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16.120 Compressible Flow (MIT) 16.120 Compressible Flow (MIT)

Description

The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear. The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.Subjects

compressible fluid dynamics | compressible fluid dynamics | fluid dynamics | fluid dynamics | external flows | external flows | internal flows | internal flows | quasi-on-dimensional | quasi-on-dimensional | quasi-1D | quasi-1D | channel flow | channel flow | multi-dimensional flows | multi-dimensional flows | nozzles | nozzles | diffusers | diffusers | inlets | inlets | loss generation | loss generation | interactions | interactions | aerodynamic shapes | aerodynamic shapes | subsonic | subsonic | supersonic | supersonic | transonic | transonic | hypersonic | hypersonic | shock waves | shock waves | vortices | vortices | disturbance behavior | disturbance behavior | unsteady | unsteady | speed of sound | speed of sound | isentropic flows | isentropic flows | non-isentropic flows | non-isentropic flows | potential flows | potential flows | rotational flows | rotational flows | shaft work | shaft work | heat addition | heat addition | mass addition | mass addition | flow states | flow states | flow regime | flow regime | velocity non-uniformities | velocity non-uniformities | density non-uniformities | density non-uniformities | fluid system components | fluid system components | lift | lift | drag | drag | continuum flow | continuum flow | shock strength | shock strength | characteristics | characteristics | governing equations | governing equations | thermodynamic context | thermodynamic context | characteristic parameters | characteristic parameters | quasi-one-dimensional flow | quasi-one-dimensional flow | disturbances | disturbances | unsteady flow | unsteady flow | gas dynamic discontinuities | gas dynamic discontinuities | detonations | detonations | linear two-dimensional flows | linear two-dimensional flows | non-linear two-dimensional flows | non-linear two-dimensional flowsLicense

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See all metadata12.820 Turbulence in Geophysical Systems (MIT) 12.820 Turbulence in Geophysical Systems (MIT)

Description

This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from the fine structure to planetary scale motions. The regimes of turbulence include homogeneous flows in two and three dimensions, geostrophic motions, shear flows, convection, boundary layers, stably stratified flows, and internal waves. This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from the fine structure to planetary scale motions. The regimes of turbulence include homogeneous flows in two and three dimensions, geostrophic motions, shear flows, convection, boundary layers, stably stratified flows, and internal waves.Subjects

Phenomena | theory | and modeling of turbulence | Phenomena | theory | and modeling of turbulence | oceans | oceans | atmosphere | atmosphere | fine structure | fine structure | planetary scale motions | planetary scale motions | homogeneous flows | homogeneous flows | geostrophic motions | geostrophic motions | shear flows | shear flows | convection | convection | boundary layers | boundary layers | stably stratified flows | stably stratified flows | internal waves | internal waves | turbulence flows | turbulence flows | earth | earth | energetics | energetics | isotropic homogeneous 2D turbulence | isotropic homogeneous 2D turbulence | isotropic homogeneous 3d flows | isotropic homogeneous 3d flows | quasi-geostrophic turbulence | quasi-geostrophic turbulence | parameterizing turbulence | parameterizing turbulence | wave dynamics | wave dynamics | turbulent dispersion | turbulent dispersion | coherent structures | coherent structuresLicense

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See all metadata16.120 Compressible Flow (MIT)

Description

The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.Subjects

compressible fluid dynamics | fluid dynamics | external flows | internal flows | quasi-on-dimensional | quasi-1D | channel flow | multi-dimensional flows | nozzles | diffusers | inlets | loss generation | interactions | aerodynamic shapes | subsonic | supersonic | transonic | hypersonic | shock waves | vortices | disturbance behavior | unsteady | speed of sound | isentropic flows | non-isentropic flows | potential flows | rotational flows | shaft work | heat addition | mass addition | flow states | flow regime | velocity non-uniformities | density non-uniformities | fluid system components | lift | drag | continuum flow | shock strength | characteristics | governing equations | thermodynamic context | characteristic parameters | quasi-one-dimensional flow | disturbances | unsteady flow | gas dynamic discontinuities | detonations | linear two-dimensional flows | non-linear two-dimensional flowsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata16.120 Compressible Flow (MIT)

