Abstract: Mixing and transport of a stratifying scalar are investigated at a density interface imbedded in a turbulent shear flow. Steady-state interfacial shear flows are generated in a laboratory water channel for layer Richardson numbers, Ri, between about 1 and 10. The flow field is made optically homogeneous, enabling the use of laser-induced fluorescence with photodiode array imaging to measure the concentration field at high resolution. False-colour images of the concentration field provide valuable insight into interfacial dynamics: when the local mean shear Richardson number, Ri_s, is less than about 0.40–0.45, interfacial mixing appears to be dominated by Kelvin–Helmholtz (K–H) instabilities; when Ri_s is somewhat larger than this, interfacial mixing appears to be dominated by shear-driven wave breaking. In both cases, vertical transport of mixed fluid from the interfacial region into adjacent turbulent layers is accomplished by large-scale turbulent eddies which impinge on the interface and scour fluid from its outer edges. Motivated by the experimental findings, a model for interfacial mixing and entrainment is developed. A local equilibrium is assumed in which the rate of loss of interfacial fluid by eddy scouring is balanced by the rate of production (local mixing) by interfacial instabilities and molecular diffusion. When a single layer is turbulent and entraining, the model results are as follows: in the molecular-diffusion-dominated regime, δ/h ~ Pe^(−1/2) and E ~ Ri^(−1)Pe^(−1/2); in the wave-breaking-dominated regime, δ/h ~ Ri^(−1/2) and E ~ Ri^(−3/2); and in the K–H-dominated regime, δ/h ~ Ri^(−1) and E ~ Ri^(−2), where δ is the interface thickness, h is the boundary-layer thickness, Pe is the Péclet number, and E is the normalized entrainment velocity. In all three regimes, the maximum concentration anomaly, Γ_m ~ Ri^(−1). When both layers are turbulent and entraining, E and δ depend on combinations of parameters from both layers.

Publication: Journal of Fluid Mechanics Vol.: 273ISSN: 0022-1120

ID: CaltechAUTHORS:20160418-125123356

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Abstract: The flow structure and entrainment mechanisms in the far field of a round vertical buoyant jet have been studied experimentally by use of an optical technique based on laser-induced fluorescence (LIF). A large number of essentially instantaneous tracer concentration profiles were recorded for each experimental run by combining LIF with linear photodiode array imaging and high-speed digital data acquisition. Analysis of the resulting high-resolution flow images indicates that the far-field region is dominated by the periodic passage of structures spanning the entire radial flow extent. Ambient fluid is entrained by vortical motions and is transported to regions deep into the flow interior. Correlation analysis discloses that the passage frequency of the structures scales with the local mean velocity and flow width. Conditional averaging of the data indicates that the downstream frontal region of the structure is well mixed and at higher concentration level than the back and side regions where ambient fluid is intermittently present. This results in an axial concentration gradient within the structure, analogous to the ramp-like pattern previously observed in heated air jets. In comparison to the momentum-driven flow the ambient fluid presence in the flow interior is greatly increased when body forces are the driving mechanism. This appears to result from the influence of buoyancy forces in the production of turbulent vortices at the integral scale. An important feature of both the momentum-driven and buoyancy-driven flows investigated is the strongly intermittent character of the concentration field. This raises the issue of the appropriateness of gradient-diffusion theories for the description of such flows.

Publication: Journal of Fluid Mechanics Vol.: 209ISSN: 0022-1120

ID: CaltechAUTHORS:20160418-152805105

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Abstract: The axial and radial velocity components w and u, and the concentration c of a Rhodamine 6G dye were measured simultaneously in a turbulent buoyant jet, using laser-Doppler anemometry combined with a recently developed laser-induced-fluorescence concentration measurement technique. These non-intrusive techniques enable measurements in a region of plume motion where conventional probe-based techniques have had difficulties. The results of the study show that the asymptotic decay laws for velocity and concentration of a tracer transported by the flow are verified experimentally in both jets and plumes. The momentum and volume fluxes and the mean dilution factor are determined in dimensionless form as a function of the normalized distance from the flow source. Contradictory results from earlier experimental plume investigations concerning the decay laws of w and c and the plume width ratio b_c/b_w are discussed. The turbulence properties and the transition from momentum-driven jets to buoyancy-driven plumes are presented. The turbulence is found to scale with the mean flow as predicted by dimensional analysis and self-similarity. Buoyancy-produced turbulence is found to transport twice as much tracer as jet turbulence. Although velocity statistics in jets and plumes are found to be highly self-similar there is a strong disparity in the distribution of tracer concentration in the two flows. This occurs in the time-average mean flows as well as the r.m.s. turbulent quantities. Instantaneous concentration fluctuations are found to exceed time averages by as much as a factor of 3. The experimental results should provide a reasonable basis for validation of computer models of axisymmetric plumes.

