Consideration of bottom roughness when determining the turbulent exchange coefficient for the threedimensional problem

Abstract

The turbulent exchange coefficient, determined by the turbulent mixing mechanism, describes not the physical properties of a fluid but the statistical characteristics of the velocity field. Therefore it, as is true of other characteristics of turbulence, is not a constant but varies in space and time. Knowledge of the turbulent exchange coefficient is necessary when calculating the vertical distribution and transport of suspended sediments by free-flowing water.Samiemplrlcal theories of turbulence [I] are based on the assumption of the dependence of this coefficient on the mean valocity gradient du/dy and moment of correlation between the longitudinal and vertical components of the velocity fluctuations ~'y' according to the following equation:.' y' .....(1)The investigations presented below were carried out for the purpose of establishing the effect of bed roughness on the character of the turbulent exchange coefficient over the depth of the flow (vertical distribution).This coefficient was compared with other statistical characteristics of the velocity field determined by three velocity components. The fluctuations of all three were measured by two-component angular hot-wlre thermal flowmeters [2] with appropriate orientation of the platinum wires. The wire was 50 ~ thick and 5 mm long. The experiments were set up in the hydrophysical laboratory, department of physics of the sea and land waters, physics faculty, Moscow State University (MGU), on a flume 7 m long and 0.2 m wide, depth of flow 8.8 cm with five types of bed: smooth glass bottom, Volsk sand of fraction 0.078 cm, glass spheres 0.24 cm in diameter, gravel of fraction 0.7 cm, and glass spheres 2 cm in diameter. Measurements were taken at 5-7 points of the average vertical at a distance of 40 flow depths from the flume entrance.