Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves, and magnetic field generation in the interiors and atmospheres of ...
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This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves, and magnetic field generation in the interiors and atmospheres of rotating planets and stars. Using a teaching method perfected in the classroom, the book begins by offering a step-by-step guide on how to design codes for simulating nonlinear time-dependent thermal convection in a 2D box using Fourier expansions in the horizontal direction and finite differences in the vertical direction. It then describes how to implement more efficient a nd accurate numerical methods and more realistic geometries in two and three dimensions. The third part of the book demonstrates how to incorporate more sophisticated physics, including the effects of magnetic field, density stratification, and rotation. The book features numerous exercises throughout, and is an ideal textbook for students and an essential resource for researchers. It explains how to create codes that simulate the internal dynamics of planets and stars, and builds on basic concepts and simple methods. The book shows how to improve the efficiency and accuracy of the numerical methods. It considers more relevant geometries and boundary conditions.Less
This book provides readers with the skills they need to write computer codes that simulate convection, internal gravity waves, and magnetic field generation in the interiors and atmospheres of rotating planets and stars. Using a teaching method perfected in the classroom, the book begins by offering a step-by-step guide on how to design codes for simulating nonlinear time-dependent thermal convection in a 2D box using Fourier expansions in the horizontal direction and finite differences in the vertical direction. It then describes how to implement more efficient a nd accurate numerical methods and more realistic geometries in two and three dimensions. The third part of the book demonstrates how to incorporate more sophisticated physics, including the effects of magnetic field, density stratification, and rotation. The book features numerous exercises throughout, and is an ideal textbook for students and an essential resource for researchers. It explains how to create codes that simulate the internal dynamics of planets and stars, and builds on basic concepts and simple methods. The book shows how to improve the efficiency and accuracy of the numerical methods. It considers more relevant geometries and boundary conditions.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter presents a model of Rayleigh–Bénard convection. It first describes the fundamental dynamics expected in a fluid that is convectively stable and in one that is convectively unstable, ...
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This chapter presents a model of Rayleigh–Bénard convection. It first describes the fundamental dynamics expected in a fluid that is convectively stable and in one that is convectively unstable, focusing on thermal convection and internal gravity waves. Thermal convection and internal gravity waves are the two basic types of fluid flows within planets and stars that are driven by thermally produced buoyancy forces. The chapter then reviews the equations that govern fluid dynamics based on conservation of mass, momentum, and energy. It also examines the conditions under which the Boussinesq approximation simplifies conservation equations to a form very similar to that of an incompressible fluid. Finally, it discusses the key characteristics of the model of Rayleigh–Bénard convection.Less
This chapter presents a model of Rayleigh–Bénard convection. It first describes the fundamental dynamics expected in a fluid that is convectively stable and in one that is convectively unstable, focusing on thermal convection and internal gravity waves. Thermal convection and internal gravity waves are the two basic types of fluid flows within planets and stars that are driven by thermally produced buoyancy forces. The chapter then reviews the equations that govern fluid dynamics based on conservation of mass, momentum, and energy. It also examines the conditions under which the Boussinesq approximation simplifies conservation equations to a form very similar to that of an incompressible fluid. Finally, it discusses the key characteristics of the model of Rayleigh–Bénard convection.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. ...
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This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. The approach involves updating for the vorticity first and then solving for the fluid velocity each time step. The chapter continues with a discussion of two very different spatial discretizations, whereby the vertical derivatives are approximated with a finite-difference method and the horizontal derivatives with a spectral method. The nonlinear terms are computed in spectral space. The chapter also considers the Adams-Bashforth time integration scheme and explains how the Poisson equation can be solved at each time step for the updated streamfunction given the updated vorticity.Less
This chapter describes a numerical method for solving equations of thermal convection on a computer. It begins by introducing the vorticity-streamfunction formulation as a means of conserving mass. The approach involves updating for the vorticity first and then solving for the fluid velocity each time step. The chapter continues with a discussion of two very different spatial discretizations, whereby the vertical derivatives are approximated with a finite-difference method and the horizontal derivatives with a spectral method. The nonlinear terms are computed in spectral space. The chapter also considers the Adams-Bashforth time integration scheme and explains how the Poisson equation can be solved at each time step for the updated streamfunction given the updated vorticity.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter explains how to write a postprocessing code, and more specifically how to study the nonlinear simulations using computer graphics and analysis. It first considers how to compute and ...
