Particles in the coastal ocean : theory and applications / Daniel R. Lynch, David A. Greenberg, Ata Bilgili, Dennis J. McGillicuddy, James P. Manning, Alfredo L. Aretxabaleta
- Published
- New York : Cambridge University Press, 2015.
- Physical Description
- xxxiii, 510 pages, 24 unnumbered pages of plates : illustrations (some color), maps ; 26 cm
- Additional Creators
- Lynch, Daniel R.
- Language Note
- Text in English.
- Contents
- Machine generated contents note: 1.The Coastal Ocean -- 1.1.Typical Motions and Scales -- 1.2.Particle Simulation -- 1.2.1.Motion -- 1.2.2.Rates -- 1.2.3.Gather, Scatter -- 1.2.4.Simulation -- 1.2.5.Aggregation and Identity -- 2.Drifters and Their Numerical Simulation -- 2.1.Introduction -- 2.2.Drifter Technology -- 2.2.1.Design -- 2.2.2.Communication -- 2.2.3.Quality Control -- 2.3.Particle Tracking -- 2.3.1.Basic Lagrangian Model -- 2.3.2.Practical Issues -- 2.4.Model Validation with Drifters -- 2.4.1.Field Experience -- 2.5.Drifter Applications -- 2.5.1.Drifter Assimilation -- 3.Probability and Statistics - A Primer -- 3.1.Basics - Random Numbers -- 3.1.1.Continuous Distributions: f and F -- 3.1.2.Properties: Survival, Hazard Rate -- 3.1.3.Properties: Mean, Variance, Moments -- 3.1.4.Properties: Median, Mode, Quartile -- 3.1.5.Properties: Other Means -- 3.1.6.Bounding Theorems -- 3.1.7.Discrete Distributions: Pi and Fj -- 3.2.Some Common Distributions -- 3.2.1.Continuous Distributions -- 3.2.2.Discrete Distributions -- 3.2.3.Importance of G, U, B, Pois -- 3.2.4.The Central Limit Theorem -- 3.3.Generating Random Numbers -- 3.3.1.General Methods -- 3.3.2.Some Specific Deviates -- 3.4.Sampling; Finite N -- 3.4.1.Sample Statistics -- 3.4.2.Sample Mean -- 3.4.3.Sample Variance -- 3.4.4.Recap -- 3.5.Covariance -- 3.5.1.Definitions -- 3.5.2.Correlation and Autocorrelation -- 3.5.3.Autocorrelated Time Series -- 3.5.3.1.Separation-Based Covariance and Correlogram -- 3.5.3.2.Correlogram and Impulse Response -- 3.5.4.Autocorrelated Eulerian Fields -- 3.5.5.Generating Covariance -- 3.5.6.Summary - Covariance -- 3.6.Particles in a Box -- 3.6.1.Individual Residence Time -- 3.6.2.Aggregate Properties: Relaxation of Initial Condition -- 3.6.3.Export Rate -- 3.6.4.Long-Run Balance -- 3.6.5.Summary - Steady State -- 3.6.6.Exit Paths -- 3.6.7.Input Paths -- 3.6.8.Autocorrelation -- 3.6.9.Example - Branch Point -- 3.6.10.A Network of Boxes -- 3.6.10.1.Transfer Rate -- 3.6.10.2.Steady State -- 3.6.11.Closing Ideas - Particles in Boxes -- 3.7.Closure -- 3.8.General Sources -- 4.Dispersion by Random Walk -- 4.1.Introduction: Discrete Drunken Walk -- 4.2.Continuous Processes -- 4.2.1.Resolved and Subgrid Motion -- 4.2.2.A Hierarchy -- 4.3.The ARO Model - Uncorrelated Random Walk and Simple Diffusion -- 4.3.1.The Displacement Process -- 4.3.2.Correspondence to Diffusion -- 4.3.3.Multi-Dimensions -- 4.3.4.Inhomogeneous Diffusion -- 4.3.5.Anisotropic Diffusion -- 4.3.6.Shear and Convergence -- 4.3.7.Metrics of Resolution -- 4.3.8.Stepsize and the Need for Autocorrelation -- 4.4.The AR1 Model - Autocorrelated Velocity -- 4.4.1.AR1: Continuous Form and Its Discretization -- 4.4.2.AR1: Discrete Canonical Form -- 4.4.3.AR1: Displacement -- 4.4.4.Some Summary Observations about the AR1 Model -- 4.5.The AR2 Model - Autocorrelated Acceleration -- 4.5.1.Discrete Canonical Forms -- 4.5.2.AR2 Velocity -- 4.5.3.AR2 Displacement and Link to Diffusion -- 4.6.The AR1-s Model - Spinning Walk -- 4.6.1.AR1-s Complex Velocity -- 4.6.2.AR1-s