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This paper deals with a longitudinal mixing of particles which are instantaneously releasedin a bounded turbulent shear flow. The movements of particles are described in view of theLagrangian particle analysis. The similarity of concerned phenomena to the turbulent diffu-sion by continuous movements in a uniform turbulent flow is studied. The discrepancy oftwo phenomena is also shown with some discussions. In the mixing the Lagrangian auto-correlation function plays the most important role. Some auto-correlation functions in aturbulent shear flow are introduced and their dependency on a released position and traveltime is discussed. The discussion gives useful information of estimating the Lagrangianauto-correlation function in a turbulent shear flow. Finally, the model of the Lagrangianauto-correlation function proposed by the authors in the other paper is referred, and thegeneral features of longitudinal mixing given by the proposed model are compared withthe past knowledge experimentally obtained.

This paper describes the internal structure of curved flows based on measurements of threedimensional velocity components in the curved reaches of smooth rectangular channels underconditions of subcritical flows.Considering the properties of three voriticity components observed, the flow through acurved section was divided into three regions: the generated region, the developed region andthe fully developed region of secondary flow. The magnitude of secondary flow predicted fromthe longitudinal vorticity equation was confirmed by the experimental results in the generatedregion. Further, the radial distribution of tangential velocity measured in the fully developedregion supported the theory of pervious papers.

As described in a previous paper', the flow through a simple curved open channel maybe divided into three regions a generated region, a developing region and a fully developedregion of secondary flow.In the first part of the present paper, the existence and the properties of these regions arereexamined by a series of experiments shown in Table- 1 . From the longitudinal distributionsof three mean vorticity components observed, it was found that the flow in the curved reach hasthe characteristics of the generated region and the developing region, and the fully developedregion will be never reached in many practical cases.In the second part, the vertical distributions of radial velocity with or without the effects ofbed wall friction are discussed. Considering small perturbations from a flow as a free vortex, thedistributions of radial velocity are derived from longitudinal vorticity equations for a laminar anda turbulent flow. The experimental results within the generated region support the theoreticalconsiderations.

It is well known that the secondary flow can be observed in a straight open channel, however, it is elusive to be detected because of its small magnitude and unstableness. The secondary flow is investigated experimentally or numerically by many researchers. In this paper vortex motions induced by the secondary flow are classified on the basis of its cause; velocity gap, flow boundary and bed-generated turbulence, and discussed by using the results of 3-D LDA measurements, flow visualization in a transverse cross section and an algebraic stress model (Naot-Rodi model). It is found that there are some difference between the time-mean secondary flow obtained by LDA and N-R model and the instanteneous secondary flow by the flow visualization.

In the previous paper^1)- the authors presented a bed-load equation which was derived from their constitutive relations of debris flow. The equation underestimates somewhat the bed-load rate in the range of non-dimensional shear stress smaller than 0.2.This paper discusses a refinement of the constitutive equations in smaller range of shear stress, but greater than the critical value of initiation of sediment movement.A bed-load equation, then, is derived from the refined constitutive relations.The formula is tested in terms of the data obtained from flume tests carried by using both of sand particles and glass beads.

This paper deals with the mixing phenomena in a main flow direction within a bounded turbulentshear flow in view of Lagrangian aspect.Data obtained by numerical simulations are analized through application of Taylor's classicturbulent diffusion theory by continuous movements: Main objectives are to disclose the relations ofLagrangian properties, such as Lagrangian auto-correlation coefficient, integral time scale and dis-persion coefficient with Eulerian Flow properties and also to obtain differences of these Lagrangianproperties between two and three dimensional turbulent shear flows.As results of this study, it is concluded that the auto-correlation coefficient in a three dimensionalturbulent shear flow is quite different from that in a two dimensional one, and that the lateral non-uniformity of velocities averaged in a vertical direction and the lateral turbulent intensity are mosteffective on the longitudinal mixing in three dimensional turbulent shear flows.

The outline of the recent investigations on the turbulence characteristics in free surface shearflows, performed by the staffs in the Ujigawa Hydraulics Laboratory, is described in this paper, which is consisted of the following two main parts.Firstly, the spectral similarities of the turbulence energy, the Reynolds stress and the con-vective process are obtained for the productive, the inertial and the viscous subrange respective-ly, through the technique of dimensional analysis. The validity of these similarities are examinedby the experimental data.Secondly, the vertical distribution of parameters on fhe turbulence field in a two-dimensionalfree surface shear flow is investigated both theoretically and experimentally, and the followingresults are obtained. The mean velocity distribution is good approximated by the well-known log-arithmic law, but the Karman constant and the integral constant are differ from these of pipe flow.The vertical distribution of the turbulence intensity, the Eulerian integral scale and the energydissipation rate are represented in form of universal functions, whose functional forms aredetermined experimentally.

Before and behind bed protection works in natural rivers, bed roughnessabruptly changes from smooth to rough and/or rough to smooth. This paper dealswith water surface profiles and turbulent structures of open channel flows producedby sudden changes in bottom roughness experimentally and theoretically.Changes in vertical distribution of sediment concentration under the fullysuspended condition are also discussed. The transition of flow depth was found tobe mainly depend on the bed slope and classified into three types of flow patterns.In the downstream reach after roughness change, distributions of the velocity andturbulence property vary with development of the internal boundary layer, in whichthe transfer of turbulence energy by convection and vertical diffusion play dominantrole in the turbulence energy budget. The calculated results of the k-e andsediment transport models agree well with the experimental ones.