Description

The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.Subjects

compressible fluid dynamics | fluid dynamics | external flows | internal flows | quasi-on-dimensional | quasi-1D | channel flow | multi-dimensional flows | nozzles | diffusers | inlets | loss generation | interactions | aerodynamic shapes | subsonic | supersonic | transonic | hypersonic | shock waves | vortices | disturbance behavior | unsteady | speed of sound | isentropic flows | non-isentropic flows | potential flows | rotational flows | shaft work | heat addition | mass addition | flow states | flow regime | velocity non-uniformities | density non-uniformities | fluid system components | lift | drag | continuum flow | shock strength | characteristics | governing equations | thermodynamic context | characteristic parameters | quasi-one-dimensional flow | disturbances | unsteady flow | gas dynamic discontinuities | detonations | linear two-dimensional flows | non-linear two-dimensional flowsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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Includes audio/video content: AV faculty introductions. 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. Includes audio/video content: AV faculty introductions. 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.Subjects

river systems | river systems | lake systems | lake systems | scalar transport in environmental flows | scalar transport in environmental flows | momentum transport in environmental flows | momentum transport in environmental flows | stratification in lakes | stratification in lakes | buoyancy-driven flows | buoyancy-driven flows | settling and coagulation | settling and coagulation | air-water exchange | air-water exchange | bed-water exchange | bed-water exchange | phase partitioning | phase partitioning | dissolution | dissolution | boundary layers | boundary layers | molecular diffusion | molecular diffusion | turbulent diffusion | turbulent diffusion | water transportation | water transportation | advection | advection | aquatic systems | aquatic systems | conservation of mass | conservation of mass | derivation | derivation | Diffusion | Diffusion | dispersion | dispersion | environmental flows | environmental flows | instantaneous point source | instantaneous point source | lakes | lakes | mass | mass | transport | transport | particle transport | particle transport | rivers | rivers | scaling | scaling | turbulence | turbulence | water flow | water flowLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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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. 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.Subjects

river systems | river systems | lake systems | lake systems | scalar transport in environmental flows | scalar transport in environmental flows | momentum transport in environmental flows | momentum transport in environmental flows | stratification in lakes | stratification in lakes | buoyancy-driven flows | buoyancy-driven flows | settling and coagulation | settling and coagulation | air-water exchange | air-water exchange | bed-water exchange | bed-water exchange | phase partitioning | phase partitioning | dissolution | dissolution | boundary layers | boundary layers | molecular diffusion | molecular diffusion | turbulent diffusion | turbulent diffusion | water transportation | water transportation | advection | advection | aquatic systems | aquatic systems | conservation of mass | conservation of mass | derivation | derivation | Diffusion | Diffusion | dispersion | dispersion | environmental flows | environmental flows | instantaneous point source | instantaneous point source | lakes | lakes | mass | mass | transport | transport | particle transport | particle transport | rivers | rivers | scaling | scaling | turbulence | turbulence | water flow | water flowLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata2.26 Compressible Fluid Dynamics (MIT) 2.26 Compressible Fluid Dynamics (MIT)

Description

2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department's sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer. The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Mey 2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department's sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer. The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-MeySubjects

conservation laws | conservation laws | isentropic flows | isentropic flows | normal shock wave relations | normal shock wave relations | oblique shock waves | oblique shock waves | weak shock | weak shock | strong shock | strong shock | ducts | ducts | heat transfer | heat transfer | unsteady flows | unsteady flows | Riemann invariants | Riemann invariants | piston | piston | shock tube | shock tube | steady 2D supersonic flow | steady 2D supersonic flow | Prandtl-Meyer function | Prandtl-Meyer function | self-similar compressible flows | self-similar compressible flowsLicense

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See all metadata12.820 Turbulence in Geophysical Systems (MIT) 12.820 Turbulence in Geophysical Systems (MIT)