Publication: Journal of Fluid Mechanics Vol.: 195ISSN: 0022-1120

ID: CaltechAUTHORS:20160418-152319876

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Abstract: The effects of a sharp density interface and a rigid flat plate on oscillating-grid induced shear-free turbulence were investigated experimentally. A two-component laser-Doppler velocimeter was used to measure turbulence intensities in and above the density interface (with matched refractive indices) and near the rigid flat plate. Energy spectra, velocity correlations, and kinetic energy fluxes were also measured. Amplification of the horizontal turbulent velocity, coupled with a sharp reduction in the vertical turbulent velocity, was observed near both the density interface and the flat plate. These findings are in agreement with some previous results pertaining to shear-free turbulence near rigid walls (Hunt & Graham 1978) and near density interfaces (Long 1978). The results imply that, near the density interface, the turbulent kinetic energy in the vertical velocity component is only a small fraction of the total turbulent kinetic energy and indicate that the effects of the anisotropy created by the density interface or the flat plate are confined to the large turbulence scales.

Publication: Journal of Fluid Mechanics Vol.: 189ISSN: 0022-1120

ID: CaltechAUTHORS:20160418-151749264

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Abstract: The interaction of a sharp density interface with oscillating-grid-induced shear-free turbulence was experimentally investigated. A linear photodiode array was used in conjunction with laser-induced fluorescence to measure the concentration of dye that was initially only in the less dense layer. A laser-Doppler velocimeter was used to measure the vertical velocity in and above the density interface at a point where the dye concentration was also measured. Potential refractive-index-fluctuation problems were avoided using solutes that provided a homogeneous optical environment across the density interface. Internal wave spectra, amplitudes and velocities, as well as the vertical mass flux were measured. The results indicate that mixing occurs in intermittent bursts and that the gradient (local) Richardson number remains constant for a certain range of the overall Richardson number R_j, defined in terms of an integral lengthscale, buoyancy jump and turbulence intensity. The spectra of the internal waves decay as f^(−3) at frequencies below the maximum Brunt-Väisälä frequency. These findings give support to a model for oceanic mixing proposed by Phillips (1977) in which the internal waves are limited in their spectral density by sporadic local instabilities and breakdown to turbulence. The results also indicate that, for a certain R_j range, the thickness of the interfacial layer (normalized by the integral lengthscale of the turbulence) is a decreasing function of R_j. At sufficiently high R_j the interfacial thickness becomes limited by diffusive effects. Finally, we discuss a simple model for entrainment at a density interface in the presence of shear-free turbulence.

Publication: Journal of Fluid Mechanics Vol.: 189ISSN: 0022-1120

ID: CaltechAUTHORS:20160418-133752149

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Abstract: The stochastic completeness of the kinetic coagulation equation depends on the extent of correlations between particle properties. Such correlations are induced by the coalescence process that causes spatial inhomogeneities in the number concentration of the particles, and are particularly strong in poorly mixed suspensions. A Monte Carlo simulation of the coalescence process is used to evaluate the suitability of the kinetic coagulation equation to simulate the coalescence process using Brownian diffusion, fluid shear and differential sedimentation collision kernels. It is demonstrated that the outcome of the kinetic equation matches well the true stochastic averages, unless the number concentration of particles involved is very small. In that case, the discrepancies between the two approaches are substantial in the large end of the particle size spectrum.

