Direct measurements of the bottom friction factor beneath surface gravity waves

Abstract

This paper describes a detailed experimental study of the laminar and turbulent oscillatory boundary layer developed under the action of waves for the purpose of evaluation of bottom energy dissipation. The measurements were conducted on hydraulically smooth and immobile rough beds and under both monochromatic conditions and a spectrum of waves in a 50 m long wave flume. Bottom friction was measured in two different ways: (i) by a flush mounted shear plate, developed as part of the project and set at the bottom of the flume, (ii) by using the momentum integral equation and the measured velocity profile within the boundary layer. The velocity profile within the boundary layer was measured using a Laser Doppler Anemometer. The roughness geometry was chosen to simulate both rough flat and rippled beds. With respect to the dissipation under a spectrum of waves, the results show that a spectrum of waves and a monochromatic wave whose maximum bottom velocity is 1.88 times the root mean square of the bed velocity of the spectrum, dissipate the same amount of energy. As a consequence, measurements of energy dissipation for monochromatic waves can be related to spectral conditions. The results for monochromatic waves were found to be in good agreement with the existing formulae for the bottom friction factor, which have mainly been based on experimental results in water tunnels or over oscillating trays. Therefore, it was concluded that the secondary effects due to the nonuniformity of the bed velocity in the horizontal direction, which can be observed under real waves, does not have substantial influence on the bed friction factor. In addition, it was concluded that the nonlinearity of waves in finite depth water does not significantly affect the results.