Book•
Turbulent Diffusion in the Environment
28 Feb 1973-
TL;DR: In this article, a simple random walk model is used to describe the effect of particle dispersions through random movement and Brownian motion on the diffusion of particles in a cloud of a small amount of water.
Abstract: I Molecular Diffusion- 11 Introduction- 12 Concentration- 13 Flux- 14 Fick's Law- 15 Conservation of Mass- 16 Instantaneous Plane Source- 17 Some Simple Examples- 18 Diffusion of Finite Size Cloud- 19 'Reflection' at Boundary- 110 Two- and Three-Dimensional Problems- 111 Continuous Sources- 112 Source in Uniform Wind- Appendix to Chapter I- Exercises- References- II Statistical Theory of Diffusion and Brownian Motion- 21 Introduction- 22 Dispersion Through Random Movements- 23 Diffusion with Stationary Velocities- 24 Brownian Motion- 25 Dispersion of Brownian Particles- 26 Simple Random Walk Model- 27 Reflecting Barrier- 28 Absorbing Barrier- 29 Connection of Random Walk to Diffusion Equation- 210 Deposition on Vertical Surfaces- 211 Deposition on Horizontal Surfaces- Exercises- References- III Turbulent Diffusion: Elementary Statistical Theory and Atmospheric Applications- 31 Fundamental Concepts of Turbulence- 32 Field Measurements of Concentration and Dosage- 33 The Statistical Approach to Environmental Diffusion- 34 'Lagrangian' Properties of Turbulence- 35 Consequences of Taylor's Theorem- 36 The Form of the Particle-Displacement Probability Distribution- 37 Mean Concentration Field of Continuous Sources- 38 Apparent Eddy Diffusivity- 39 Application to Laboratory Experiments- 310 Application to Atmospheric Diffusion- 311 Initial Phase of Continuous Plumes- 312 Atmospheric Cloud Growth far from Concentrated Sources- 313 The Non-Stationary Character of Atmospheric Turbulence- 314 The Hay-Pasquill Method of Cloud-Spread Prediction- Exercise- References- IV 'Relative' Diffusion and Oceanic Applications- 41 Experimental Basis- 42 Mean Concentration Field in a Frame of Reference Attached to the Center of Gravity- 43 Probability Distributions of Particle Displacements- 44 Kinematics of Particle Movements in a Moving Frame- 45 Phases of Cloud Growth- 46 History of a Concentrated Puff- 47 Initially Finite Size Cloud- 48 Use of the Diffusion Equation- 49 Horizontal Diffusion in the Ocean and Large Lakes- 410 Application to Diffusion of Sewage Plumes- 411 Vertical Diffusion in Lakes and Oceans- Exercise- References- V Dispersion in Shear Flow- 51 Introduction- 52 Properties of the Planetary Boundary Layer- 53 Particle Displacements in a Wall Layer- 54 Continuous Ground-Level Line Source- 55 Flux and Eddy Diffusivity- 56 Comparison with Experiment- 57 Continuous Point Source at Ground Level- 58 Use of the Diffusion Equation- 59 Elevated Sources- 510 Longitudinal Dispersion in Shear Flow- 511 Shear-Augmented Diffusion in a Channel- 512 Dispersion in Natural Streams- 513 Shear-Augmented Dispersion in Unlimited Parallel Flow- 514 Diffusion in Skewed Shear Flow- References- VI Effects of Density Differences on Environmental Diffusion- 61 Introduction- 62 Fundamental Equations- 63 Approximate Forms of the Equations- 64 Equations for Turbulent Flow- 65 Turbulent Energy Equation- 66 Diffusion Floors and Ceilings- 67 Diffusion in a Continuously Stratified Fluid- 68 Velocity Autocorrelation and Particle Spread in Stratified Fluid Model- 69 Bodily Motion of Buoyant and Heavy Plumes- 610 Dynamics of a Line Thermal- 611 Similarity Theory- 612 Bent-Over Chimney Plumes- 613 Theory of Buoyancy Dominated Plumes in a Neutral Atmosphere- 614 Comparison with Observation- 615 Flow Pattern within a Plume- 616 Effect of Atmospheric Stratification- 617 Approximate Arguments for Plumes in Stratified Surroundings- 618 Engineering Assessment of Ground Level Pollution from Buoyancy Dominated Plumes- 619 Effects of Plume Rise on Ground-Level Concentration- Appendix to Chapter VI- A61 Momentum Plumes- Exercise- References- VII The Fluctuation Problem in Turbulent Diffusion- 71 Introduction- 72 Probability Distribution of Concentration- 73 The Functional Form of the Probability Distribution- 74 Hazard Assessment on the Basis of Concentration Probabilities- 75 The Variance of Concentration Fluctuations- 76 Self-Similar Fluctuation Intensity Distribution- 77 Fluctuating Plume Model- References
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TL;DR: An attempt is made to describe the motion of grouping individuals kinematically as distinct from simple diffusion or random walk, to model the grouping on the basis of dynamics of animal motion, and to interpret the grouping from the standpoint of advection-diffusion processes.