Publication: Journal of the Atmospheric Sciences Vol.: 41 No.: 16 ISSN: 0022-4928

ID: CaltechAUTHORS:VALjas84

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Abstract: A method for the Monte Carlo simulation, by digital computer, of the evolution of a colliding and coagulating population of suspended particles is described. Collision mechanisms studied both separately and in combination are: Brownian motion of the particles, and laminar and isotropic turbulent shearing motions of the suspending fluid. Steady-state distributions are obtained by adding unit-size particles at a constant rate and removing all particles once they reach a preset maximum volume. The resulting size distributions are found to agree with those obtained by dimensional analysis (Hunt 1982).

Publication: Journal of Fluid Mechanics Vol.: 143ISSN: 0022-1120

ID: CaltechAUTHORS:20120709-072813258

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Abstract: Hunt (1982) and Friedlander (1960a, b) used dimensional analysis to derive expressions for the steady-state particle-size distribution in aerosols and hydrosols. Their results were supported by the Monte Carlo simulation of a non-interacting coagulating population of suspended spherical particles developed by Pearson, Valioulis & List (1984). Here the realism of the Monte Carlo simulation is improved by accounting for the modification to the coagulation rate caused by van der Waals', electrostatic and hydrodynamic forces acting between particles. The results indicate that the major hypothesis underlying the dimensional reasoning, that is, collisions between particles of similar size are most important in determining the shape of the particle size distribution, is valid only for shear-induced coagulation. It is shown that dimensional analysis cannot, in general, be used to predict equilibrium particle-size distributions, mainly because of the strong dependence of the interparticle force on the absolute and relative size of the interacting particles.

Publication: Journal of Fluid Mechanics Vol.: 143ISSN: 0022-1120

ID: CaltechAUTHORS:20120709-080438815

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Abstract: A method for the numerical simulation of a rectangular sedimentation basin operating under steady or unsteady conditions is described. The computer model follows the spatial and temporal development of the influent particle size distribution toward the outlet of the tank. It is based on the fundamental mechanisms which govern particle motion and growth. The model accounts for the variability of the flow field and the particle size distribution in the tank and, from the local development of the particle size spectrum, predicts the overall performance of the settling basin.

Publication: Environmental Science and Technology Vol.: 18 No.: 4 ISSN: 0013-936X

ID: CaltechAUTHORS:20140922-103532038

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Abstract: A numerical model of a rectangular settling tank is used to study the importance of selective variables on the settling process while demonstrating the capabilities of the computer simulation. The computer model follows the spatial and temporal development of the influent particle size distribution toward the outlet of the tank based on the fundamental mechanisms which govern particle motion and growth. It is shown that both the removal efficiency of a flocculating suspension and the effluent particle size distribution are influenced strongly by the mass concentration in the inflow, the influent particle size distribution, the floc size-density relationship, and the collision efficiencies of the particles. It is suggested that future experimental work should focus on obtaining information on the size-density relationship, the reentrainment of the deposits, and the collision efficiencies of floes.

Publication: Environmental Science and Technology Vol.: 18 No.: 4 ISSN: 0013-936X

ID: CaltechAUTHORS:20140917-101040541

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Abstract: A practical limitation of the application of Smoluchowski's classical estimate for the collisions probability of two diffusing spherical particles in Brownian motion is the non-consideration of interparticle forcves. For suspended particles in water such forces can arise from the disturbance the particle causes in the fluid (hydrodynamic forces), from the cloud of ions which surround an electrically charged particle (double layer forces) or they can be of molecular origin (van der Waals forces). In this paper corrections to Smoluckhowski's collision probability are computed when such forces operate Scoluchowski's collision probability are computed when such forces operate between two approaching particles of various sizes. Results for several values of the van der Waals energy of attraction and the ionic strength of the electrolyte are presented in a way convenient for particle collision modeling.

Publication: Advances in Colloid and Interface Science Vol.: 20 No.: 1 ISSN: 0001-8686

ID: CaltechAUTHORS:20140922-104615615

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Abstract: Turbulent jets are fluid flows produced by a pressure drop through an orifice. Their mechanics, although studied for over fifty years, has recently received research attention that has resulted in a much improved understanding of the process by which they entrain surrounding fluid. Turbulent plumes are fluid motions whose primary source of kinetic energy and momentum flux is body forces derived from density inhomogeneities. Plumes have not been studied in the same detail as jets but nevertheless there have been some recent gains in the understanding of their mechanics. In this article we will review this progress, especially in relation to how jets and plumes interact with environmental factors, such as density stratification or uniform motion of the ambient fluid. As will become evident, many problems remain and, in some circumstances, we simply cannot describe precisely what does occur. In such cases we will try to provide current references and suggest approaches for future research.