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This chapter explains how to write a postprocessing code, and more specifically how to study the nonlinear simulations using computer graphics and analysis. It first considers how to compute and store results in a file during the computer simulation, assuming the Fourier transforms to x-space are done within the main computational code during the simulation. It then describes the postprocessing code for reading these files and displaying the various fields, along with the use of graphics software packages that provide additional, more sophisticated visualizations of the scalar and vector data. It also discusses the computer analysis of several additional properties of the solution, focusing on measurements of nonlinear convection such as Rayleigh number, Nusselt number, Reynolds number, and kinetic energy spectrum.Less
This chapter explains how to write a postprocessing code, and more specifically how to study the nonlinear simulations using computer graphics and analysis. It first considers how to compute and store results in a file during the computer simulation, assuming the Fourier transforms to x-space are done within the main computational code during the simulation. It then describes the postprocessing code for reading these files and displaying the various fields, along with the use of graphics software packages that provide additional, more sophisticated visualizations of the scalar and vector data. It also discusses the computer analysis of several additional properties of the solution, focusing on measurements of nonlinear convection such as Rayleigh number, Nusselt number, Reynolds number, and kinetic energy spectrum.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter focuses on internal gravity waves in a stable thermal stratification. When the amplitude of the fluid velocity is small relative to the amplitude of the phase velocity, a linear ...
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This chapter focuses on internal gravity waves in a stable thermal stratification. When the amplitude of the fluid velocity is small relative to the amplitude of the phase velocity, a linear analysis, which neglects advection, provides insight to the relation between the wavelength and frequency of internal gravity waves. Furthermore, when thermal and viscous diffusion play relatively minor roles the system can be further simplified by neglecting diffusion. The chapter first describes the linear dispersion relation before discussing the computer code modifications and simulations. In particular, it explains what modifications would be needed to convert one's thermal convection code to a code that simulates internal gravity waves, including the nonlinear and diffusive terms. Finally, it considers the computer analysis of wave energy.Less
This chapter focuses on internal gravity waves in a stable thermal stratification. When the amplitude of the fluid velocity is small relative to the amplitude of the phase velocity, a linear analysis, which neglects advection, provides insight to the relation between the wavelength and frequency of internal gravity waves. Furthermore, when thermal and viscous diffusion play relatively minor roles the system can be further simplified by neglecting diffusion. The chapter first describes the linear dispersion relation before discussing the computer code modifications and simulations. In particular, it explains what modifications would be needed to convert one's thermal convection code to a code that simulates internal gravity waves, including the nonlinear and diffusive terms. Finally, it considers the computer analysis of wave energy.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter discusses double-diffusive convection, with a particular focus on the initial instability and eventual nonlinear evolution. It first considers the “salt-fingering” instability and then ...