Description

This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from the fine structure to planetary scale motions. The regimes of turbulence include homogeneous flows in two and three dimensions, geostrophic motions, shear flows, convection, boundary layers, stably stratified flows, and internal waves. This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from the fine structure to planetary scale motions. The regimes of turbulence include homogeneous flows in two and three dimensions, geostrophic motions, shear flows, convection, boundary layers, stably stratified flows, and internal waves.Subjects

phenomena | theory | and modeling of turbulence | phenomena | theory | and modeling of turbulence | oceans | oceans | atmosphere | atmosphere | fine structure | fine structure | planetary scale motions | planetary scale motions | homogeneous flows | homogeneous flows | geostrophic motions | geostrophic motions | shear flows | shear flows | convection | convection | boundary layers | boundary layers | stably stratified flows | stably stratified flows | internal waves | internal wavesLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.997 Topics in Combinatorial Optimization (MIT) 18.997 Topics in Combinatorial Optimization (MIT)

Description

In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms. In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.Subjects

combinatorial optimization | combinatorial optimization | Ear decompositions | Ear decompositions | Nonbipartite matching | Nonbipartite matching | Gallai-Milgram and Bessy-Thomasse theorems on partitioning/covering graphs by directed paths/cycles | Gallai-Milgram and Bessy-Thomasse theorems on partitioning/covering graphs by directed paths/cycles | Minimization of submodular functions | Minimization of submodular functions | Matroid intersection | Matroid intersection | Polymatroid intersection | Polymatroid intersection | Jump systems | Jump systems | Matroid union | Matroid union | Matroid matching | path matchings | Matroid matching | path matchings | Packing trees and arborescences | Packing trees and arborescences | Packing directed cuts and the Lucchesi-Younger theorem | Packing directed cuts and the Lucchesi-Younger theorem | Submodular flows and the Edmonds-Giles theorem | Submodular flows and the Edmonds-Giles theorem | Graph orientation | Graph orientation | Connectivity tree and connectivity augmentation | Connectivity tree and connectivity augmentation | Multicommodity flows | Multicommodity flows | Connectivity tree | Connectivity tree | connectivity augmentation | connectivity augmentation | Gallai-Milgram Theorem | Gallai-Milgram Theorem | Bessy-Thomasse Theorem | Bessy-Thomasse Theorem | paritioning graphs | paritioning graphs | covering graphs | covering graphs | directed paths | directed paths | directed cycles | directed cycles | matroid matching | matroid matching | path matching | path matching | packing directed cuts | packing directed cuts | Luchessi-Younger Theorem | Luchessi-Younger Theorem | packing trees | packing trees | arborescences | arborescences | submodular flows | submodular flows | Edmonds-Giles Theorem | Edmonds-Giles TheoremLicense

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See all metadata12.820 Turbulence in Geophysical Systems (MIT) 12.820 Turbulence in Geophysical Systems (MIT)

Description

This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from the fine structure to planetary scale motions. The regimes of turbulence include homogeneous flows in two and three dimensions, geostrophic motions, shear flows, convection, boundary layers, stably stratified flows, and internal waves. This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from the fine structure to planetary scale motions. The regimes of turbulence include homogeneous flows in two and three dimensions, geostrophic motions, shear flows, convection, boundary layers, stably stratified flows, and internal waves.Subjects

phenomena | theory | and modeling of turbulence | phenomena | theory | and modeling of turbulence | oceans | oceans | atmosphere | atmosphere | fine structure | fine structure | planetary scale motions | planetary scale motions | homogeneous flows | homogeneous flows | geostrophic motions | geostrophic motions | shear flows | shear flows | convection | convection | boundary layers | boundary layers | stably stratified flows | stably stratified flows | internal waves | internal wavesLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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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.Technical RequirementsRealOne™ Player software is required to run the .rm files found on this course site.RealOne™ is a trademark or a registered trademark of RealNetworks, Inc.  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.Technical RequirementsRealOne™ Player software is required to run the .rm files found on this course site.RealOne™ is a trademark or a registered trademark of RealNetworks, Inc. Subjects