Publication: Annual Review of Fluid Mechanics Vol.: 14ISSN: 0066-4189

ID: CaltechAUTHORS:20161019-133155006

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Abstract: The mechanics of submerged turbulent jets has received a good deal of research attention. This work has resulted in an understanding of the process by which jets grow by entrainment of surrounding fluid. While of direct scientific interest, this work has practical implications that are of interest to engineers concerned with the design of systems that utilize jet concepts. A fluid motion is called a jet if its primary source of kinetic energy and momentum flux is a pressure drop through an orifice. A fluid motion whose main source of kinetic energy and momentum flux is body forces is called a plume. The flows, whose motion is in transition from a jet to a plume, are called a forced plume or a buoyant jet. Almost all jets whose fluid density differs from the ambient fluid density become plumes. This chapter discusses the mechanics of jets and plumes whose interactions with their environment are self-generated. It discusses how such jets and plumes are influenced by changes in the environment such as density stratification of the surrounding fluid, uniform motion of the ambient fluid, or turbulence within the ambient fluid.

No.: 6
ID: CaltechAUTHORS:20170718-090132397

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Abstract: It is apparent from the literature on LNG spills that there is a considerable lack of knowledge in many areas of technical importance to the safety assessment of LNG receiving terminals. For this reason, a thorough critical review of the state-of-the-art regarding the technical aspects of LNG spill evaluation is in preparation. The purpose of this review is to focus attention on these aspects of the problem that are least understood and which are crucial to a proper assessment of the hazards. It is realized that ERDA has already conducted an LNG Safety and Control Workship, the outcome of which was a set of conclusions and recommendations regarding the safety and control issues of LNG operations.

No.: 80-7
ID: CaltechAUTHORS:20120928-152411731

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Abstract: The successful development of western coal and oil shale deposits is dependent, to a significant degree, on the availability of adequate water supplies. EQL is involved in a study of the aggregate effects of various energy activities in the upper Colorado River Basin on downstream water quantity and quality. These activities will tend to reduce the available water in the river, and could increase its salinity, which is already so high as to interfere with downstream domestic and agricultural use.

No.: 80-2
ID: CaltechAUTHORS:20120928-120924127

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Abstract: The successful development of Western coal and oil shale deposits is dependent, to a significant degree, on the availability of adequate water supplies. EQL is involved in a study of the aggregate effects of various energy activities in the upper Colorado River Basin on downstream water quantity and quality. These activities will tend to reduce the available water in the river, and could increase its salinity, which is already so high as to interfere with downstream domestic and agricultural use.

No.: 79-5
ID: CaltechAUTHORS:20120928-162004047

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Abstract: This book is an outgrowth of research contributions and teaching experiences by all the authors in applying modern fluid mechanics to problems of pollutant transport and mixing in the water environment. It should be suitable for use in first year graduate level courses for engineering and science students, although more material is contained than can reasonably be taught in a one-year course, and most instructors will probably wish to cover only selected potions. The book should also be useful as a reference for practicing hydraulic and environmental engineers, as well as anyone involved in engineering studies for disposal of wastes into the environment. The practicing consulting or design engineer will find a thorough explanation of the fundamental processes, as well as many references to the current technical literature, the student should gain a deep enough understanding of basics to be able to read with understanding the future technical literature evolving in this evolving field.

ID: CaltechAUTHORS:20200318-080524092

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Abstract: During FY77, with financial support from Los Angeles County, U. S. Geological Survey, Orange County, U. S. Army Corps of Engineers, and discretionary funding provided by a grant from the Ford Foundation, substantial progress was made at EQL and SPL in achieving the objectives of the initial Planning and Assessment Phase of the CIT/SIO Sediment Management Project. The current timetable for completion of this phase is June 1978. This report briefly describes the project status including general administration, special activities, and technical work.