850 citations
TL;DR: A comprehensive survey of molecular communication (MC) through a communication engineering lens is provided in this paper, which includes different components of the MC transmitter and receiver, as well as the propagation and transport mechanisms.
Abstract: With much advancement in the field of nanotechnology, bioengineering, and synthetic biology over the past decade, microscales and nanoscales devices are becoming a reality. Yet the problem of engineering a reliable communication system between tiny devices is still an open problem. At the same time, despite the prevalence of radio communication, there are still areas where traditional electromagnetic waves find it difficult or expensive to reach. Points of interest in industry, cities, and medical applications often lie in embedded and entrenched areas, accessible only by ventricles at scales too small for conventional radio waves and microwaves, or they are located in such a way that directional high frequency systems are ineffective. Inspired by nature, one solution to these problems is molecular communication (MC), where chemical signals are used to transfer information. Although biologists have studied MC for decades, it has only been researched for roughly 10 year from a communication engineering lens. Significant number of papers have been published to date, but owing to the need for interdisciplinary work, much of the results are preliminary. In this survey, the recent advancements in the field of MC engineering are highlighted. First, the biological, chemical, and physical processes used by an MC system are discussed. This includes different components of the MC transmitter and receiver, as well as the propagation and transport mechanisms. Then, a comprehensive survey of some of the recent works on MC through a communication engineering lens is provided. The survey ends with a technology readiness analysis of MC and future research directions.
762 citations
TL;DR: In this paper, simple mathematical models for the turbulent diffusion of a passive scalar field are developed with an emphasis on the symbiotic interaction between rigorous mathematical theory (including exact solutions), physical intuition, and numerical simulations.
511 citations
TL;DR: In this paper, the authors estimate time and space scales for 3D displacements of phytoplankton caused by turbulent mixing, internal waves, Langmuir circulations, and double diffusive processes.
Abstract: The dependence of phytoplankton photosynthesis on light intensity may be altered by the range and frequency of variations in light intensity recentlv experienced by the organisms. A major source of the fluctuations in light intensity experienced by phytoplankton in the upper ocean is vertical motion. We estimate time and space scales for \\Tertical displacements of phytoplankton caused by turbulent mixing, internal waves, Langmuir circulations, and double diffusive processes. In the surface layer, depending on windspeed, current shear and stratification, we find that time scales for cycling of phytoplankton by turbulent eddies and mixing vary from about 0.5 h to hundreds of hours for vertical displacements of the order of 10 m. In the seasonal thermocline, turbulent diffusive time scales for displacements as small as several meters are weeks to months, whereas similar displacements by internal waves occur over periods of several minutes to several hours, according to the strength of the density stratification, and are then dominant. Langmuir cells seem to scale as the large turbulent eddies and need not be treated separately, and double diffusive processes seem to be of minor importance. The formulation used here of a vertical turbulent diffusion coefficient K, as a function of observable quantities-e the rate of dissipation of turbulent kinetic energy, and N the local buoyancy frequency-should also be us&d for estimating vertical fluxes of nutrients. In addition, this formulation is reversible in time and can be used to estimate the recent depth and light history of phytoplankton taken from the upper ocean. Traditionally the dependence of the photosynthetic production rate of phytoplankton on light intensity has been described by “P vs. I” curves relating the rate of photosynthetic production, P, to increasing light intensity, I, determined usually from experiments where portions of the same sample are incubated at several different constant light intensities for the same period. The uptake of labeled carbon over that period is measured and considered to be an index of the photosynthetic production (Peterson 1980). Division by the time interval gives the photosynthetic rate. A smooth curve fitted through the data resembles one of the family of curves shown in Fig. 1 (which, for illustration, has been generated from the model equation of Platt et al. 1980): P(I) = aem”‘( 1 eeVr). (1) Several problems exist: different curves are often found at different times of day (provided the incubation period is sufficiently brief, say 2-4 h), at different depths, during different seasons, and with different organisms (Harris 1973; MacCaull and Platt 1977; Platt et al. 1980). Furthermore, time-course measurements of varying photosynthetic production P(t)
495 citations
Cites background from "Turbulent Diffusion in the Environm..."
...9 becomes Z(t)” = 2&t (10) a familiar formulation derived from Taylor’s (1921) work to estimate turbulent eddy coefficients from dye release experiments (Csanady 1973; Kullenberg 1978)....
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...eddy coefficients from dye release experiments (Csanady 1973; Kullenberg 1978)....
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01 Jan 1988
TL;DR: Even the most casual observer notices the changes in the wind and the details of its swirls and eddies seem infinitely variable as mentioned in this paper, and its strength changes day to day as weather systems evolve, and day to night as the sun rises and sets.
Abstract: Even the most casual observer notices the changes in the wind. Though it has a certain persistence in time, the details of its swirls and eddies seem infinitely variable. Its strength changes day to day as weather systems evolve, and day to night as the sun rises and sets. It is modulated strongly by terrain features and by urban architecture. How can we hope to describe such a complicated phenomenon?
426 citations