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This chapter discusses double-diffusive convection, with a particular focus on the initial instability and eventual nonlinear evolution. It first considers the “salt-fingering” instability and then the “semiconvection” instability before discussing the possibility that the onsets of these instabilities at marginal stability have an amplitude that oscillates in time. The goal is to find the conditions that would result in a zero growth rate of the oscillation amplitude in order to determine the marginal stability constraint on the Rayleigh numbers for the onset of an oscillating instability. The chapter also shows how, after evolving beyond the onset of the instability, thermal diffusion between the moving parcel and the surroundings can alter the initial linear vertical profile of the horizontal-mean temperature into a “staircase” profile. This evolution of the temperature profile is investigated via nonlinear simulations.Less
This chapter discusses double-diffusive convection, with a particular focus on the initial instability and eventual nonlinear evolution. It first considers the “salt-fingering” instability and then the “semiconvection” instability before discussing the possibility that the onsets of these instabilities at marginal stability have an amplitude that oscillates in time. The goal is to find the conditions that would result in a zero growth rate of the oscillation amplitude in order to determine the marginal stability constraint on the Rayleigh numbers for the onset of an oscillating instability. The chapter also shows how, after evolving beyond the onset of the instability, thermal diffusion between the moving parcel and the surroundings can alter the initial linear vertical profile of the horizontal-mean temperature into a “staircase” profile. This evolution of the temperature profile is investigated via nonlinear simulations.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0008
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter focuses on time integration schemes, including fourth-order accurate Runge–Kutta and predictor-corrector schemes as well as schemes that allow larger time steps (and therefore fewer ...
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This chapter focuses on time integration schemes, including fourth-order accurate Runge–Kutta and predictor-corrector schemes as well as schemes that allow larger time steps (and therefore fewer steps for a given amount of simulated time) by treating the linear diffusion terms implicitly. The nonlinear terms, however, couple all the modes and so would be extremely expensive to treat implicitly; therefore they are usually treated explicitly. Such “semi-implicit” schemes considerably improve the efficiency of the computer code. The chapter also describes the Crank–Nicolson scheme and concludes by showing how the current numerical model can easily be modified to study mantle convection (also called “geodynamics”) using the vorticity equation in the limit of an infinite Prandtl number.Less
This chapter focuses on time integration schemes, including fourth-order accurate Runge–Kutta and predictor-corrector schemes as well as schemes that allow larger time steps (and therefore fewer steps for a given amount of simulated time) by treating the linear diffusion terms implicitly. The nonlinear terms, however, couple all the modes and so would be extremely expensive to treat implicitly; therefore they are usually treated explicitly. Such “semi-implicit” schemes considerably improve the efficiency of the computer code. The chapter also describes the Crank–Nicolson scheme and concludes by showing how the current numerical model can easily be modified to study mantle convection (also called “geodynamics”) using the vorticity equation in the limit of an infinite Prandtl number.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0009
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter considers two ways of employing a spatial resolution that varies with position within a finite-difference method: using a nonuniform grid and mapping to a new coordinate variable. It ...
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This chapter considers two ways of employing a spatial resolution that varies with position within a finite-difference method: using a nonuniform grid and mapping to a new coordinate variable. It first provides an overview of nonuniform grids before discussing coordinate mapping as an alternative way of achieving spatial discretization. It then describes an approach for treating both the vertical and horizontal directions with simple finite-difference methods: defining a streamfunction, which automatically satisfies mass conservation, and solving for vorticity via the curl of the momentum conservation equation. It also explains the use of the Chebyshev–Fourier method to simulate the convection or gravity wave problem by employing spectral methods in both the horizontal and vertical directions. Finally, it looks at the basic ideas and some issues that need to be addressed with respect to parallel processing as well as choices that need to be made when designing a parallel code.Less
This chapter considers two ways of employing a spatial resolution that varies with position within a finite-difference method: using a nonuniform grid and mapping to a new coordinate variable. It first provides an overview of nonuniform grids before discussing coordinate mapping as an alternative way of achieving spatial discretization. It then describes an approach for treating both the vertical and horizontal directions with simple finite-difference methods: defining a streamfunction, which automatically satisfies mass conservation, and solving for vorticity via the curl of the momentum conservation equation. It also explains the use of the Chebyshev–Fourier method to simulate the convection or gravity wave problem by employing spectral methods in both the horizontal and vertical directions. Finally, it looks at the basic ideas and some issues that need to be addressed with respect to parallel processing as well as choices that need to be made when designing a parallel code.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter examines how boundary and geometry affect convection. It begins with a discussion of how one can implement “absorbing” top and bottom boundaries, which reduce the large-amplitude ...