No.: 77-4
ID: CaltechAUTHORS:20140624-145908791

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Abstract: An integral technique suggested for the analysis of turbulent jets by Corrsin & Uberoi (1950) and Morton, Taylor & Turner (1956) is re-examined in an attempt to improve the description of the entrainment. It is determined that the hypothesis of Priestley & Ball (1955), that the entrainment coefficient is a linear function of the jet Richardson number, is reasonable, and that two empirically determined plume parameters are sufficient to describe the transition of buoyant jets to plumes. The results of a series of experiments in which both time-averaged velocity and time-averaged temperature profiles were recorded in a substantial number of plane turbulent buoyant jets of varying initial Richardson numbers are used to verify the basic ideas. In addition, measurements of the mean tracer flux in a series of buoyant jets indicate that as much as 40% of the transport in plumes is by the turbulent flux.

Publication: Journal of Fluid Mechanics Vol.: 81 No.: 1 ISSN: 0022-1120

ID: CaltechAUTHORS:KOTjfm77a

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Abstract: During 1976, with financial support from Los Angeles County, U. S. Geological Survey, and discretionary funding provided by a grant from the Ford Foundation, substantial progress was made at EQL and SPL in achieving the objectives in the initial Planning and Assessment Phase of the CIT/SIO Sediment Management Project. The current timetable for completion of this phase is June 1978. This report briefly describes the project activities during the year including general administration, special activities, and technical work; and is submitted in accordance with the letter of agreement between Los Angeles County and Caltech dated 1 April 1976.

No.: 77-1
ID: CaltechAUTHORS:20140624-133116283

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Abstract: The results of a time series analysis of several years of coastal ocean temperature records are presented for discussion. The records have been analyzed by using digital filtering, covariance and spectral analysis. The low-frequency component of the temperature signal shows a strong seasonal component in southern California. There is little seasonal fluctuation between Point Conception and Pacific Grove. A period of midwinter warming is apparent in southern California. Intermediate frequency components show strong correlations in southern California with the presence of distinct and substantial temperature events occurring almost simultaneously over distances of the order of 200 km. High-frequency components have a large standard deviation in summer (0.8°C) and a low standard deviation in winter (0.4°C); these components are uncorrelated at stations even a few miles apart. Some coastal stations show a strong possible diurnal component; others, including the offshore islands, show no such components. Morro Bay appears to have an extraordinarily large diurnal component of temperature fluctuation. No attempt has been made in this paper to relate these phenomena to other oceanographic or meteorological variables.

Publication: Journal of Geophysical Research Vol.: 81 No.: 12 ISSN: 0148-0227

ID: CaltechAUTHORS:20170419-084049797

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Abstract: This report presents and interpretation of results obtained during the hydraulic model study previously documented in "Hydraulic Modeling of Thermal Outfall Diffusers for the San Onofre Nuclear Power Plant" which described the hydraulic laboratory studies conducted to investigate outfall configurations for the thermal discharge from proposed Units 2 and 3 at the San Onofre Nuclear Generating Station, jointly owned by the Southern California Edison Company and San Diego Gas and Electric Company. A number of different experimental investigations were performed to develop the conceptual design for the new Units 2 and 3 discharge diffusers. The primary reason for the investigations was the new California thermal standards (essentially ambient temperature increment less than 4°F), which in effect precluded the use of shoreline or single outlet discharges for new units and necessitated the use of multiport diffusers. The result of the investigations of different diffuser concepts was the establishment of a preliminary design for the discharge structures for Units 2 and 3, each consisting of a diffuser 2500 ft long containing 76 discharge nozzles with a nominal discharge velocity of 13 ft/sec. This preliminary design was later modified somewhat by the engineers of the Southern California Edison Company (SCE) in consideration of other factors such as structural requirements, cost, construction problems, and more accurate bathymetric details at the site. As a result the final design for each diffuser contains 63 discharge ports of diameters varying from 21.85 to 23.9 inches. The discharge ports are nozzle-riser assemblies at alternate angles of ±25° with respect to the longitudinal axis of the diffuser and 20° up from horizontal. The nozzles are positioned approximately 6 ft from the ocean bottom. The diffusers are aligned perpendicular to shore and extend from approximately 3500 ft to 8500 ft offshore. The performance of the final diffuser design was evaluated in a series of confirming tests. The major results will be summarized and discussed in section 3 of this report. Sections 3 and 4 will also include projections and elaborations on several aspects of the diffuser performance to be expected in the prototype. The possible interactions of the proposed diffuser operation with existing site factors such as ocean currents, water temperature, heat losses, and the existing power plant (Unit 1) will also be discussed in section 4.

