The paper discusses the state-of-the-art of turbulence modeling and presents possible ways for improvement in the future turbulence models. Based on a set of turbulence closure postulations, a variation of second-order turbulence models, such as the Reynolds stress model (RSM), the algebraic stress model (k-ε-A), and the eddy viscosity model (k-ε-E), are obtained. Examples of prediction made are free shear flows, cavity flows, and flows past an off-set channel. Although a complete turbulence model does not exist at the present time, some prediction capability has been achieved by the secondorder turbulence model. The incompleteness of turbulence modeling may be attributed to the inadequacy of isotropic dissipation and single turbulent scale postulations. Use of multiple turbulence scale concepts, including use of fractal dimension of turbulent eddies may improve turbulence prediction.

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A time series of hydrologic data occurs in well defined groups possessing collective properties of the data. Such a collection of properties can be called a hydrologic pattern. The pattern indicates the inter-relationship between adjacent values within the groups i. e. the persistence. A method of streamflow synthesis based on the concept of pattern recognition was first described by Panu et al. The present paper aims at improving Panu's method using the ISODATA algorithm for pattern analysis to adapt to highly variable hydrologic data in Japan. The new model is applied to monthly precipitation data at Kanazawa, Fukui and Toyama in the Hokuriku region.

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The time of concentration for surface runoff is the important factor of the rational formula. The propagation process of overland flow on a sloping plane for unsteady rainfall is investigated using the kinematic wave theory. The relationship between time of concentration and mean rainfall intensity during the time is theoretically revealed. Based on such a relationship, we propose the method of estimating the time of concentration from the observed hyetographs and hydrographs. The proposed method is verified through applying it to several river basins. We can appropriately account for the runoff characteristics of each basin by comparing the estimated time of concentration with the geographical factors of the basin.

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The flow in an open channel with the non-uniformly sloping bed represents the complicated flow pattern, and the feature of the flows are made clear by the experiments. The following 3 types of flows can be observed: I) the super-critical flow, II) the subcritical flow, and III) the transitional flow with the undular jump. A distinct inner turbulent boundary layer can be observed for each type of flow.
It is important to analyze the flow pattern in the case II) practically. The velocity distribution near the bed follows the 1/n-th power law even in such cases. The bed shear stress can be estimated by turbulent boundary layer equation, and the distribution of vorticity along the stream bed can be estimated by using the power law of velocity distribution.
Consequently, the numerical simulation model based on the above facts is proposed by using the rotational form of Navier-Stokes equation.

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The study on the structure of turbulent flow behind a hemisphere on the bed seems to offer a fundamental information on the energy loss in a boulder-bed stream or the flow characteristics around the river constructions such as the foot protection block.
In this paper, the mean-velocity distribution and turbulence characteristics behind a hemisphere on the bed are studied in detail. The equation of mean-velocity distribution is obtained in the connection between axisymmetric wake and logarithmic law, and the values are compared with those which are observed. The turbulent structure can be explained on the basis of examination on the distributions of Reynolds stress and turbulent kinetic energy, and the energy balance.

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A numerical simulation of the vortex-street model for the coherent structures in a turbulent plane jet and plume is described. Attension is focussed on the topological features of the coherent structures detected experimentally. The model formulation includes the streamwise development of von Karman-type vortex street pattern in terms of the similarity-scaling relationships. The model was found to predict the lateral profiles of mean flow and turbulence quantities including the Reynolds stress, in particular, the differences of their quantities in a jet and a plume reasonably well. The non-symmetric arrangement of coherent structures is the essential mechanism for the production of the Reynolds stress and the entrainment.

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When the sediment supply from the upstream region is suppressed, the bed-surface composed of graded material becomes coarsened as self-adjustment of fluvial bed so as to make the bed-load discharge on it equivalent to the supplied load through non-equilibrium process of bed-load transport for each grain size. When no sediment is supplied, the bed is “armored”; while for finite but suppressed sediment supply the bed is “paved”. Under equilibrium states, no sediment is transported on armored bed, but some on paved bed. Although these two coarsened beds have different properties, both processes can be reasonably described without any difference by a model constituted by pick-up rate and step length for each grain size. Several properties empirically induced from laboratory-experiments and field-observations are discussed based on the present analytical model.

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A theoretical model is presented that describes deepening of a surface mixed layer under the action of wind. The model is an extention of DIM (Dynamic Instability Model) which is applicable for the situation where turbulence produced by wind-induced shear flow rather than water stirring by wind itself controls the entrainment process. Comparative considerations of existing results lead to an idea that the meanings of self-similarity must be followed up for a reasonable modeling. Present study therefore adopts some assumptions on self-similarity not only of density and velocity profiles but also of energetic balance and of mass and momentum transport. Consistency of these assumptions is described through a simple imaginary mixing model associated with K-H instability mixing. The resulted model, including no unknown parameter, successfully predicts the entrainment rate observed by authors in Lake Kasumigaura.