In a curved channel there are spiral motions occurred by centrifugal force. And in an openchannel that consists of a main channel and flood plains, the flow has a complex turbulent structurebecause of interaction between flow in a main channel and it in flood plains. So it is difficult to clarifycharacteristics of an open channel flow in bend with flood plains.In this paper it is the objective to elucidate the turbulent structure of this flow by measurementsof velocity and flow visualization. From experimental results it is comfirmed that three independentspiral motions exist in bend with two flood plains.

This paper describes an experimental investigation of the profiles of mean velocitiesand some turbulence properties in a two-dimensional free surface shear flow. The exper-iments were performed under the condition of greater aspect ratio than 10, to obtain thetwo-dimensional flow in a rectangular open channel.The experimental results show that the mean velocity profiles are well described bythe logarithmic distribution, and that the Karman constant k and the integral constantAs, Ar may be treated as constants which are independent of the Reynolds number, theFroude number and the relative roughness height. However, the values of theses con-stants in a free surface shear flow are somewhat different from these in a pipe flow, andthe following values may be recommended, that is, k=0.33, As=2.2 and Ar=8.3.According to the Reynolds number similarity, the turbulence properties are normalizedwith the flow depth, the friction velocity and the local mean velocity. And the verticaldistribution of the normalized turbulence properties, such as, the turbulence intensity, theEulerian mean scale, the energy dissipation rate, the Taylor's dissipation scale, the Kol-mogorov's lacal scale, the Lagrangian mean scale and the turbulent diffusion coefficientare described by the universal function of the relative depth, respectively.

Open-channel turbulent flows often present three dimensional aspects because of the exis-tence of the longitudinal eddies. The longitudinal eddies can be separated into those of the firstkind (originated from the shape of the cross-section) and those of the second kind (rerated to thebursting phenomenon in the boundary layer).In this paper the characteristics of the longitudinal eddies in the small width-to-depth ratiochannel are investigated using experimental results of the boundary shear stress distribution, sand-ridges visualized by Cameron effect and velocity vectors measured by laser doppler anemome-ter. Experimental results show that the shape of the cross-section has an effect on the arrange-ment, stability and scale of the longitudinal eddies.

This paper deals with the characteristics of open channel flows around a circular cylinder, which are investigated on the basis of experimental results. The measurments of velocity weremade by a hot-film flowmeter, and the measurements of the bottom shear stress by a flush-mounting-probe. From these experimental data, some qualitative properties of the structure of turbulence ina wake are revealed, that is, the distribution of mean velocity, Reynolds stress and the eddy viscositynear the bed can be approximated by the result of two dimensional wake.

The graph theory is used to express the complex structure of pipe and channel networks inthis paper. First, a generalized new method and its applicability to analize steady flows in pipenetworks are discussed. This new method is also applied to steady flows in open-channel net-works. As for unsteady flows in open-channel networks, another new method is proposed. Thesenew methods for open-channel networks are applied to numerical simulations of a river networkin Osaka City and computed values are compared with observed ones.

This paper describes an experimental investigation of the spatial structure of turbulence ina free surface shear flow, carried out at the Nobi agricultural canal, using 4 current meters of apropeller-dynamo type. A convective process of turbulence is investigated through a techniqueof the space-time correlation, with and without frequency filtering, for the longitudinal componentof the velocity fluctuation.The experimental results are as follows. 1) Different turbulent spectral components of anopen channel flow are convected with different velocity, that is, the large scale disturbances nearthe free surface are convected more slowly than the small scale ones. 2) The departure of the fro-zen pattern in the period of the disturbance is remarkable for the disturbance of long period, but, in the same distance, it is remarkable for the disturbance of short period.

The hydraulic similitude to guarantee any scale model test for one-dimensional flowsin pipes and open channels can be derived from one-dimensional equations of continuity, energy or linear momentum in the control volume method of hydraulic analysis.Recently, the first author has derived the exact formulation of one-dimensional systemof equations of continuity, energy and linear momentum in the curvilinear orthogonalcoordinates from the original system in theoretical hydrodynamics, and the authors haveshown a special system of equations for the open channel flow in a rectangular channel.The results obtained indicate that the classical dynamic equation must be supplementedby additional terms concerning three-dimensional variations of transverse velocity andstage in the unsteady behaviour, which suggests the classical treatment for the hydraulicsimilitude of unsteady open channel flows should be modified. This paper treats withthe order effects of additional terms to the classical equation for the unsteady open channelflow and the derivation of new formulation for the hydraulic similitude of unsteady openchannel flows.Preliminary experimentations made in a laboratory test flume will also verify thetheoretical results and predict careful treatments for proceeding the hydraulic scale testwith distorted dimensions.

This paper describes the turbulence characteristies of curved flows on the basis ofthe results of velocity measurements by a small propeller type current-meter. Themeasurements were conducted in two kinds of 1800 curved open channels with 50 cm inwidth and different central radii of 50cm and 150cm each other under conditions ofsupercritical flows. The turbulence characteristics obtained from the statistical analysisof longitudinal velocity component are summarized as follows.The intensity and the length scale of turbulence decrease in the curved and thedownstream straight reaches except the outer part of the inlet region of the curved reachwith the smaller central radius. In the outer part of the region, the turbulence intensityincrease, but the r. m. a. of the velocity fluctuation are no more than that of the upperstraight reach and the turbulence scale also decrease. The decrease of turbulence inte-nsity and scale is due to the decrease of energy spectral density in the lower frequencyrange.

Studies on the effects of a turbulent wall shear are b coming to be required in the fields of hydraulics. This paper plesents the power spectra of the wall shear flucturations computed from directly measured bottom shear in an open channel. The obtained spectra show that there exists two regions in which the spectral laws of shear are k3 and k9 in a lower wave number range, where k is the wave number. It seems that the spectral laws of shear k3 and k9 correspond to the spectral Jaws of energy k1 and k4 in a theory of isotropic turbulence, respectively.