Turbulent Near-Critical Open Channel Flow: Serre’s Similarity Theory

The transition across the critical depth in free-surface flows in- volves large streamline curvature, which increases as the flow depth deviates from the asymptotic normal depth. Consideration of the asymptotic behavior of a free-surface flow to the normal depth re- quires inclusion of turbulent friction. Potential flow methods for the analysis of near-critical flow are limited to short channel reaches ( Fawer 1937 ; Castro-Orgaz 2010 ) for the energy grade line to be horizontal, yet in cases including the undular hydraulic jump, a potential flow solution does not exist ( Mandrup Andersen 1978 ; Mandrup Anderson 1980 ; Montes 1979 ). The backwater ap- proach of gradually varied flows is known to break down at the critical depth ( Montes 1998 ). Thus, a rapidly varied flow model allowing for turbulent friction is required to simultaneously treat the transition across the critical section and the asymptotic condi- tions at uniform flow. The original model developed by Serre ( 1953 ) following Boussinesq ( 1877 ) satisfies these requirements, but regretfully, his original work is almost unknown, except in cross-reference to other works ( Hager and Hutter 1984a , b ; Montes and Chanson 1998 ).