river systems | river systems | lake systems | lake systems | scalar transport in environmental flows | scalar transport in environmental flows | momentum transport in environmental flows | momentum transport in environmental flows | stratification in lakes | stratification in lakes | buoyancy-driven flows | buoyancy-driven flows | settling and coagulation | settling and coagulation | air-water exchange | air-water exchange | bed-water exchange | bed-water exchange | phase partitioning | phase partitioning | dissolution | dissolution | boundary layers | boundary layers | molecular diffusion | molecular diffusion | turbulent diffusion | turbulent diffusion | water transportation | water transportationLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from centimeter to planetary scale motions. The regimes of turbulence include homogeneous isotropic three dimensional turbulence, convection, boundary layer turbulence, internal waves, two dimensional turbulence, quasi-geostrophic turbulence, and macrotrubulence in the ocean and atmosphere. This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from centimeter to planetary scale motions. The regimes of turbulence include homogeneous isotropic three dimensional turbulence, convection, boundary layer turbulence, internal waves, two dimensional turbulence, quasi-geostrophic turbulence, and macrotrubulence in the ocean and atmosphere.Subjects

phenomena | theory | and modeling of turbulence | phenomena | theory | and modeling of turbulence | oceans | oceans | atmosphere | atmosphere | fine structure | fine structure | planetary scale motions | planetary scale motions | homogeneous flows | homogeneous flows | geostrophic motions | geostrophic motions | shear flows | shear flows | convection | convection | boundary layers | boundary layers | stably stratified flows | stably stratified flows | internal waves | internal wavesLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from centimeter to planetary scale motions. The regimes of turbulence include homogeneous isotropic three dimensional turbulence, convection, quasi-geostrophic turbulence, shallow water turbulence, baroclinic turbulence, macroturbulence in the ocean and atmosphere. This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from centimeter to planetary scale motions. The regimes of turbulence include homogeneous isotropic three dimensional turbulence, convection, quasi-geostrophic turbulence, shallow water turbulence, baroclinic turbulence, macroturbulence in the ocean and atmosphere.Subjects

phenomena | phenomena | theory | theory | and modeling of turbulence | and modeling of turbulence | oceans | oceans | atmosphere | atmosphere | fine structure | fine structure | planetary scale motions | planetary scale motions | homogeneous flows | homogeneous flows | geostrophic motions | geostrophic motions | shear flows | shear flows | convection | convection | boundary layers | boundary layers | stably stratified flows | stably stratified flows | internal waves | internal wavesLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata12.820 Turbulence in Geophysical Systems (MIT)

Description

This course presents the phenomena, theory, and modeling of turbulence in the Earth's oceans and atmosphere. The scope ranges from the fine structure to planetary scale motions. The regimes of turbulence include homogeneous flows in two and three dimensions, geostrophic motions, shear flows, convection, boundary layers, stably stratified flows, and internal waves.Subjects

Phenomena | theory | and modeling of turbulence | oceans | atmosphere | fine structure | planetary scale motions | homogeneous flows | geostrophic motions | shear flows | convection | boundary layers | stably stratified flows | internal waves | turbulence flows | earth | energetics | isotropic homogeneous 2D turbulence | isotropic homogeneous 3d flows | quasi-geostrophic turbulence | parameterizing turbulence | wave dynamics | turbulent dispersion | coherent structuresLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata13.012 Hydrodynamics for Ocean Engineering (MIT) 13.012 Hydrodynamics for Ocean Engineering (MIT)

Description

Development of the fundamental equations of fluid mechanics and their simplifications for several areas of marine hydrodynamics. Application of these principles to the solution of practical ocean engineering problems. Topics include the principles of conservation of mass, momentum and energy; hydrostatic behavior of floating and submerged bodies; lift and drag forces; dimensional anaylsis; wave forces on ships and offshore platforms; laminar and turbulent flows. Experimental projects will be conducted in ocean engineering laboratories illustrating concepts taught in class, including ship resistance and model testing, lift and drag forces on submerged bodies, and vehicle propulsion.Technical RequirementsMicrosoft Excel software is recommended for viewing the .xls files found on thi Development of the fundamental equations of fluid mechanics and their simplifications for several areas of marine hydrodynamics. Application of these principles to the solution of practical ocean engineering problems. Topics include the principles of conservation of mass, momentum and energy; hydrostatic behavior of floating and submerged bodies; lift and drag forces; dimensional anaylsis; wave forces on ships and offshore platforms; laminar and turbulent flows. Experimental projects will be conducted in ocean engineering laboratories illustrating concepts taught in class, including ship resistance and model testing, lift and drag forces on submerged bodies, and vehicle propulsion.Technical RequirementsMicrosoft Excel software is recommended for viewing the .xls files found on thiSubjects

