Theoretical topics of fluid dynamics relevant to natural phenomena or man-made hazards in water and atmosphere. Basic law of fluid motion. Scaling and approximations. Slow flows, with applications to drag on a particle and mud flow on a slope. Boundary layers: jets and plumes in pure fluids or in porous media. Thermal and buoyancy effects, selective withdrawal and internal waves. Transient boundary layers in impulsive flows or waves. Induced streaming and mass transport. Dispersion in steady flows or in waves. Effects of earth rotation on coastal flows. Wind induced flow in shallow seas. Stratified seas and coastal upwelling.
" The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc."
A comprehensive treatment of the theory of partial differential equations (pde) from an applied mathematics perspective. Equilibrium, propagation, diffusion, and other phenomena. Initial and boundary value problems. Transform methods, eigenvalue and eigenfunction expansions, Green's functions. Theory of characteristics and shocks. Boundary layers and other singular perturbation phenomena. Elementary concepts for the numerical solution of pde's. Illustrative examples from fluid dynamics, nonlinear waves, geometrical optics, and other applications.
Fundamentals of subsurface flow and transport, emphasizing the role of groundwater in the hydrologic cycle, the relation of groundwater flow to geologic structure, and the management of contaminated groundwater. Topics include: Darcy equation, flow nets, mass conservation, the aquifer flow equation, heterogeneity and anisotropy, storage properties, regional circulation, unsaturated flow, recharge, stream-aquifer interaction, well hydraulics, flow through fractured rock, numerical models, groundwater quality, contaminant transport processes, dispersion, decay, and adsorption. Includes laboratory and computer demonstrations. Core requirement for Environmental and Geoenvironmental M.Eng. program.
Fundamentals of subsurface flow and transport, emphasizing the role of groundwater in the hydrologic cycle, the relation of groundwater flow to geologic structure, and the management of contaminated groundwater. Topics include: Darcy equation, flow nets, mass conservation, the aquifer flow equation, heterogeneity and anisotropy, storage properties, regional circulation, unsaturated flow, recharge, stream-aquifer interaction, well hydraulics, flow through fractured rock, numerical models, groundwater quality, contaminant transport processes, dispersion, decay, and adsorption. Includes laboratory and computer demonstrations.
Advanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, finite elements, well-posedness and stability, particle methods and lattice gases, boundary and nonlinear instabilities.
This course develops logical, empirically based arguments using statistical techniques and analytic methods. It covers elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation. Emphasis is placed on the use and limitations of analytical techniques in planning practice. This course is required for and restricted to first-year M.C.P. students.
This NASA educator guide tells the story of why it is important to observe celestial objects from outer space and how to study the entire electromagnetic spectrum. It features a set of hands-on activities and demonstrations which can be performed by teachers to reinforce the concept that Earth's atmosphere interferes with the passage of electromagnetic radiation and to investigate the properties and uses of radiation throughout the electromagnetic spectrum.
Statistics play a vital role in the scientific enterprise. This activity provides background information and tutorials on basic statistics (mean, median, standard deviation, etc.) used in science. Topics include descriptive statistics. l
Subject:
Mathematics and Statistics, Science and Technology
Introduction to momentum and scalar transport in environmental flows, with emphasis given to river and lake systems. Derivation and solutions to the differential form of mass conservation equations. Topics include: molecular and turbulent diffusion, boundary layers, dissolution, phase partitioning, bed-water exchange, air-water exchange, settling and coagulation, buoyancy-driven flows, and stratification in lakes.
" This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport."
Basic ideas of geophysical wave motion in rotating, stratified, and rotating-stratified fluids. Subject begins with general wave concepts of phase and group velocity. The dynamics and kinematics of gravity waves with a focus on dispersion, energy flux, initial value problems, etc. Subject foundation used to study internal and inertial waves, Kelvin, Poincare, and Rossby waves in homogeneous and stratified fluids. Laplace tidal equations are applied to equatorial waves. Other topics include: resonant interactions, potential vorticity, wave-mean flow interactions, and instability.
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