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Under stormy waves on a sandy beach, a flat movable bed may appear when ripples have been washed out. Study on the sheet flow has recently received much attention because huge amount of sand is transported under such condition However, very little understanding has been obtained thus far because of difficulties of the measurement.
To simulate the flow field, the present study has developed a numerical model based on a two-phase flow approach. The calculated results on the fluid velocity, sediment transport velocity and sediment concentration show fairly good agreements with existing experimental results under sheet flow condition. The increase of apparent bottom roughness due to sediment movement is also depicted by the present model.

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The study of bed-load fluctuation due to fluctuating bed shear stress is useful to improve the accuracy of bed-load measurements as well as to inspect the bed-load transport model from the aspect of dynamic response of bed-load motion to the fluctuation of bed shear stress. In this paper, by applying the bed-load model constituted by pick-up rate and step length, the characteristics of stochastic response of bed-load transport to fluctuating bed shear stress are clarified and they are represented by spectral relations. Two examples, bed load fluctuation purely brought about by turbulence (without any other irregularities such as sand waves) and that due to wind-generated surface wave are analyzed. The former is compared with the laboratory data of bed-load fluctuation on a flat bed composed of uniform gravels. This study clarfies that the variation coefficient of bed-load discharge becomes maximum near the critical tractive force and decreases against the bed shear stress. The variance of bed-load discharge can be well predicted on a flat bed by this study.

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An investigation on three-dimensional turbulent structure accompanied with turbulence-driven secondary currents in compound open-channel flows is very important in basic hydraulics as well as river engineering to elucidate the friction law of the flow and sediment transport. In this study, accurate measurements in fully developed compound open-channel flows were conducted by making use of fiber-optic laser Doppler Anemometer (FLDA) and X-type hot-film anemometer. Strong inclined upflow which is associated with a pair of longitudinal vortices is generated in a junction region between a main channel and a flood plain. Primary mean velocity is directly influenced by the secondary currents. The structures of turbulence intensities and Reynolds stresses are observed in detail. The contribution of secondary currents to spanwise momentum transport from the main channel to the flood plain is found to be very large.

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Bed-load transport at unsteady flow is studied. In gravel-bed streams, the direct effect of flow unsteadiness on bed-load motion promotes the transport discharge and brings positive or negative phase shift. Meanwhile, in sand beds with dunes, the relaxation effect suppresses the sediment discharge and causes the phase lag. Particularly in gravel beds, steep hydrograph often appears, and the former effect dominates. The linear analysis reveals that the amplification of bed-load discharge is reversally proportional to the dimensionless time scale of hydrograph, and that it is correlated to the intensity of phase shift. With the increase of the Froude number and the ratio of bed slope to the relative flow depth, the phase shift increases to become positive. The analytical results are qualitatively well consistent with the flume experiments, and they are helpful to obtain semi-empirical predicting formula for unsteady effect of bed-load transport.

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Bed material load is composed of bed-load motion and suspension interacted each other, and the interaction is represented by transition from saltation to suspension, of which quantitative evaluation must support a reasonable description of bed material load transport process. The trajectory of a saltation particle is rather deterministic though it fluctuates due to turbulence. When such a shift of particle's position from the deterministic trajectory is larger than a threshold value, it brings a transition from saltation to suspension. Such an event is explained by a kind of logistic equation deduced from the equation of particle's motion. The probability that the shift of the particle's position from the deterministic trajectory overcomes the threshold value expresses the probability of transition. The probability density per unit time for a bed-load particle to turn into suspension is reasonably calculated and a convenient mathematical expression of the relation between bed shear stress and it is proposed.

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A row of two-dimensional vortices forms in an offshore zone when regular surface waves run up a sloping flat bed. This vortex row has been called the offshore vortex train. Its formation region and quantitative properties have been investigated on the basis of experiments for three slopes of the bed. The vortex train is independent of types of wave breaking and forms when the steepness of deep water waves is smaller than 4.2×10^-2. The formation region can be expressed universally in the H/L and (1+6.4 tan θ) h/L coordinates system, where H is the wave height, L the wavelength, h the water depth and tan θ the bed slope. The net shoreward velocity near the sloping bed is given by an empirical relation independent of tan θ. The horizontal interval between the vortices is expressed by 1.2×10^-2 (tan θ)^1/3 (h/L)^-1 h. The length of the vortex train is dominated by the wavelength and the water depth at the breaking point. The velocity of the vortex movement is given by 3.6×10¹ (tan θ)^2/3 (h/L) U_max. where U_max is the maximum velocity of steady offshoreward flow induced on a horizontal bed.