Hydrodynamics | | Hydrodynamics | | fluid mechanics | | fluid mechanics | | hydrostatic behavior | | hydrostatic behavior | | laminar flows | | laminar flows | | turbulent flows | | turbulent flows | | fluid motion | fluid motion | 2.016 | 2.016License

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See all metadata1.061 Transport Processes in the Environment (MIT)

Description

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.Subjects

river systems | lake systems | scalar transport in environmental flows | momentum transport in environmental flows | stratification in lakes | buoyancy-driven flows | settling and coagulation | air-water exchange | bed-water exchange | phase partitioning | dissolution | boundary layers | molecular diffusion | turbulent diffusion | water transportation | advection | aquatic systems | conservation of mass | derivation | Diffusion | dispersion | environmental flows | instantaneous point source | lakes | mass | transport | particle transport | rivers | scaling | turbulence | water flowLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata1.061 Transport Processes in the Environment (MIT)

Description

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.Subjects

river systems | lake systems | scalar transport in environmental flows | momentum transport in environmental flows | stratification in lakes | buoyancy-driven flows | settling and coagulation | air-water exchange | bed-water exchange | phase partitioning | dissolution | boundary layers | molecular diffusion | turbulent diffusion | water transportation | advection | aquatic systems | conservation of mass | derivation | Diffusion | dispersion | environmental flows | instantaneous point source | lakes | mass | transport | particle transport | rivers | scaling | turbulence | water flowLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization. Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.Subjects

Scientific computing: Fast Fourier Transform | Scientific computing: Fast Fourier Transform | finite differences | finite differences | finite elements | finite elements | spectral method | spectral method | numerical linear algebra | numerical linear algebra | Complex variables and applications | Complex variables and applications | Initial-value problems: stability or chaos in ordinary differential equations | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | wave equation versus heat equation | conservation laws and shocks | conservation laws and shocks | dissipation and dispersion | dissipation and dispersion | Optimization: network flows | Optimization: network flows | linear programming | linear programming | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Optimization: network flows | linear programming | Optimization: network flows | linear programmingLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.854J Advanced Algorithms (MIT) 6.854J Advanced Algorithms (MIT)

Description

6.854J is a first-year graduate course in algorithms, continuing where 6.046J left off. The course emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Topics include: data structures, network flows, linear programming, computational geometry, approximation algorithms. 6.854J is a first-year graduate course in algorithms, continuing where 6.046J left off. The course emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Topics include: data structures, network flows, linear programming, computational geometry, approximation algorithms.Subjects

algorithm design and analysis | algorithm design and analysis | algorithms | algorithms | fundamental algorithms | fundamental algorithms | advanced methods of algorithmic design | advanced methods of algorithmic design | analysis | analysis | implementation | implementation | data structures | data structures | network flows | network flows | linear programming | linear programming | computational geometry | computational geometry | approximation algorithms | approximation algorithms | algorithmic design | algorithmic design | algorithmic analysis | algorithmic analysis | string algorithms | string algorithms | maximum flows | maximum flows | online algorithms | online algorithms | scheduling | scheduling | external memory algorithms | external memory algorithms | 6.854 | 6.854 | 18.415 | 18.415License

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See all metadata10.52 Mechanics of Fluids (MIT) 10.52 Mechanics of Fluids (MIT)

Description

This course is an advanced subject in fluid and continuum mechanics. The course content includes kinematics, macroscopic balances for linear and angular momentum, stress tensors, creeping flows and the lubrication approximation, the boundary layer approximation, linear stability theory, and some simple turbulent flows. This course is an advanced subject in fluid and continuum mechanics. The course content includes kinematics, macroscopic balances for linear and angular momentum, stress tensors, creeping flows and the lubrication approximation, the boundary layer approximation, linear stability theory, and some simple turbulent flows.Subjects

fluid mechanics | fluid mechanics | continuum mechanics | continuum mechanics | kinematics | kinematics | macroscopic balances for linear momentum | macroscopic balances for linear momentum | macroscopic balances for angular momentum | macroscopic balances for angular momentum | the stress tensor | the stress tensor | creeping flows | creeping flows | lubrication approximation | lubrication approximation | boundary layer approximation | boundary layer approximation | linear stability theory | linear stability theory | simple turbulent flows | simple turbulent flowsLicense

