The models for flood propagation in an open channel are governed by Saint-Venant's equations or by their simplified forms. Assuming the full form of hyperbolic type nonlinear expressions, the complete or dynamic wave model is obtained. Hence, after first-order linearization procedure, the dispersion relation is obtained by using the classical Fourier analysis. From this expression, the phase and group speed, and the variations of the amplitude of the waves are defined and investigated. Adopting Manning's resistance formula, the effects of the variations of the Froude number, of the Courant number, and of the friction parameter are examined in the wave number domain, for progressive and regressive waves. For small and high wave number, the simplified kinematic and gravity wave models are recovered, respectively. Moreover, the analysis confirms, according to Vedernikov criterion, the Froude number value corresponding to the stability condition to contrast the development of roll waves. In addition, for stable flow, on the group speed versus wave number curves the results show critical points, maximum and minimum for progressive and regressive waves, respectively.
Analysis of Dynamic Wave Model for Unsteady Flow in an Open Channel
VENUTELLI, MAURIZIO
2011-01-01
Abstract
The models for flood propagation in an open channel are governed by Saint-Venant's equations or by their simplified forms. Assuming the full form of hyperbolic type nonlinear expressions, the complete or dynamic wave model is obtained. Hence, after first-order linearization procedure, the dispersion relation is obtained by using the classical Fourier analysis. From this expression, the phase and group speed, and the variations of the amplitude of the waves are defined and investigated. Adopting Manning's resistance formula, the effects of the variations of the Froude number, of the Courant number, and of the friction parameter are examined in the wave number domain, for progressive and regressive waves. For small and high wave number, the simplified kinematic and gravity wave models are recovered, respectively. Moreover, the analysis confirms, according to Vedernikov criterion, the Froude number value corresponding to the stability condition to contrast the development of roll waves. In addition, for stable flow, on the group speed versus wave number curves the results show critical points, maximum and minimum for progressive and regressive waves, respectively.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