Displacement -- 4.6.3.AR1-s Results -- 4.6.4.Vorticity Sources -- 4.7.Summary - Four Random Walk Models -- 4.7.1.ARO Model -- 4.7.2.AR1 Model -- 4.7.3.AR2 Model -- 4.7.4.AR1 -s Model -- 4.8.Concluding Remarks - Random Motion -- 5.Boundary Conditions, Boundary Layers, Sources -- 5.1.Boundary Layers: Continuum and Discretization -- 5.2.Discretized Boundaries -- 5.2.1.Particle Motion and Change -- 5.2.2.States and Transitions -- 5.2.3.Boundary Types -- 5.2.4.Basic Needs for Boundary Particles -- 5.2.5.Boundary Sources -- 5.3.The Law of the Wall -- 5.4.A Repellant Boundary Layer -- 5.4.1.Boundary Particles -- 5.4.2.The Gaussian Case -- 5.4.3.Pelagic Particles -- 5.4.4.The Steady State -- 5.5.Examples -- 5.5.1.Oiling the Coast -- 5.5.2.Bioaccumulation -- 5.5.3.Wetland Harvesting -- 5.6.Beyond the Boundary - Exogenous Sources -- 5.7.Summary Comments -- 6.Turbulence Closure -- 6.1.Reynolds Stresses and the Gradient Flux Relation -- 6.1.1.The Gradient Flux Relation -- 6.2.Vertical Closure -- 6.2.1.Early Models -- 6.2.2.Turbulent Kinetic Energy -- 6.2.3.Turbulent Length Scale -- 6.3.Vertical Closure Examples -- 6.3.1.Level 2.5 Formulation -- 6.3.1.1.Governing Equations -- 6.3.1.2.Vertical Boundary Conditions -- 6.3.2.Level 2.0 Formulation -- 6.3.3.The Point Model -- 6.3.4.Steady-State Point Model, Level 2 Closure -- 6.3.4.1.Wind Only -- 6.3.4.2.Wind and Gravity -- 6.3.4.3.Rotation and Wind - The Ekman Layer -- 6.3.5.Some Implementations -- 6.4.Horizontal Closure -- 6.5.The Main Points -- 7.Meshes: Interpolation, Navigation, and Fields -- 7.1.The Horizontal Mesh -- 7.1.1.Triangles -- 7.1.2.Geometry -- 7.1.3.Triangle Basics -- 7.1.4.Depth -- 7.1.5.Spherical-Polar Coordinates -- 7.1.6.Horizontal Interpolation -- 7.1.6.1.Higher Order Interpolation -- 7.1.7.Gradient -- 7.1.8.Location and Navigation -- 7.1.8.1.Global and Local Coordinates -- 7.1.8.2.Is a Particle in an Element? -- 7.1.8.3.Motion within an Element -- 7.1.8.4.When Does a Particle Leave an Element? -- 7.2.Vertical Discretization -- 7.2.1.Separation of Variables -- 7.2.2.Special Functions and Global z-Interpolation -- 7.2.3.Piecewise Local z-Interpolation -- 7.2.4.Vertical Interpolation -- 7.3.3-D Location, Interpolation, Navigation -- 7.3.1.Interpolation on a Single Element -- 7.3.2.Is a Particle in an Element? -- 7.3.3.Motion within an Element -- 7.3.4.When Does a Particle Leave an Element? -- 7.3.5.Summary: An Overlay of Horizontal Meshes -- 7.4.Meshes -- 7.4.1.The Union of Elements -- 7.4.2.Essential Data Structures -- 7.4.3.Example -- 7.4.4.Subsidiary Data Structures -- 7.4.5.The Galerkin Projection -- 7.4.6.Mesh Generators -- 7.4.7.Some Mesh Generation Packages -- 7.4.8.Mesh Diagnostics -- 7.4.9.Graphics -- 7.5.Quadrilateral Elements -- 7.5.1.Local Coordinates and Interpolation -- 7.5.2.Jacobian -- 7.5.3.Locating -- 8.Particles and Fields -- 8.1.Introduction -- 8.2.Scattering among Elements -- 8.3.Scattering within an Element -- 8.3.1.Triangles -- 8.3.1.1.Uniform Distribution on a Triangle -- 8.3.1.2.Linear Distribution on a Triangle -- 8.3.1.3.Examples -- 8.3.2.Quadrilaterals -- 8.4.Projections: The Density of a Set of Particles -- 8.4.1.Simple Fixed Mesh Projections -- 8.4.2.The Least Squares Projection -- 8.4.3.Mass Conservation -- 8.4.4.Example: Particles on a Mesh -- 8.4.5.Convergence - The Small Δx Problem -- 8.4.6.Kernel Methods -- 9.Noncohesive Sediment - Dense Particles -- 9.1.Introduction -- 9.2.Three States: P, M, B -- 9.3.Sediment Particles -- 9.4.Settling Velocity -- 