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This chapter examines how boundary and geometry affect convection. It begins with a discussion of how one can implement “absorbing” top and bottom boundaries, which reduce the large-amplitude convectively driven flows within shallow boundary layers or the reflection of internal gravity waves off these boundaries in a stable stratification. It then considers how to replace the impermeable side boundary conditions with permeable periodic side boundary conditions to allow fluid flow through these boundaries and nonzero mean flow. It also introduces “two and a half dimensional” geometry within a cartesian box geometry and describes how a fully 3D cartesian box model could be constructed. Finally, it presents a model of convection in a fully 3D spherical-shell and shows how it can be easily reduced to a 2.5D spherical-shell model. The horizontal structures are represented in terms of spherical harmonic expansions.Less
This chapter examines how boundary and geometry affect convection. It begins with a discussion of how one can implement “absorbing” top and bottom boundaries, which reduce the large-amplitude convectively driven flows within shallow boundary layers or the reflection of internal gravity waves off these boundaries in a stable stratification. It then considers how to replace the impermeable side boundary conditions with permeable periodic side boundary conditions to allow fluid flow through these boundaries and nonzero mean flow. It also introduces “two and a half dimensional” geometry within a cartesian box geometry and describes how a fully 3D cartesian box model could be constructed. Finally, it presents a model of convection in a fully 3D spherical-shell and shows how it can be easily reduced to a 2.5D spherical-shell model. The horizontal structures are represented in terms of spherical harmonic expansions.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0011
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter focuses on magnetoconvection, which refers to thermal convection of an electrically conducting fluid within a background magnetic field maintained by some external mechanism. It first ...
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This chapter focuses on magnetoconvection, which refers to thermal convection of an electrically conducting fluid within a background magnetic field maintained by some external mechanism. It first provides a brief overview of magnetohydrodynamics and the magnetohydrodynamic equations before explaining how to make a 2D model of magnetic field. In this approach, the case of a uniform vertical background field and the case of a uniform horizontal background field are both considered. The chapter then describes how one could simulate a case of a uniform background field that is tilted relative to both the vertical and horizontal axes. It also considers what can be learned about the stability and structure of magnetoconvection and the dispersion relation for magneto-gravity waves from analytical analyses without the nonlinear terms. Finally, it discusses nonlinear simulations of magnetoconvection in a box with impermeable side boundaries, along with magnetoconvection with a horizontal background field and an arbitrary background field.Less
This chapter focuses on magnetoconvection, which refers to thermal convection of an electrically conducting fluid within a background magnetic field maintained by some external mechanism. It first provides a brief overview of magnetohydrodynamics and the magnetohydrodynamic equations before explaining how to make a 2D model of magnetic field. In this approach, the case of a uniform vertical background field and the case of a uniform horizontal background field are both considered. The chapter then describes how one could simulate a case of a uniform background field that is tilted relative to both the vertical and horizontal axes. It also considers what can be learned about the stability and structure of magnetoconvection and the dispersion relation for magneto-gravity waves from analytical analyses without the nonlinear terms. Finally, it discusses nonlinear simulations of magnetoconvection in a box with impermeable side boundaries, along with magnetoconvection with a horizontal background field and an arbitrary background field.
Gary A. Glatzmaier
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691141725
- eISBN:
- 9781400848904
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691141725.003.0013
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter examines the effects of rotation on convection and gravity waves. Flows in the atmospheres, oceans, and liquid cores of terrestrial planets are dominated by the Coriolis forces, as are ...
