐averaged equations of continuity and motion. Because both approaches are based on shallow‐water theory, the values of obtained from both approaches should be identical, yet in the literature they are not. This suggests that a defect exists in at least one of the two approaches. After examining the governing equations used in both approaches, one finds that the existing cross‐section‐averaged equation of motion is dependent on the frame of reference. To correct this defect, one can formulate a frame‐independent equation of motion relative to a coordinate system moving with constant velocity, then derive a new expression for that is generally applicable to both laminar and turbulent flows in prismatic channels of arbitrary cross‐sectional geometry. For laminar sheet flow, the new expression for obtained from the second approach yields , which agrees with that obtained from the first approach.
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Information & Authors
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Published In
Journal of Hydraulic Engineering
Volume 119 • Issue 7 • July 1993
Pages: 816 - 829
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Apr 27, 1992
Published online: Jul 1, 1993
Published in print: Jul 1993
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