9.5.Bottom Boundary Layer -- 9.6.Entrainment -- 9.6.1.The Threshold of Motion - The Shields Parameter -- 9.6.2.Entrainment Rate -- 9.6.3.Initial Vertical Position - Entrainment Lift -- 9.7.Vertical Motion: The Rouse Number and ze -- 9.8.Profiles -- 9.9.Flight Simulations -- 9.10.Saltation -- 9.11.Burial -- 9.12.Theoretical Extensions -- 9.13.A Simple Particle Model -- 9.14.2-D -- 9.14.1.Bed-Load - Suspended Load Transport -- 9.14.2.Bed-Load Particle Velocity -- 9.14.3.Suspended Load Particle Velocity -- 9.14.4.Sediment Dispersion Coefficients -- 9.14.5.A Generic Scheme -- 9.14.6.Results -- 9.15.Summary of Notation -- 10.Oil - Chemically Active Particles -- 10.1.Introduction -- 10.1.1.Composition -- 10.1.2.Motion -- 10.1.3.Weathering -- 10.1.4.Subsurface Releases -- 10.2.Oil as Parcels -- 10.2.1.Surface and Subsurface Parcels -- 10.2.2.Generic Model Needs -- 10.3.Surface Parcels -- 10.3.1.Spreading -- 10.4.Weathering Processes -- 10.4.1.Evaporation -- 10.4.2.Emulsification -- 10.4.3.Density and Viscosity -- 10.4.4.A Simple Weathering Model -- 10.4.5.Entrainment -- 10.5.Motion -- 10.5.1.Stokes Drift and Surface Velocity -- 10.5.2.Random Walk Models -- 10.5.3.Droplet Rise Velocity -- 10.5.4.Droplet Size Distribution -- 10.6.Density and Crowding -- 10.6.1.Mass Field -- 10.6.2.Crowding -- 10.7.Submerged Parcels -- 10.7.1.Surface Source - Entrainment -- 10.7.2.Shear Dispersion -- 10.7.3.Subsurface Source - Blowout -- 10.7.4.Dissolution -- 10.8.Field Tests -- 10.8.1.Surface Releases -- 10.8.2.Subsurface Releases -- 10.8.3.The Deepwater Horizon Incident -- 10.9.Impact Assessment -- 11.Individual-Based Models - Biotic Particles -- 11.1.Introduction -- 11.2.Diversity in the Cohort -- 11.3.Individual-Based States -- 11.3.1.Mixing and Aggregation -- 11.3.2.Life Histories -- 11.3.3.Eulerian and Lagrangian Quantities -- 11.3.4.Continuous and Logical States; State Transitions -- 11.4.Vital Rates -- 11.4.1.Growth Rate Distribution - Analytic Example -- 11.4.2.Growth Rate Distribution: Simulation -- 11.4.3.Multiple Equilibria -- 11.4.4.Rate Estimation -- 11.5.Mortality -- 11.5.1.Simulations: Individual-Based Mortality -- 11.5.2.Individual Survivorship Probability: Geometric Distribution -- 11.5.3.Lifetime Distribution -- 11.5.4.Cohort Abundance: Binomial Distribution -- 11.5.5.Cohort Death Rate -- 11.5.6.Example: Growth, Mortality, Motion -- 11.6.Stage Progression -- 11.6.1.Example: Three Stages -- 11.6.2.Stage Completion Rate, Residence Time - Constant α -- 11.6.3.The General Case - Variable α -- 11.6.4.Recap: Stage Completion -- 11.7.Reproduction -- 11.8.Motion - Advection + Random Walk -- 11.9.Motion - Behavior -- 11.9.1.Example Formulations -- 11.10.Benthic Exchange -- 11.11.Plankton IBMs -- 11.11.1.Larval Fish -- 11.11.1.1.Groundfish -- 11.11.1.2.Shellfish -- 11.11.1.3.Recent Summaries - Larval Fish -- 11.11.2.Zooplankton -- 11.11.3.Phytoplankton -- 11.11.3.1.The Gulf of Maine -- 11.11.3.2.Implementation -- 11.11.4.Summary - Plankton IBMs -- 11.12.Population Connectivity -- 11.13.Summary - Individual-Based Modeling -- A.Series, Sums, Limits -- B.Complex Numbers -- C.Wiener Integrals -- D.Rates and Rate Limiters -- E.Diffusion Solutions -- F.Covariance Matrix for Shear and Convergence -- G.Summary - ARn Recursions -- H.Distribution Properties for Linear Triangles.
- Subject(s)
- ISBN
- 110706175X
9781107061750 - Bibliography Note
- Includes bibliographical references (pages 479-505) and index.
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