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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/...

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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.

532.5.032 and V. P. Petrov Natural river beds and canals are characterized by a considerable diversity of shapes, sizes, and arrangement of bottom roughness elements which are formed by the interaction of the flow and bed and affect considerably the kinematic makeup of the flow. The available published works present data on the effect of roughness on the average velocity, its standard deviation close to the analogous characteristic of the horizontal velocity component, and sometimes the standard deviation of the vertical velocity component. There are almost no data on the pulsating characteristics of the third component (the transverse velocity component). But at the same rune knowledge of these characteristics is necessary, particularly for determining the character of transverse circulation, which has a considerable effect on the transport of sediment by the flow.During movement of the flow along a rough bottom eddies are formed behind the roughness projections, the scale and frequency of formation of which apparently depend on the size, shape, and mutual arrangement of the roughness elements. The near-bottom region, when there is a direct interaction between the flow and the rough bottom is the main region. It is indicated in [1] that the maximum standard deviation of the longitudinal velocity componentcoincides in height with the upper boundary of the near-bottom layez and decreases toward the surface and bottom of the flow. It is noted in [2] that turbulent exchange between the flow core and eddy regions formed beyond the roughnesses plays the main role in the mechanism of action of wall roughnesses on the flow, the introduction of roughness increasing the velocity fluctuations. It was found that the fluctuations expressed in a dynamic velocity scale are close in magnitude for quite different flow conditions, including for different roughnesses.An investigation of the average and pulsating velocity characteristics on small mountain rivers in the Tadzhik SSR [3] showed that the maximum fluctuations of the longitudinal velocity component occur at the level of the peaks of the roughness projections of the bottom. These investigations confirm the importance of the problem formulated in this work, the content of which is an investigation of the vertical distribution of the average values of the horizontal component ~, standard deviations of the horizontal oU and transverse oW velocity components, and coefficient of correlation rU,W between them: and determination of their relation to the size, shape, and mutual arrangement of the roughness elements.The experiments were carried out jointly by the All-Union Scientific-Research Institute of Physieotechnical and Radiotechnieal Measurements (VNIIFTRI) and Department of Physics of the Sea and Land Waters, Physics Faculty, Moscow State University. Before the start of the experiment a layer of glass plates with roughnesses glued on them by means of nitrocellulose lacquer was placed on the bottom of a flume '/m long, 0.4 m high, and 0.2 m wide. The roughness was selec...