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This chapter examines the effects of rotation on convection and gravity waves. Flows in the atmospheres, oceans, and liquid cores of terrestrial planets are dominated by the Coriolis forces, as are the interiors of giant planets and stars. The sum of gravitational and centrifugal forces can go to zero at the top boundary of a rapidly rotating star or accretion disk. The time rate of change of the planetary rotation rate gives rise to Poincaré forces. The chapter first considers Coriolis, centrifugal, and Poincaré forces before explaining the modifications needed to add these effects of rotation to previous models of convection and gravity waves in 2D cartesian box and cylindrical annulus geometries, both of which now lie within a rotating equatorial plane. It also describes 2.5D rotating models and 3D spherical-shell magnetohydrodynamic dynamo models.Less
This chapter examines the effects of rotation on convection and gravity waves. Flows in the atmospheres, oceans, and liquid cores of terrestrial planets are dominated by the Coriolis forces, as are the interiors of giant planets and stars. The sum of gravitational and centrifugal forces can go to zero at the top boundary of a rapidly rotating star or accretion disk. The time rate of change of the planetary rotation rate gives rise to Poincaré forces. The chapter first considers Coriolis, centrifugal, and Poincaré forces before explaining the modifications needed to add these effects of rotation to previous models of convection and gravity waves in 2D cartesian box and cylindrical annulus geometries, both of which now lie within a rotating equatorial plane. It also describes 2.5D rotating models and 3D spherical-shell magnetohydrodynamic dynamo models.
Steven L. Chown and Sue W. Nicolson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198515494
- eISBN:
- 9780191705649
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515494.003.0003
- Subject:
- Biology, Animal Biology
Energy is a currency common to all animals, and the suite of responses shown by insects to the environments they inhabit is dependent on the metabolism of substrates. This chapter deals largely with ...
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Energy is a currency common to all animals, and the suite of responses shown by insects to the environments they inhabit is dependent on the metabolism of substrates. This chapter deals largely with aerobic catabolism and gas exchange, although anaerobic metabolism, which is relatively uncommon in insects, is also discussed. Gas exchange is typically via spiracles and tracheae, with oxygen and carbon dioxide exchange being divided both spatially and temporally to varying extents. Discontinuous gas exchange is characteristic of several insect species and it is thought to have evolved either to limit water loss, prevent oxidative damage, improve gas exchange under certain conditions, or simply as the outcome of interacting feedback systems. These mechanisms have all proven controversial. Metabolic rate varies with temperature, size, activity, feeding, and time of day. Insects in flight have some of the highest metabolic rates so far measured in any animals, and the costs of transport in caterpillars are relatively high. Understanding metabolic rate variation may provide a key to understanding global patterns in diversity.Less
Energy is a currency common to all animals, and the suite of responses shown by insects to the environments they inhabit is dependent on the metabolism of substrates. This chapter deals largely with aerobic catabolism and gas exchange, although anaerobic metabolism, which is relatively uncommon in insects, is also discussed. Gas exchange is typically via spiracles and tracheae, with oxygen and carbon dioxide exchange being divided both spatially and temporally to varying extents. Discontinuous gas exchange is characteristic of several insect species and it is thought to have evolved either to limit water loss, prevent oxidative damage, improve gas exchange under certain conditions, or simply as the outcome of interacting feedback systems. These mechanisms have all proven controversial. Metabolic rate varies with temperature, size, activity, feeding, and time of day. Insects in flight have some of the highest metabolic rates so far measured in any animals, and the costs of transport in caterpillars are relatively high. Understanding metabolic rate variation may provide a key to understanding global patterns in diversity.
Leon Mestel
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198526728
- eISBN:
- 9780191707049
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526728.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
Most stars appear to show some degree of magnetic activity. For example, the varying magnetic field of the Sun shows up in the familiar sun-spot cycle. Similar behaviour is observationally inferred ...