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Numerical analysis was carried out to obtain the near-bottom flow velocity and the suspended sediment concentration in the wave and current co-existing system. The near-bottom flow velocity was computed by the turbulent boundary layer theory. The shear stress was evaluated by using the time-independent eddy viscosity proposed by Grant-Madsen.
Suspended sediment concentration was computed by the turbulent diffusion theory. The diffusion coefficient was evaluated by using the horizontal and vertical components of flow velocity. The results for near-bottom flow velocity were compared with the laboratory data obtained by Asano et al. For opposing current, as the depth-averaged current velocity exceeds to 1/10-1/5 of the maximum bottom velocity in wave field, the direction of sediment transport is reversed.

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The fall velocity of spherical particle is analyzed theoretically in taking account of the effects of fluid turbulence. The method of Fourier transformation is applied to the theory, from which the mean fall velocity of spheres is predicted in terms of the power spectral density function of vertical fluid oscillation. The method is applied to the suspended sand particles in a river, and the effect of turbulence on the fall velocity of sand particles is found to be negligible in natural geophysical flows as far as the nonlinear drag is concerned.

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The present paper provides a summary of the runoff characteristics in four small neighboring experimental basins with deciduous forest located near Sapporo city. Topographically, these basins consist of V-shaped, about 6m long, steep slopes along stream channels and the following gentle slopes in the middle of the mountain. Through field observation, it was found that the saturated area is apt to occur in the converging head of valleys more easily than in the non-converging steep slopes along the streams. Also the geographic effects on runoff coefficient, peak discharge, the characteristics of the rising or decending part of hydrograph, and storage-discharge relations are discussed. Finally, a synthesized numerical model of runoff is proposed and applied to each basins in order to verify the several results of the field observation stated above.

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Rapid urbanization brought changes to the social and hydrologic conditions of urban watersheds. Present urban drainage plan gives rise to a mismatch between design capacity and real discharge resulting frequent localized floods in the urban watershed. This paper proposes a practical scheme to allocate urban flood control facilities among subbasins with different land use and runoff characteristics. First, capacity of each of alternative facilities is calculated by model simulation (Tank Model). Multi-Criteria Analysis (MCA) is applied to evaluate the order of priority of alternatives, quantifying their representative costs, risks and benefits for flood control. This enables to select the adaptable facilities for each drainage basin. Then, the combination of selected facilities are evaluated by MCA using criteria appropriate for a basinwide approach. Two steps achieve an effective scheme useful for preventing floods in urban watershed.

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A three-dimensional numerical model of the atmosphere incorporating basin orography has been used to study the rainfall distribution in a basin at the storm-event level. It was shown that under a certain balance of time and space scale, the rainfall distribution in a basin is mostly dominated by orographical factors—the main effect being that of ground-forced-induced ascending current of the air. The numerical model was used to estimate the regions in a basin where the ascending current of air can occur, for any wind direction. A new concept called Directional-Probability-of-Storm-Event (DiPoSE) has been proposed by the authors. It was shown that severe storms are likely to occur when wind blows from a high DiPoSE direction, compared to that from a low DiPoSE one. The method of determining the wind direction from a DiPoSE analysis for use in the numerical model, has been used to show the severe rainfall regions in 18 river basins in Japan.

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This study aims at the stochastic evaluation of the water utility function of reservoir with discrete Markovian correlated inflows. Matrix algebraic analysis has been carried out with two-step transition model proposed by the authors. Some statistics have been clarified for the quantitative and sequential characters of the reservoir, for example, the passage time to the first emptiness. Taking account of various characteristics of emptiness, the analytical representation of criteria for effectiveness of water utility in the reservoir is developed, and stochastic consideration are presented. Numerical calculation is carried out for the comparison with the operation of non-prediction, ideal stochastic DP, and linear regression model with inflow information for the case of correlated Binomial inputs. It is found that linear regression model is useful according to the probabilistic judgement of vulnerability of water-shortage.

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This paper aims to discuss experimentally the vertical wave forces acting on a submerged sphere located near the bottom and free surface boundaries. The time variations and maximum values of the vertical wave forces are investigated in relation to the appropriate dimensionless physical quantities.
The lift force caused by the asymmetric pressure distribution and the flow separation dominates over the vertical inertia and drag forces in the case that the sphere is located near the bottom boundary. The lift force enlarges the maximum vertical force. However, in case of the sphere located near the free surface, the free surface proximity effects little to the maximum vertical force.
This paper proposes new equations which estimate well the wave force acting on the sphere located near the boundaries. Good agreement between the measured and calculated wave forces is confirmed.

