Boundary Layer Growth of Open Channel Flows on a Smooth Bed and its Contribution to Practical Application to Channel Design

The hydraulic behavior of the boundary layer growth, which has been investigated in connection with the practical application to the air-entrainment into flows by turbulence, is concerned in the light of mathematical and physical interpretation made possible by the combination of three basic equations of boundary layer, main flow and discharge in hydrodynamics and of experimental verification conducted at the Hydraulics Laboratory, Engineering Research Institute, Kyoto University, with results of the clear difference between the behavior of boundary layer of open channel flows and that along the flat plate in the unconfined flow. Furthermore, the application to design problem of steep chutes and the hydraulic behavior of flows in transition to the fully developed turbulent flow near an entrance of channel are discussed

The Criterion for Instability of Steady Uniform Flows in Open Channels

In this paper, the instability criterion of steady uniform flows in open channels with any section is derived by considering the time growth or decay of an infinitesimal disturbed motion of fluid surface. The mathematical analysis shows that the criterion by this approach, based upon the momentum equation neglecting the curvature of fluid surface, is identical with the expression of V. V. Vedernikov's criterion for instability of free surface in real fluids, using certain approximations of Saint Venant. It is well interesting to note that this expression of the criterion for instability becomes the same condition to maintain final patterns of roll-waves in steep inclined channels, obtained by argumenting their hydraulic characteristics

General Theory on Steady Behaviours of Open Channel Flows by Means of One Dimensional Procedures of Analysis

This paper concerns with the general theory of steady behaviours of open channel flows by means of the one dimensional procedures of analysis. The theory described herein is essentially formed by the transitional characteristics of steady flows in channel transitions and controls, and it can provide the unified treatment for hydraulic behaviours of gradually varied flows, which mainly treat with the determination of surface profiles of water, and of rapidly varied flows, which are counterpart of gradually varied flows and deal with local variations of flow behaviours occured by sudden changes in channel characteristics

Hydraulic Significance of Transitional Behaviours of Flows in Channel Transitions and Controls : Application of Geometric Theory of Differential Equation to Surface Configuration of Transition Flow in Divergent or Convergent Channels

As one of the research projects of clear formulation in hydraulic characteristics of transitional behaviours from subcritical to supercritical or vice versa, this paper deals with the hydraulic behaviours of channel characteristics in geometry and boundary to the functional variety of channel transitions and controls in divergent or convergent channels. The gradually varied flow in divergent or convergent channels changes its flow regime at a singular point of surface profile equation imposed by particular discharge and channel characteristics, and consequently the theoretical approach in analysis of hydraulic behaviours of transition flow will be established with the application of the geometric theory of differential equation, which is known in problems of non-linear mechanics. The classification of singular points as transitional points and the significance of transitional characteristics of flow passing through a transitional point, and especially from a standpoint of practical hydraulic engineering, those for flows of Chézy and Manning are presented. The present procedure of analysis is applied not only to the flow behaviours discussed in this study but also to the flow with side in- or outflows and similar problems in the hydraulics of open channel flows

Analytical Considerations on Cnoidal and Solitary Waves

In this paper, the mathematical theory on progressive translation waves of the permanent type is developed. The analysis of the second approximation based upon the momentum and energy approaches considering the effects of the vertical acceleration shows that the surface profile of waves is expressed in terms of an elliptic function which is designated as the cn-function, the name cnoidal being derived therefrom as analogous to sinusoidal, and the solitary wave is included as a special case of the cnoidal wave. It should be noticed that the behaviour of cnoidal waves may be reduced to that of classical sinusoidal waves at a special limiting approximation

Hydraulic Efficiency of Flood Detention Pools Evaluated by Means of Mathematical Simulation

The hydraulic efficiency to secure optimization of the flood detention pool system will be treated through mathematical simulation. The mathematical model is approximated by the point-sink virtually located at the center of the deversoir section. Numerical computations show that the optimization of the system in hydraulic efficiency will be given through a combination of the deversoir length and the initial diversion discharge. Furthermore, it is seen the whole pool volume will be nearly constant for any possible combination

Estimation of Dispersion Coefficients on Free Surface by Means of Particle Simulation Method

The present paper deals with a theoretical treatment of the size effect of solid particles on the estimation of dispersion coefficients at the free surface of flow by means of the tracer simulation method and experimental evidences made at a test flume in the laboratory and a navigation canal. The results obtained through experimentations indicate that the fluctuating velocites of solid particles on the free surface are of outstanding periodicity and therefore the Lagrangian correlation coefficient is not simply expressed in terms of an exponential function as done by Taylor, which must be further investigated by more extensive research programs

Interfacial Mixing in Two-Layered System of Fresh and Salt Waters

This paper deals with the physical behaviours of the two-layered system of fresh and salt waters in the light of the mixing at the interface through experimentations. The result obtained in the study reveals that the fetch will be a significant characteristic in the physical process of the interfacial mixing

On the Velocity Defect Law of Open Channel Flow

This paper describes the theoretical procedures for deriving a velocity defect law from the equations of motion and energy for turbulent mean flows in open channels, and the verification of the theoretical results from the experimental data of velocity distribution. Furthermore, by the use of the velocity defect law obtained and the boundary conditions imposed in the region near the wall, the velocity profile of turbulent mean flows in open channels and the mean velocity formula are presented

Hydraulic Performances of a Vertical Gate to Effluxes

This paper concerns hydraulic performances of a vertical gate to free and submerged underflows in the light of the one-dimensional treatment of hydraulic analysis. For the free underflow, main emphasis is placed on the contraction of efflux influential to the stage-discharge relationship for practical uses, through a thorough research of past works added to by further experimentations by the authors. A possible scale effect in physical simulation for the present problem will be also explained. For the submerged underflow, the transition problem from free to submerged flow at the gate will be accented. Some discussions of the discharge coefficient of the gate to the submerged underflow are also made