Free-Surface Stability Criterion as Affected by Velocity Distribution

Abstract

This paper examines how the velocity distribution of flow in open channels affects the kinematic and dynamic wave velocities, from which the various forms of the Vedernikov number ( V ) can be formulated. When V > 1, disturbances created in open-channel flow will amplify in the form of roll waves; when V < 1, some (though not all) disturbances will attenuate. The specific state of flow at V = 1 represents a limiting case of neutral stability. A study of the Vedernikov stability criterion ( V ⪋ 1) reveals that it can be readily deduced within the framework of the kinematic and dynamic wave theories by comparing the kinematic wave velocity to the corresponding dynamic wave velocity. This in effect recasts V as the ratio of the kinematic and dynamic wave velocities. This ratio further proves equivalent to F /Fs, the ratio of the Froude number ( F ) to the stability limit for the Froude number ( Fs ). Thus, distinguishing among theoretical Fs -values for laminar and turbulent flows with various velocity distributions enables one to evaluate the role that the velocity distribution plays in the formulation of the Vedernikov stability criterion.