Investigation of the kinematic structure of a flow in the case of an undulating bed

Abstract

The dynamic interaction of a flow and movable bed leads to the formation of periodic structures on the bottom and, in particular, undulations in the bed.The formation of such undulations is due mainly to the large-scale part of the turbulence of the flow.In existing investigations the kinematic characteristics of a turbulent flow are considered for two velocity components, longitudinal and vertical.In this case the flow is considered twodimensional or it is indicated that the third (transverse) component of velocity was not measured.The energy spectra are usually presented either for the velocity modulus or for its longitudinal component, and only in a few works are there data on correlation functions and spectral density functions for the vertical velocity component.An investigation of the kinematic structure of a flow in the case of an undulating bed form with respect to the transverse and longitudinal velocity components and a detailed investigation of their energy spectra and modulus of their mutual spectrum were carried out in the hydrophysical laboratory, Department of Physics of the Sea and Land Waters, Physics Faculty, Moscow State University.Regular periodic bed forms as secured undulations 1.75 m long and 0.09 m high made of gravel with an average size to 0.01 m were modeled in a hydraulic flume 25.5 m long, 0.5 m high, and 0.6 m wide.The surface of the undulations was secured by cement mortar.Thus, the relief characteristics were constant over the flow width. There were eight undulations over the length of the flume.The geometric relations corresponded approximately to those observed on the Polomet' River with a similar flow regime [I, 6]. According to the 1960 observations, undulations up to 1.5 m long and 0.i m high propagated along the gravel--sand bed of the river at an average flow velocity of 47 cm/sec. Originally they were created in the flume by a flow at the indicated average velocity on the movable bed, and the average geometric size obtained was calculated, which was then taken as the basis for creating the secured roughness.Measurements of the average and fluctuation values of the velocity were made along the axial line of the flow at six verticals located over the fourth and fifth undulations (Fig. ib).Special attention was paid to the least investigated region, in the trough, where a vortex zone with a horizontal axis perpendicular to the direction of the flow was noted earlier [3,4]. The level of the undulation crest is taken here as the zero elevation of the bed.Thus, the heights of the measurement points above this level are positive and below it, negative.An analysis of the curves confirms the results of other investigations on the relation of the depth distribution of ~, ~u, and ~w to the location of the vertical with respect to the undulation. There are inflections in the curves of Ou and Ow on different verticals. On vertical 1 (crest level) o u and Ow change little with depth and amount, respectively, to 17 and 19% of the average (with respect to depth) velocity, equal to 47 cm/...