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Numerical Method

Gary A. Glatzmaier

in Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation

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. ... More


ALGORITHMS FOR INCOMPRESSIBLE FLOWS

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0008
Subject:
Mathematics, Numerical Analysis

This chapter presents different ways of formulating the incompressible Navier-Stokes equations based on primitive variables, that is, velocity and pressure, as well as velocity-vorticity algorithms. ... More


Acquisition of knowledge

John J. Videler

in Avian Flight

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199299928
eISBN:
9780191714924
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199299928.003.0001
Subject:
Biology, Ornithology

This chapter discusses the development of the understanding of bird flight and the physical laws governing flight, taking Aristotle’s philosophy and observations as a starting point. From the ... More


Barotropic aspects of large-scale atmospheric turbulence

Theodore G. Shepherd

in Fundamental Aspects of Turbulent Flows in Climate Dynamics: Lecture Notes of the Les Houches Summer School: Volume 109, August 2017

Published in print:
2020
Published Online:
March 2020
ISBN:
9780198855217
eISBN:
9780191889172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198855217.003.0004
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The chapter begins with a phenomenological treatment of the observed atmospheric circulation. It then goes on to discuss how the barotropic model arises as a so-calledbalanced model of the slow, ... More


Waves

Tim Woollings

in Jet Stream: A Journey Through our Changing Climate

Published in print:
2019
Published Online:
September 2019
ISBN:
9780198828518
eISBN:
9780191867002
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198828518.003.0005
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The chapter opens with a description of severe weather events which occurred across Asia in the summer of 2010. These events were linked in atmospheric physics by a Rossby wave, which causes the jet ... More


Reliability without Truth

in Science in the Age of Computer Simulation

Published in print:
2010
Published Online:
March 2013
ISBN:
9780226902029
eISBN:
9780226902050
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226902050.003.0007
Subject:
Philosophy, Philosophy of Science

This chapter examines the source of credibility of computer simulation models. It suggests that the practice of using fictions in building credible simulations is worthy of closer scrutiny by ... More


The equations of fluid mechanics

P. A. Davidson

in Turbulence: An Introduction for Scientists and Engineers

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198722588
eISBN:
9780191789298
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198722588.003.0002
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

Chapter 2 reviews the fundamental equations and laws of fluid mechanics, particularly those which are relevant to turbulence. The focus is on vortex dynamics, which underpins much of turbulence.


The role of numerical simulations

P. A. Davidson

in Turbulence: An Introduction for Scientists and Engineers

Published in print:
2015
Published Online:
August 2015
ISBN:
9780198722588
eISBN:
9780191789298
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198722588.003.0007
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

Chapter 7 discusses the role of numerical simulations in turbulence. The emphasis is on the new physical insights these numerical experiments have yielded, as well as some of the limitations of ... More


Physics and Dynamics of the Oceans

Han Dolman

in Biogeochemical Cycles and Climate

Published in print:
2019
Published Online:
June 2019
ISBN:
9780198779308
eISBN:
9780191824388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198779308.003.0007
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

This chapter focuses on the physics and dynamics of the ocean. It describes the variability of salinity and surface temperature, as well as the vertical temperature structure of the ocean, with the ... More


Primitive Equations Model

Vladimir Zeitlin

in Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models

Published in print:
2018
Published Online:
April 2018
ISBN:
9780198804338
eISBN:
9780191842627
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198804338.003.0002
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The chapter gives the foundations of modelling of large-scale atmospheric and oceanic motions and presents the ‘primitive equations’ (PE) model. After a concise reminder on general fluid mechanics, ... More


Simplifying Primitive Equations: Rotating Shallow-Water Models and their Properties

Vladimir Zeitlin

in Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models

Published in print:
2018
Published Online:
April 2018
ISBN:
9780198804338
eISBN:
9780191842627
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198804338.003.0003
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

