Haruo Higuchi

Horizontal turbulent diffusivity in the sea

Abstract New methods are proposed to estimate horizontal turbulent diffusivity by excluding the effect of shear flow from the results of diffusion experiments using dye or floats in the sea. The rate of change of apparent variances of dye spreading or float dispersion depends mainly on the vertical or horizontal shear of current in the field. The horizontal turbulent diffusivity can be calculated by the rate of change of real variances of dye clouds or floats that exclude the effects of shear flow.

TRANSFORMATION OF TSUNAMIS IN A COASTAL ZONE

A significant portion of the damage by hurricanes is the storm surges. The National Weather Service has developed a dynamical-numerical model to forecast hurricane storm surges. The model is used operationally for prediction, warning, and planning purposes. The model requires fixed oceanographic and real time meteorological input data. The oceanographic data were prepared for the Gulf and East coasts of the U.S. and are stored as an essential part of the program. Meteorological data for any tropical storm are supplied by the forecasters or planners using the model. The model was applied to hurricane Camille 1969. Comparison between the observed and computed surges for Camille was satisfactory for prediction purposes.The main consideration in harbor master planning is to maximize the amount of time that the harbor can be used. The potential level of harbor utilization can be evaluated by analyzing vessel performance during harbor operations in terms of the range of imposed environmental conditions. The harbor utilization level is expressed statistically as the probable amount of time that the harbor can be used as planned.The design and construction of a major ocean outfall and diffuser system for disposal of wastewater effluents is a complex process involving an interplay of requirements originating from various disciplines. These include, among others, considerations of physical oceanography, mixing and dispersion, treatment processes, regulatory requirements, marine geology, economics and construction. The recently completed Sand Island Outfall and the newly designed Barbers Point Outfall are both on the southern coast of the island of Oahu, Hawaii, and are designed for treated sewage effluents from the densely populated portion of the City and County of Honolulu. In this paper, some design considerations of these outfalls will be examined. The emphasis in this paper is on the hydrodynamics, although other design aspects are also discussed briefly.The height of dikes and other coastal structures can only be calculated after determination of the wave run-up. Several formulas for the calculation of wave run-up are developed after model tests as a rule. But the influences of scale effects and natural wind conditions are practically unknown. To clear these questions further investigations and especially field measurements should be carried out. By measuring the markerline of floating trash on the slope of the seadikes the maximum wave run-up could be found out after four storm surges in 1967 and 1973In two graphs it will be shown that on the tidal flats the run-up depends on the waterdepth. The run-up was higher than it could be expected after model tests of 1954. With a newly developed special echo sounder the run-up could be measured in January 1976. The waves and the run-up could be registrated synchronously during two severe storm surges. As shown in Fig. 9 it was found a logarithmic distribution of the wave height, wave period and the higher part of the wave run-up. The found wave run-up is considerably higher than estimated before. The measured 98 % run-up is found about twice the computed value. That is an interesting and important result of the first synchronous recording of wave run-up on sea dikes.In March 1972 the authors firm in association with two Portuguese firms of consulting engineers, Consulmar and Lusotecna, were appointed by the Portuguese Government agency Gabinete da Area de Sines to prepare designs for the construction of a new harbour at Sines on the west coast of Portugal. The location is shown in Figure 1. The main breakwater, which is the subject of this paper, is probably the largest breakwater yet built, being 2 km long and in depths of water of up to 50 m. It is exposed to the North Atlantic and has been designed for a significant wave height of 11 m. Dolos units invented by Merrifield (ref. 1) form the main armour. The project programme required that studies be first made of a wide range of alternative layouts for the harbour. After the client had decided on the layout to be adopted, documents were to be prepared to enable tenders for construction to be invited in January 1973. This allowed little time for the design to be developed and only one series of flume tests, using regular waves, was completed during this period. Further tests in the regular flume were completed during the tender period and a thorough programme of testing with irregular waves was commenced later in the year, continuing until August 1974 when the root of the breakwater was complete and the construction of the main cross-section was about to start. The model tests, which were carried out at the Laboratorio Nacional de Engenharia Civil in Lisbon, were reported by Morals in a paper presented to the 14th International Coastal Engineering Conference in 1974. (ref. 2)Estuaries may be sequentially classified into highly stratified, moderately mixed and vertically homogeneous. An important difference between moderately stratified or vertically homogeneous estuaries, and highly stratified estuaries (salt wedges) is that, in the former, tidal currents are sufficient to cause turbulent mixing of fresh water and sea water over the full depth of the estuary. In the latter, a distinct interface or interfacial layer exists which separates the two nearly homogeneous layers. The vertical advectlon of salt in this two-layer flow is the dominant process in maintaining the salt balance. This paper presents an analytical model describing this process. Experiments have been conducted in the laboratory to compare with the developed theory.