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Most stars appear to show some degree of magnetic activity. For example, the varying magnetic field of the Sun shows up in the familiar sun-spot cycle. Similar behaviour is observationally inferred in other solar-type stars. Radio and X-ray pulsars are enormously dense, rapidly rotating neutron stars that carry nearly steady magnetic fields, which are far stronger than the average magnetic field of the Sun. Likewise, many uncollapsed stars behave like rotating permanent magnets. Furthermore, magnetic fields may partly control the formation of new stars, especially through interaction with angular momentum, as well as the spectacular phenomena observed in galactic nuclei. Stellar magnetism is therefore a rapidly developing field of astrophysics. In this book, most of the important topics are treated in mathematical depth, with reference given to other relevant literature. Some of the studies, especially those on accretion discs, dynamos, and winds are applicable to galaxies and galactic nuclei.Less
Most stars appear to show some degree of magnetic activity. For example, the varying magnetic field of the Sun shows up in the familiar sun-spot cycle. Similar behaviour is observationally inferred in other solar-type stars. Radio and X-ray pulsars are enormously dense, rapidly rotating neutron stars that carry nearly steady magnetic fields, which are far stronger than the average magnetic field of the Sun. Likewise, many uncollapsed stars behave like rotating permanent magnets. Furthermore, magnetic fields may partly control the formation of new stars, especially through interaction with angular momentum, as well as the spectacular phenomena observed in galactic nuclei. Stellar magnetism is therefore a rapidly developing field of astrophysics. In this book, most of the important topics are treated in mathematical depth, with reference given to other relevant literature. Some of the studies, especially those on accretion discs, dynamos, and winds are applicable to galaxies and galactic nuclei.
Andrew P. Ingersoll
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691145044
- eISBN:
- 9781400848232
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691145044.003.0001
- Subject:
- Environmental Science, Climate
This book examines the fundamental physical processes that control planetary climates, from convection and radiation to escape of atmospheres, evaporation, condensation, atmospheric chemistry, and ...
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This book examines the fundamental physical processes that control planetary climates, from convection and radiation to escape of atmospheres, evaporation, condensation, atmospheric chemistry, and the dynamics of rotating fluids. It looks at the climates of the planets in order of distance from the Sun, starting with Venus and ending with planets around other stars. The greenhouse effect and climate evolution are discussed, along with basic physical processes such as convection, radiation, Hadley cells, and the accompanying winds. It also considers the “faint young Sun paradox,” illustrated by Mars, and the effect of planetary rotation on climate, the influence of sunlight and rotation on weather patterns, and Neptune's extraordinary strong winds.Less
This book examines the fundamental physical processes that control planetary climates, from convection and radiation to escape of atmospheres, evaporation, condensation, atmospheric chemistry, and the dynamics of rotating fluids. It looks at the climates of the planets in order of distance from the Sun, starting with Venus and ending with planets around other stars. The greenhouse effect and climate evolution are discussed, along with basic physical processes such as convection, radiation, Hadley cells, and the accompanying winds. It also considers the “faint young Sun paradox,” illustrated by Mars, and the effect of planetary rotation on climate, the influence of sunlight and rotation on weather patterns, and Neptune's extraordinary strong winds.
Andrew P. Ingersoll
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691145044
- eISBN:
- 9781400848232
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691145044.003.0003
- Subject:
- Environmental Science, Climate
This chapter examines the modern-day climate of Venus, focusing on the role of winds in energy transfer. It first explains how radiation and convection influence the temperature structure of Venus's ...
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This chapter examines the modern-day climate of Venus, focusing on the role of winds in energy transfer. It first explains how radiation and convection influence the temperature structure of Venus's atmosphere before discussing other basic physical processes such as Hadley cells and the accompanying winds. It also considers gases in hydrostatic equilibrium, adiabatic lapse rate and stability, the flux and intensity of electromagnetic radiation, blackbody radiation and the Planck function, blackbodies in the solar system, radiative transfer, optically thick atmosphere, radiative-convective equilibrium, emission of radiation to space, equilibrium temperature, energy transport by fluid motions and eddies, eddy momentum transport, and the phenomenon of superrotation.Less
This chapter examines the modern-day climate of Venus, focusing on the role of winds in energy transfer. It first explains how radiation and convection influence the temperature structure of Venus's atmosphere before discussing other basic physical processes such as Hadley cells and the accompanying winds. It also considers gases in hydrostatic equilibrium, adiabatic lapse rate and stability, the flux and intensity of electromagnetic radiation, blackbody radiation and the Planck function, blackbodies in the solar system, radiative transfer, optically thick atmosphere, radiative-convective equilibrium, emission of radiation to space, equilibrium temperature, energy transport by fluid motions and eddies, eddy momentum transport, and the phenomenon of superrotation.
