Bottom Stress in Non Stationary Free Surface Flow

Abstract

This paper describes studies of the bed friction factor in nonstationary free surface flow, for the specific case of bores moving in shallow water and breaking waves on beaches. Data from a set of experiments carried out in a laboratory flume, including measurements of water level displacement and fluid velocity through LDV, are used to evaluate the bottom stress and the mean flow velocity. The results of other measurement techniques in similar conditions are used to critically assess our results. It is found that the friction factor is higher and the transition from laminar to turbulent boundary layer takes place at higher Re numbers than values obtained in separate studies of turbulent bottom boundary layer including an additional source of turbulence. INTRODUCTION Bottom friction and boundary layer dynamics play a major role in many nonstationary flee surface physical flows such as roll waves and bores in shallow water and over beaches. This subject is of interest because the stability analysis of free surface flows aiming to detect the presence of roll waves is sensitive to the friction, and also, bore dynamics in shallow water and the maximum run-up of waves over beaches depends on the bottom friction. Flow resistance is usually expressed through a friction factor. The friction factor is an integral expression of the efficiency in fluid momentum transport and is useful in modeling stream processes without resolving the detail in the turbulence and the velocity distribution. In general, in stationary flows the resisting force per unit length acting on a control volume is the product of the wetted perimeter of the section and the mean intensity of the boundary stress. If the flow is accelerating there are forces working Assistant Professor, Department of Civil Engineering, University of Parma, Parco Area delle Scienze, 181/A, 1-43100 Parma, Italy. slongo@unipr.it Professor, Department of Georisorse e Territorio, University of Udine, Via Cotonificio, 114, 133100 Udine, Italy. petti@uniud.it Research Scientist, Department of Georisorse e Territorio, University of Udine, Via Cotonificio, 114, 1-33100 Udine, Italy.