ID: CaltechKHR:KH-R-31

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Abstract: Various hydraulic model tests were performed in connection with the design and performance of the offshore thermal outfalls for the San Onofre Nuclear Generating Station (jointly owned by the Southern California Edison Company and the San Diego Gas and Electric Company)near San Clemente, California. These include model investigations of: (i) the multiple port discharges for the proposed Units 2 and 3, (ii) the existing submerged single outlet from Unit 1, (iii) the discharge of heated water from the Units 2 and 3 intakes during heat treatment, and (iv) hydraulic characteristics of discharge ports. On the basis of these investigations, the diffusion structure for each of the proposed new units was designed to be 2500 feet long aligned perpendicular to shore. The diffuser for Unit 3 will extend from 3500 to 6000 feet from shore, and that for Unit 2 from 6000 to 8500 feet from shore. Each diffuser will have 63 discharge nozzles aimed offshore (±25° from the pipe axis, 20° above horizontal). The momentum of the discharge produces and offshore drift of the diluted warm-water plume. The maximum temperature rise on the surface caused by the discharge was found to decrease with increasing longshore current speed, and the discharge momentum from the jets was effective in preventing significant re-entrainment in the event of reversing or low currents. Although the California thermal discharge requirements specify a maximum surface temperature increase of 4°F (beyond 1000 feet from the discharge structure), the laboratory target maximum was established at 2.5°F, to account for possible model-prototype differences and unmodeled effects. The hydraulic model studies showed that the proposed outfall design meets the laboratory target value for a variety of possible longshore current conditions; therefore, it is predicted that the prototype outfall operation will meet the California thermal discharge requirements.

ID: CaltechKHR:KH-R-30

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No.: 4
ID: CaltechAUTHORS:20160121-153353232

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Abstract: Energy use in California in 1969 and its implications for thermal and. air pollution are examined. The State is considered in terms of the energy consumed within each of the eleven designated air basins, both with respect to the source of the energy and its uses. It is shown that 94% of the energy for the State was provided by hydrocarbon fossil fuels, mainly natural gas (50% of total energy supplied) and gasoline (27% of the total). Half of the energy demand for the State was within the 9200 square miles constituting the South Coast Air Basin; 36.5% of the total demand was within Los Angeles County alone. Air pollution emission factors characterizing each fuel source for a given use are compiled in the form of units of emittant per unit of energy. It is shown that some fuels for some purposes are inherently "dirty" energy sources and possible fuel substitutions are suggested. Emissions resulting from the combustion of fuels in 1969 are computed for each air basin. In an attempt to calculate the lowest emissions theoretically possible, that is, the residual pollution when all emitters are as clean as we know how to make them, minimum emission factors for each fuel use are given and the minimum combustion emissions determined. Possible strategies for the reduction of polluting emissions are discussed in some detail. Ambient air heating problems (thermal pollution) from energy released within air basins are considered and the resulting possible changes in ambient air temperature are discussed.

No.: 3
ID: CaltechEQL:EQL-R-3

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Abstract: Solutions are presented for creeping flows induced by two-and three-dimensional horizontal and vertical momentum jets in a linearly stratified unbounded diffusive viscous fluid. These linear problems are solved by replacing the momentum jet by a body force singularity represented by delta functions and solving the partial differential equations of motion by use of multi-dimensional Fourier transforms. The integral representations for the physical variables are evaluated by a combination of residue theory and numerical integration. The solutions for vertical jets show the jet to be trapped within a layer of finite thickness and systems of rotors to be induced. The horizontal two-dimensional jet solution shows return flows above and below the jet and a pair of rotors. The three-dimensional horizontal jet has no return flow at finite distance and the diffusive contribution is found to be almost negligible in most situations, the primary character of the horizontal flows being given by the non-diffusive solution. Stokes's paradox is found to be non-existent in a density-stratified fluid.