Andrew P. Ingersoll
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691145044
- eISBN:
- 9781400848232
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691145044.003.0009
- Subject:
- Environmental Science, Climate
This chapter compares the climate of Saturn with that of Jupiter. Both Jupiter and Saturn have no oceans and no solid surfaces, but they have lightning storms and rain clouds that dwarf the largest ...
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This chapter compares the climate of Saturn with that of Jupiter. Both Jupiter and Saturn have no oceans and no solid surfaces, but they have lightning storms and rain clouds that dwarf the largest thunderstorms on Earth. Saturn's weather is normally very calm, but every 20–30 years a giant storm erupts. These storms last for a few months and then disappear. In contrast, Jupiter's giant storms endure without change for decades or centuries. Saturn's winds are stronger than Jupiter's. The chapter first reviews the variables that might control the planets' climates before discussing how the climates actually differ. It examines Saturn's rotation, giant storms, effective radiating temperature, electrostatic discharges and lightning, enrichment relative to solar composition, helium raindrops, moist convection and conditional instability, and ortho-para instability.Less
This chapter compares the climate of Saturn with that of Jupiter. Both Jupiter and Saturn have no oceans and no solid surfaces, but they have lightning storms and rain clouds that dwarf the largest thunderstorms on Earth. Saturn's weather is normally very calm, but every 20–30 years a giant storm erupts. These storms last for a few months and then disappear. In contrast, Jupiter's giant storms endure without change for decades or centuries. Saturn's winds are stronger than Jupiter's. The chapter first reviews the variables that might control the planets' climates before discussing how the climates actually differ. It examines Saturn's rotation, giant storms, effective radiating temperature, electrostatic discharges and lightning, enrichment relative to solar composition, helium raindrops, moist convection and conditional instability, and ortho-para instability.
Phil Attard
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199662760
- eISBN:
- 9780191745287
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199662760.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book builds from basic principles to advanced techniques, and covers the major phenomena, methods, and results of time-dependent systems. The book treats time-dependent systems by close analogy ...
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This book builds from basic principles to advanced techniques, and covers the major phenomena, methods, and results of time-dependent systems. The book treats time-dependent systems by close analogy with their static counterparts, with most of the familiar equilibrium results being generalised to the non-equilibrium case. The book is notable for its unified treatment of thermodynamics, hydrodynamics, stochastic processes, and statistical mechanics; for its coherent derivations of a variety of theorems; and for its quantitative tests against experimental measurements and computer simulations. Systems that evolve over time are more common than static systems, and yet until recently, they lacked any over-arching theory. This book provides a unified presentation of the theory of non-equilibrium systems, which has now reached the stage of quantitative experimental and computational verification. The novel perspective and deep understanding that this book brings offers the opportunity for new direction and growth in the study of time-dependent phenomena.Less
This book builds from basic principles to advanced techniques, and covers the major phenomena, methods, and results of time-dependent systems. The book treats time-dependent systems by close analogy with their static counterparts, with most of the familiar equilibrium results being generalised to the non-equilibrium case. The book is notable for its unified treatment of thermodynamics, hydrodynamics, stochastic processes, and statistical mechanics; for its coherent derivations of a variety of theorems; and for its quantitative tests against experimental measurements and computer simulations. Systems that evolve over time are more common than static systems, and yet until recently, they lacked any over-arching theory. This book provides a unified presentation of the theory of non-equilibrium systems, which has now reached the stage of quantitative experimental and computational verification. The novel perspective and deep understanding that this book brings offers the opportunity for new direction and growth in the study of time-dependent phenomena.