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The run-up of an incident bore onto a dry bed was investigated by the flow visualization of hydrogen bubbles. The time control of the equipments in millisecond enabled the precise quantitative measurements of the velocity profile at the shoreline. It is shown that the development of the boundary layer is close to that of the Rayleigh problem. The numerical analyses of the characteristics installing this result give good estimate of the run-up phenomena. The local term and the convective term of the momentum equation are shown to be dominant near the front.

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Under severe storm condition, mooring system of a floating body will become taut condition. To estimate motion and mooring tension on such condition, a practical calculation method considering dynamic effect of mooring line is presented. Also experimental study on a floating cylinder moored by relatively small chain is carried out and following conclusions are derived.
Based on simple formulations, presented method can predict experimental results with fairly good agreement. On the other hand, results obtained by static calculation disagree with not only mooring tension but also motion of a floating body.

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An auxiliary statistic is defined for the largest data of a sample using the sample mean and standard deviation. The 5% and 95% nonexceedance levels of this statistic are employed for rejection of distribution fitting to the sample, and these nonexceedance levels are formulated for the Fisher-Tippett I and II, the Weibull, and the log-normal distributions by means of Monte Carlo simulations with a minimum of 10000 samples for each combination of sample size, censoring rate, and distribution functions. The new rejection criteria are effectively applied for the extreme data of annual maximum wind speed at 128 sites, annual maxima of daily rainfall at 58 sites, and peak storm wave heights at 29 sites. The population distributions for these extreme data emerge through this analysis.

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A numerical model has been developed to investigate the nonlinear sloshing motion in a circular basin in response to forced horizontal oscillation. The method is based on the complete boundary value problem of velocity potential and employs no additional assumptions other than those inherent in the potential theory. Experimental observations are in good agreement with the numerical results indicating that the fluid response, both in terms of wave height and hydrodynamic force, is significantly affected by the higher harmonics when the exitation is in the neighborhood of the first characteristic frequency. Moreover, the numerical analyses revealed that the observed secondary peak in the hydrodynamic force response near the predominant peak is caused by the internal resonance with the pumping mode.

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This paper presents a new method for the matched eigenfunction expansions on the boundary-value problem of wave-structure interactions. When the solutions of divided subdomains are matched on the common boundaries, pointwise convergence is specified in the new method instead of mean convergence in the conventional one. Theoretical formulation and computer programing become extremely simple because no tedious evaluations of the integrals related to the eigen functions are needed. Numerical calculations based on both the methods are carried out for floating rectangular bodies and submerged horizontal plates. The mean square errors of the matching conditions are always much smallar in the new method than in the conventional one.

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There exist three solutions for the transient wave-induced porewater pressures in seabed, the seepage flow solution, the exact solution and the boundary region approximation solution of Biot's consolidation equations. Applicability of three solutions is shown graphically in terms of non-dimensional parameter for surf zone conditions. One of the important parameters is the ratio of the shear modulus of solid skelton to the effective bulk modulus of porewater. Another is a non-dimensional quantity proportional to the permeability coefficient and the shear modulus. As the former becomes large and the latter becomes small, the seepage flow solution can not be used but the boundary region approximation solution becomes applicable. Under such situation, the possibility of the vertical effective stress of solid skelton being zero under the wave trough increases. The maximum depth of zero stress is about one half of the wave height.

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In a previous paper (1980), the author derived analytically a friction coefficient for a wave-current coexisting motion as well as its approximation for practical use. This approximate formula is, however, given in an implicit form so that an iteration is always needed in the calculation. The present paper proposes an approximate formula in an explicit expression. The accuracy is found to be within 3% compared with the exact solution, better than that of the previous approximate formula. The persent formula is thereby useful in reducing the number of arithmatric operation in computer programs.

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The Fisher-Tippett type II distribution is presented in a three-parameter formula, which converges to the FT type I as the shape parameter approaches infinity. The best plotting position formula with least bias of return values is selected on the basis of Monte Carlo simulations with 10000 samples for each sample size and shape parameter. The confidence intervals of the estimates of the scale and location parameters based on the least square method are tabulated for the shape parameters of 2.5, 3.33, 5.0, and 10.0. An empirical formula is derived for the standard error of the return values for the above values of the shape parameter. The range of variation of the correlation coefficient between the extreme data and its reduced variate is evaluated for selection of the best fitting distribution.

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