In this chapter, one- and two-layer versions of the rotating shallow-water model on the tangent plane to the rotating, and on the whole rotating sphere, are derived from primitive equations by ... More


Intermezzo: Effects of Increasing Reynolds Number

Troy Shinbrot

in Biomedical Fluid Dynamics: Flow and Form

Published in print:
2019
Published Online:
June 2019
ISBN:
9780198812586
eISBN:
9780191850721
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812586.003.0007
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Effects of increasing fluid speed are analyzed. The Bernouilli and vorticity equations are derived, and the method of matching solutions is described for the Rankine vortex. Cases in which rotational ... More


A Phenomenological Theory of Superconductivity: The London Equations

J. B. Ketterson

in The Physics of Solids

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198742906
eISBN:
9780191821523
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198742906.003.0032
Subject:
Physics, Condensed Matter Physics / Materials

This chapter focuses on superconductors. Many metals, alloys, and intermetallic compounds undergo a phase transition at some (generally low) temperature to a state having zero electrical resistance, ... More


Superfluid4He

J. B. Ketterson

in The Physics of Solids

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198742906
eISBN:
9780191821523
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198742906.003.0036
Subject:
Physics, Condensed Matter Physics / Materials

Liquid helium is the only substance which, below some temperature-dependent pressure, does not solidify on cooling to absolute zero. The fact that it does not freeze is due to the large quantum ... More


Vorticity, Vortex Dynamics and Rotating Flows

Etienne Guyon, Jean-Pierre Hulin, Luc Petit, and Catalin.D. Mitescu

in Physical Hydrodynamics, 2nd Edn

Published in print:
2015
Published Online:
March 2015
ISBN:
9780198702443
eISBN:
9780191772153
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198702443.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Vorticity characterizes the local rotation within a fluid. It can be continuously distributed or nonzero only on singular lines: the study of such “vortex filaments” suggests an analogy with ... More


An Introduction to Finite Differencing

T. N. Krishnamurti, H. S. Bedi, and V. M. Hardiker

in An Introduction to Global Spectral Modeling

Published in print:
1998
Published Online:
November 2020
ISBN:
9780195094732
eISBN:
9780197560761
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195094732.003.0004
Subject:
Earth Sciences and Geography, Meteorology and Climatology

This chapter on finite differencing appears oddly placed in the early part of a text on spectral modeling. Finite differences are still traditionally used for vertical differencing and for time ... More


Mathematical Aspects of Spectral Models

T. N. Krishnamurti, H. S. Bedi, and V. M. Hardiker

in An Introduction to Global Spectral Modeling

Published in print:
1998
Published Online:
November 2020
ISBN:
9780195094732
eISBN:
9780197560761
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195094732.003.0008
Subject:
Earth Sciences and Geography, Meteorology and Climatology

In this chapter we provide an introduction to the topic of spherical harmonics as basis functions for a global spectral model. The spherical harmonics are made up of trigonometric functions along ... More


Relevant Subjects

Adrian F. Tuck

in Atmospheric Turbulence: a molecular dynamics perspective

Published in print:
2008
Published Online:
November 2020
ISBN:
9780199236534
eISBN:
9780191917462
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199236534.003.0006
Subject:
Earth Sciences and Geography, Atmospheric Sciences

Atmospheric composition played an important part in the development of chemistry, following the work of Priestley, Lavoisier, and Dalton. Since air is a mixture of gases, many of them chemically ... More


The Statistical Physics of Subsurface Solute Transport

Garrison Sposito

in Vadose Zone Hydrology: Cutting Across Disciplines

Published in print:
1999
Published Online:
November 2020
ISBN:
9780195109900
eISBN:
9780197561058
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195109900.003.0007
Subject:
Earth Sciences and Geography, Oceanography and Hydrology

The first detailed study of solute movement through the vadose zone at field scales of space and time was performed by Biggar and Nielsen (1976). Their experiment was conducted on a 150-ha ... More


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