Publication: Journal of Fluid Mechanics Vol.: 45 No.: 3 ISSN: 0022-1120

ID: CaltechAUTHORS:20160418-123344546

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Abstract: It is shown that Yih's exact solution for the non-diffusive flow of a non-homogeneous fluid into a sink in a confined porous medium is equivalent to a class of diffusive flows with isopycnic lateral boundaries.

Publication: Journal of Fluid Mechanics Vol.: 36 No.: 1 ISSN: 0022-1120

ID: CaltechAUTHORS:20160418-124620937

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Abstract: A solution is offered for the flow induced by a two-dimensional line sink in a saturated, density-stratified porous medium. It is found that fluid is selectively withdrawn from a thin layer at the elevation of the line sink and not from the entire medium. The velocity distributions predicted by the theory are checked by experiments in a Hele–Shaw cell and good agreement found.

Publication: Journal of Fluid Mechanics Vol.: 33 No.: 3 ISSN: 0022-1120

ID: CaltechAUTHORS:20160418-124108630

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Abstract: The mixing of two miscible fluids in motion in a saturated isotropic porous medium and the stability of the density interface between them has been studied. The density interface was formed by a line source introducing a denser fluid into a uniform confined horizontal flow. It was shown that the half-body thus formed may be approximated to within the density difference by the shape when the densities are equal. The mixing of the two fluids by lateral dispersion along such an interface was investigated experimentally and it was found that up to density differences of at least 1 per cent there was no observable effect on the lateral dispersion coefficient. A theoretical investigation has been made of the stability of the uniform two-dimensional horizontal motion of two miscible fluids of different density in a saturated, isotropic, homogeneous porous medium. The fluid of higher density overlay the lower density fluid and both were moving with the same seepage velocity in the same direction. The analytical solution for the stability was obtained from the continuity equation, Darcy's law and the dispersion equation by investigating the stability of arbitrary sinusoidal perturbations to the velocity vector and the density profile prescribed by the lateral dispersion of one fluid into the other. A stability equation similar to the Orr-Sommerfeld equation was obtained and a neutral stability curve in a wave number-Rayleigh number plane was found by two approximate methods. The growth rates of instabilities were investigated for a linear density profile and it has been found that although the flow was always unstable the growth rates of unstable waves could be so low as to form a quasi-stable flow; examples of such flows have been demonstrated experimentally.

No.: 11
ID: CaltechKHR:KH-R-11

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Abstract: Existing analytical solutions for vertical influent seepage flow to an infinite series of tile drains underlain by an impervious layer do not adequately consider the free surface nor give solutions for the drain diameter (see Figure 1). The theoretical investigations described herein basically sought to find a method whereby an engineer could find the required diameter, depth, and spacing of an adequate tile drainage system when given the ratio of infiltration to soil hydraulic conductivity and the depth of the impervious layer. From a study of the available literature it was decided the problem would be exceedingly difficult to solve exactly but it seemed as if an approximate solution of good accuracy could be obtained by approximating the shape of the impervious layer, where the flow is sluggish, and satisfying the conditions exactly at the free surface, a critical region of flow. Previously published solutions invariably adopt the opposite viewpoint, with a consequent loss in accuracy. The solution to the problem when the impervious layer is at infinite depth had been solved exactly using the rather laborious hodograph technique. This work employs to advantage an image method developed by Davison and Rosenhead (1940). Detailed results are obtained herein for the condition when no water stands over the tile lines and these are given in a graphical form which enables a ready computation of drain depth diameter and spacing when the field data are known (ratio of rate of infiltration to hydraulic conductivity and the depth of the impervious layer). A comparison with field results shows that the solutions are probably as accurate as could be desired. The case which occurs when water stands over the tile lines has not been extensively tabulated for reasons explained in the report. A method is given whereby adequate tile drainage systems may be designed on a long term basis. The design curves given are not for intermittent unsteady flows such as irrigation schemes (a more difficult problem) but should prove exceedingly useful for engineers concerned with land reclamation schemes and marsh drainage.

No.: 9
ID: CaltechKHR:KH-R-9

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