Velocity profile approximations for two-dimensional potential open channel flow

Abstract

Two-dimensional flow over channel transitions including round-crested weirs or slope changes is described by the potential flow equations. An approximation widely used in hydraulic engineering relates to the simplification of the 2D potential flow problem using a 1D approach, introducing a suitable hypothesis for the vertical variation of the velocity components, namely the Boussinesq approximation. The current knowledge cannot answer whether this approximation can be used for highly-curved flows. Furthermore, there is no information as to the order of accuracy in the Boussinesq approximation of the velocity functions. In this work, the potential velocity profiles originating from the Boussinesq approximation are tested for highly-curved flows using a new 2D solution. Furthermore, the second- and third-order accurate approximations for u are systematically assessed to study its accuracy behaviour. The implications of a linear vertical velocity profile are particularly addressed. A formulation in curvilinear coordinates leading to the widely used free-vortex-type velocity profile is compared with the 2D results and the Cartesian Boussinesq equations.

Keywords:

• Boussinesq model
• hydraulics
• open channel flow
• potential flow

Acknowledgements

This research was supported by the Junta de Andalucia, Spain (research project P09-AGR-4782).