Igor S. Aranson and Lev S. Tsimring
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199534418
- eISBN:
- 9780191714665
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534418.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter contains an overview of experiments and theories on segregation occurring in heterogeneous granular materials. One of the most fascinating features of heterogeneous (i.e., consisting of ...
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This chapter contains an overview of experiments and theories on segregation occurring in heterogeneous granular materials. One of the most fascinating features of heterogeneous (i.e., consisting of different distinct components) granular materials is their tendency to segregate under external agitation rather than to mix, as one would expect from the naive entropy consideration. Various basic segregation mechanisms (e.g., entropic segregations, kinetic sieving, granular convection, condensation, etc.) and various experimental manifestations of granular segregation (e.g., granular stratification in surface flows, radial and axial segregation in rotating drums and related theoretical concepts, including discrete cellular automata and continuum phenomenological models) are discussed.Less
This chapter contains an overview of experiments and theories on segregation occurring in heterogeneous granular materials. One of the most fascinating features of heterogeneous (i.e., consisting of different distinct components) granular materials is their tendency to segregate under external agitation rather than to mix, as one would expect from the naive entropy consideration. Various basic segregation mechanisms (e.g., entropic segregations, kinetic sieving, granular convection, condensation, etc.) and various experimental manifestations of granular segregation (e.g., granular stratification in surface flows, radial and axial segregation in rotating drums and related theoretical concepts, including discrete cellular automata and continuum phenomenological models) are discussed.
Kyösti Kontturi, Lasse Murtomäki, and José A. Manzanares
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199533817
- eISBN:
- 9780191714825
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533817.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter presents an introduction to thermodynamics of irreversible processes. The fundamental thermodynamic concepts required for studying the irreversible processes taking place in a moving ...
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This chapter presents an introduction to thermodynamics of irreversible processes. The fundamental thermodynamic concepts required for studying the irreversible processes taking place in a moving fluid are described. A local approach is followed in which the state variables are functions of time and the spatial coordinates. The local equilibrium hypothesis and its key role in irreversible thermodynamics are explained. The transport processes involve the exchange of matter, electric charge, linear momentum, energy, entropy, etc., between the neighbouring volume elements in the fluid. The balance equations that rule these exchanges are explained in detail, and the entropy balance equation receives special attention. The differences between the transport mechanisms of convection, chemical diffusion, electrodiffusion, ionic diffusion, ionic migration, and electric conduction are explained. The chapter discusses the concept of electric potential in thermodynamics and electrochemistry.Less
This chapter presents an introduction to thermodynamics of irreversible processes. The fundamental thermodynamic concepts required for studying the irreversible processes taking place in a moving fluid are described. A local approach is followed in which the state variables are functions of time and the spatial coordinates. The local equilibrium hypothesis and its key role in irreversible thermodynamics are explained. The transport processes involve the exchange of matter, electric charge, linear momentum, energy, entropy, etc., between the neighbouring volume elements in the fluid. The balance equations that rule these exchanges are explained in detail, and the entropy balance equation receives special attention. The differences between the transport mechanisms of convection, chemical diffusion, electrodiffusion, ionic diffusion, ionic migration, and electric conduction are explained. The chapter discusses the concept of electric potential in thermodynamics and electrochemistry.
Stephen J. Blundell and Katherine M. Blundell
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0035
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter applies some of the concepts of thermal physics developed earlier in this book to stellar astrophysics. Astrophysics is the study of the physical properties of the Universe and the ...
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This chapter applies some of the concepts of thermal physics developed earlier in this book to stellar astrophysics. Astrophysics is the study of the physical properties of the Universe and the objects therein. The chapter examines how gravity, nuclear reactions, convection, and conduction all lead to the observed properties of stellar material.Less
This chapter applies some of the concepts of thermal physics developed earlier in this book to stellar astrophysics. Astrophysics is the study of the physical properties of the Universe and the objects therein. The chapter examines how gravity, nuclear reactions, convection, and conduction all lead to the observed properties of stellar material.