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See all metadata1.061 Transport Processes in the Environment (MIT)

Description

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.Subjects

river systems | lake systems | scalar transport in environmental flows | momentum transport in environmental flows | stratification in lakes | buoyancy-driven flows | settling and coagulation | air-water exchange | bed-water exchange | phase partitioning | dissolution | boundary layers | molecular diffusion | turbulent diffusion | water transportation | advection | aquatic systems | conservation of mass | derivation | Diffusion | dispersion | environmental flows | instantaneous point source | lakes | mass | transport | particle transport | rivers | scaling | turbulence | water flowLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata1.061 Transport Processes in the Environment (MIT)

Description

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.Subjects

river systems | lake systems | scalar transport in environmental flows | momentum transport in environmental flows | stratification in lakes | buoyancy-driven flows | settling and coagulation | air-water exchange | bed-water exchange | phase partitioning | dissolution | boundary layers | molecular diffusion | turbulent diffusion | water transportation | advection | aquatic systems | conservation of mass | derivation | Diffusion | dispersion | environmental flows | instantaneous point source | lakes | mass | transport | particle transport | rivers | scaling | turbulence | water flowLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year. Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.Subjects

fluid dynamics | fluid dynamics | fluid motion | fluid motion | Cartesian tensor convention | Cartesian tensor convention | scaling | scaling | approximations | approximations | slow flow | slow flow | Stokes flow | Stokes flow | Oseen | Oseen | spreading | spreading | gravity | gravity | stratified fluid | stratified fluid | boundary layer | boundary layer | high speed flow | high speed flow | jets | jets | thermal plume | thermal plume | pure fluids | pure fluids | porous media | porous media | similarity method of solution | similarity method of solution | shear | shear | stratification | stratification | Orr-Sommerfeld | Orr-Sommerfeld | capillary phenomena | capillary phenomena | bubbles | bubbles | drops | drops | Marangoni instability | Marangoni instability | contact lines | contact lines | geophysical fluid dynamics | geophysical fluid dynamics | coastal flows | coastal flows | wind-induced flows | wind-induced flows | coastal upwelling | coastal upwelling | transient boundary layer | transient boundary layer | buoyancy | buoyancy | convection porous media | convection porous media | dispersion | dispersion | hydrodynamic instability | hydrodynamic instability | Kelvin-Helmholtz instability | Kelvin-Helmholtz instabilityLicense

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See all metadata2.26 Compressible Fluid Dynamics (MIT)

Description

2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department's sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer. The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-MeySubjects

conservation laws | isentropic flows | normal shock wave relations | oblique shock waves | weak shock | strong shock | ducts | heat transfer | unsteady flows | Riemann invariants | piston | shock tube | steady 2D supersonic flow | Prandtl-Meyer function | self-similar compressible flowsLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.997 Topics in Combinatorial Optimization (MIT)

Description

In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.Subjects

combinatorial optimization | Ear decompositions | Nonbipartite matching | Gallai-Milgram and Bessy-Thomasse theorems on partitioning/covering graphs by directed paths/cycles | Minimization of submodular functions | Matroid intersection | Polymatroid intersection | Jump systems | Matroid union | Matroid matching | path matchings | Packing trees and arborescences | Packing directed cuts and the Lucchesi-Younger theorem | Submodular flows and the Edmonds-Giles theorem | Graph orientation | Connectivity tree and connectivity augmentation | Multicommodity flows | Connectivity tree | connectivity augmentation | Gallai-Milgram Theorem | Bessy-Thomasse Theorem | paritioning graphs | covering graphs | directed paths | directed cycles | matroid matching | path matching | packing directed cuts | Luchessi-Younger Theorem | packing trees | arborescences | submodular flows | Edmonds-Giles TheoremLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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