On the Scale Effects of the Hydraulic Tidal Model —A Comparative Study of two Seto Inland Sea Models—

ABSTRACTThe scale effect on the tides, tidal currents, residual flows and the diffusions in the Seto Inland Sea is studied by use of two models, that is, the larger model with the horizontal and vertical scales of 1/2000 and 1/159, and the smaller model with those of 1/50000 and 1/500 respectively. The semidiurnal (M2) tide was generated in the models. The horizontal distributions of tidal range in both models coincide with that in the prototype after adding some adequate artificial roughness in the models. The M2 constituent of the tidal current in the smaller model is larger by 20 to 50% than that in the larger model. The tidal residual circulation develops well in several bays in the both models and the pattern of circulation is quite similar to each other, though the strength of circulation in the smaller model is almost two times as strong as in the larger model.The difference in the amplitude of the tidal currents in the both models dose not affect the distribution of the tidal range because it is c...

EXPERIMENTAL STUDIES OF TIDAL FLOW AND DIFFUSION

The steady state profile of the longshore current induced by regular, obliquely incident, breaking waves, over a bottom with arbitrary parallel bottom contours, is predicted. A momentum approach is adopted. The wave parameters must be given at a depth outside the surf zone, where the current velocity is very small. The variation of the bottom roughness along the given bottom profile must be prescribed in advance. Depth refraction is included also in the calculation of wave set-down and set-up. Current refraction and rip-currents are excluded. The model includes two new expressions, one for the calculation of the turbulent lateral mixing, and one for the turbulent bottom friction. The term for the bottom friction is non-linear. Rapid convergent numerical algorithms are described for the solution of the governing equations. The predicted current profiles are compared with laboratory experiments and field measurements. For a plane sloping bottom, the influence of different eddy viscosities and constant values of bottom roughness is examined.The calculation of turbulent flow using Naviers equations assumes the introduction of a turbulent viscosity coefficient the value of which is normally constant, conforming with Boussinesqs hypothesis. It was shown that setting aside this hypothesis, a velocity profile quite different to that resulting from the classic theory is obtained in the case of flow induced by wind. This result appears to be confirmed by the tests carried out in the Mediterranean. The advantage of this method is that it gives the vertical turbulent diffusion which is of particular interest to pollution studies.In the numerical method of prediction of wind waves in deep water, Hasselmanns nonlinear interaction theory is applied. This method assumes the energy balance of individual component waves. However, the total energy balance must exist in the transformation of irregular waves in shoaling water. In this investigation, experiments were carried out on the transformations in shoaling water of composite waves having two components and random waves having one or two main peaks. It was found that the elementary component wave height of the composite waves and the elementary peak power of the random waves decrease with decrease in the water depth. This reason can be explained qualitatively by the theory of the elementary component wave height change of finite amplitude waves in shoaling water. The secondary component wave height of the composite waves and the secondary peak power of the random waves increase with decrease in the water depth. This can be explained qualitatively by Hamadas theory of nonlinear interaction in uniform depth.Experiments have been carried out by using non-breaking waves and breaking waves to investigate the wave forces on a vertical circular cell located in the shallow water. Based on the experimental data, the drag coefficient and the inertia coefficient of a circular cylinder and the curling factor of breaking waves are estimated, and the computation methods of wave forces are examined. As a result, it is shown that the phase lag of inertia forces behind the accelerations of water particles should be considered for the estimation of the drag coefficient as well as the inertia coefficient. In addition the previous formula of the maximum breaking wave forces acting on a cell or a pile is revised by introducing the effects of the above-mentioned phase lag and another phase difference, both of which are functions of the ratio of the cell diameter to the wave length. • It is confirmed that the proposed formula is applicable even to the large cell with the diameter comparable to the wave length. INTRODUCTION Many studies have been done on the impulsive pressures acting on a vertical wall, but there has been very little investigation of breaking wave forces on a cell-type structure. The breaking wave forces should be taken into consideration all the same in the design of pile-type or cell-type structures in nearshore area, because breaking waves cause extreme shock pressures on a cell structure asThe air bubble plume induced by the steady release of air into water has been analyzed with an integral technique based on the equations for conservation of mass, momentum and buoyancy. This approach has been widely used to study the behavior of submerged turbulent jets and plumes. The case of air-bubble induced flow, however, includes additional features. In this study the compressibility of the air and the differential velocity between the rising air bubbles ,and the water are introduced as basic propertie s of the air bubble plume in addition to a fundamental coefficient of entrainment and a turbulent Schmidt number characterizing the lateral spreading of the air bubbles. Theoretical solutions for twoand three-dimensional air-bubble systems in homogeneous, stagnant water are presented in both dimensional and normalized form and compared to existing experimental data. The further complication of a stratified environment is briefly discussed since this case is of great practical interest. This paper is to be considered as a progress report, as future experimental verification of various hypotheses is needed.

HORIZONTAL DIFFUSION IN A TIDAL MODEL

The steady state profile of the longshore current induced by regular, obliquely incident, breaking waves, over a bottom with arbitrary parallel bottom contours, is predicted. A momentum approach is adopted. The wave parameters must be given at a depth outside the surf zone, where the current velocity is very small. The variation of the bottom roughness along the given bottom profile must be prescribed in advance. Depth refraction is included also in the calculation of wave set-down and set-up. Current refraction and rip-currents are excluded. The model includes two new expressions, one for the calculation of the turbulent lateral mixing, and one for the turbulent bottom friction. The term for the bottom friction is non-linear. Rapid convergent numerical algorithms are described for the solution of the governing equations. The predicted current profiles are compared with laboratory experiments and field measurements. For a plane sloping bottom, the influence of different eddy viscosities and constant values of bottom roughness is examined.The calculation of turbulent flow using Naviers equations assumes the introduction of a turbulent viscosity coefficient the value of which is normally constant, conforming with Boussinesqs hypothesis. It was shown that setting aside this hypothesis, a velocity profile quite different to that resulting from the classic theory is obtained in the case of flow induced by wind. This result appears to be confirmed by the tests carried out in the Mediterranean. The advantage of this method is that it gives the vertical turbulent diffusion which is of particular interest to pollution studies.In the numerical method of prediction of wind waves in deep water, Hasselmanns nonlinear interaction theory is applied. This method assumes the energy balance of individual component waves. However, the total energy balance must exist in the transformation of irregular waves in shoaling water. In this investigation, experiments were carried out on the transformations in shoaling water of composite waves having two components and random waves having one or two main peaks. It was found that the elementary component wave height of the composite waves and the elementary peak power of the random waves decrease with decrease in the water depth. This reason can be explained qualitatively by the theory of the elementary component wave height change of finite amplitude waves in shoaling water. The secondary component wave height of the composite waves and the secondary peak power of the random waves increase with decrease in the water depth. This can be explained qualitatively by Hamadas theory of nonlinear interaction in uniform depth.Experiments have been carried out by using non-breaking waves and breaking waves to investigate the wave forces on a vertical circular cell located in the shallow water. Based on the experimental data, the drag coefficient and the inertia coefficient of a circular cylinder and the curling factor of breaking waves are estimated, and the computation methods of wave forces are examined. As a result, it is shown that the phase lag of inertia forces behind the accelerations of water particles should be considered for the estimation of the drag coefficient as well as the inertia coefficient. In addition the previous formula of the maximum breaking wave forces acting on a cell or a pile is revised by introducing the effects of the above-mentioned phase lag and another phase difference, both of which are functions of the ratio of the cell diameter to the wave length. • It is confirmed that the proposed formula is applicable even to the large cell with the diameter comparable to the wave length. INTRODUCTION Many studies have been done on the impulsive pressures acting on a vertical wall, but there has been very little investigation of breaking wave forces on a cell-type structure. The breaking wave forces should be taken into consideration all the same in the design of pile-type or cell-type structures in nearshore area, because breaking waves cause extreme shock pressures on a cell structure asThe air bubble plume induced by the steady release of air into water has been analyzed with an integral technique based on the equations for conservation of mass, momentum and buoyancy. This approach has been widely used to study the behavior of submerged turbulent jets and plumes. The case of air-bubble induced flow, however, includes additional features. In this study the compressibility of the air and the differential velocity between the rising air bubbles ,and the water are introduced as basic propertie s of the air bubble plume in addition to a fundamental coefficient of entrainment and a turbulent Schmidt number characterizing the lateral spreading of the air bubbles. Theoretical solutions for twoand three-dimensional air-bubble systems in homogeneous, stagnant water are presented in both dimensional and normalized form and compared to existing experimental data. The further complication of a stratified environment is briefly discussed since this case is of great practical interest. This paper is to be considered as a progress report, as future experimental verification of various hypotheses is needed.