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ADVECTION AND ADVECTION DIFFUSION

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/9780198528692.003.0006
Subject:
Mathematics, Numerical Analysis

This chapter focuses on the scalar advection equation and develops a Galerkin discretization using the techniques described in Chapter 4. It includes an extended presentation of the discontinuous ... More


Internal Gravity Waves

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/9780691141725.003.0006
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 ... More


Fluid Mechanics: A Geometrical Point of View

S. G. Rajeev

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.001.0001
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using ... More


Climate

David Greenland and Mark Losleben

in Structure and Function of an Alpine Ecosystem: Niwot Ridge, Colorado

Published in print:
2001
Published Online:
November 2020
ISBN:
9780195117288
eISBN:
9780197561171
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195117288.003.0007
Subject:
Environmental Science, Applied Ecology

Climate is one of the most important determinants of biotic structure and function in the alpine. High winds and low temperatures are defining elements of ... More


Second Moments of Rain

Ilya Polyak

in Computational Statistics in Climatology

Published in print:
1996
Published Online:
November 2020
ISBN:
9780195099997
eISBN:
9780197560938
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195099997.003.0010
Subject:
Computer Science, Mathematical Theory of Computation

The first part of this chapter presents a description of the GATE rain rate data (Polyak and North, 1995), its two-dimensional spectral and correlation ... More


Basic Concepts

Eric B. Kraus and Joost A. Businger

in Atmosphere-Ocean Interaction

Published in print:
1995
Published Online:
November 2020
ISBN:
9780195066180
eISBN:
9780197560204
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195066180.003.0005
Subject:
Earth Sciences and Geography, Oceanography and Hydrology

Both Cartesian tensor and vector notation will be used in this text. The notation xi means the i-component of the vector x = (x1 x2, x3). When used in the argument of ... More


Particle Absorption and Scatter

Michael E. Thomas

in Optical Propagation in Linear Media: Atmospheric Gases and Particles, Solid State Components, and Water

Published in print:
2006
Published Online:
November 2020
ISBN:
9780195091618
eISBN:
9780197560679
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195091618.003.0015
Subject:
Earth Sciences and Geography, Atmospheric Sciences

Particles are composed of solids and/or liquids, thus the bulk optical properties of these media must be known before propagation modeling within a medium ... More


Non-Equilibrium Statistical Mechanics

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/9780199236534.003.0010
Subject:
Earth Sciences and Geography, Atmospheric Sciences

The Earth’s atmosphere is far from equilibrium; it is constantly in motion from the combined effects of gravity and planetary rotation, is constantly absorbing and ... More


Evaporation : Use of Fast-Response Turbulence Sensors, Raman Lidar, and Passive Microwave Remote Sensing

Marc B. Parlance and John D. Albertson

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/9780195109900.003.0014
Subject:
Earth Sciences and Geography, Oceanography and Hydrology

Since evaporation represents some 60% of precipitation over land surfaces, it is crucial for hydrologic purposes to know with some degree of certainty the magnitude of ... More


Porous Media Flows

David Jon Furbish

in Fluid Physics in Geology: An Introduction to Fluid Motions on Earth's Surface and Within its Crust

Published in print:
1997
Published Online:
November 2020
ISBN:
9780195077018
eISBN:
9780197560358
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195077018.003.0017
Subject:
Earth Sciences and Geography, Geophysics: Earth Sciences

So far our treatment of fluid motions has not emphasized the behavior of fluids residing within porous geological materials. Let us now turn to this topic and, in ... More


Flow and dispersion

Paul T. Callaghan

in Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199556984
eISBN:
9780191774928
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556984.003.0002
Subject:
Physics, Condensed Matter Physics / Materials, Nuclear and Plasma Physics

This chapter, which discusses the basics of fluid dynamics, including the Lagrangan and Eulerian description, advection, and the substantive derivative, introduces the Navier-Stokes equation and ... More


Diffusion

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/9780198812586.003.0012
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

The diffusion equation is derived and solved for simple geometries. Fourier series are described, and superposition is used to combine simple solutions into more complicated ones. Advection is ... More


The Finite-Volume Method

Heiner Igel

in Computational Seismology: A Practical Introduction

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198717409
eISBN:
9780191835070
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198717409.003.0008
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The finite-volume method is introduced as a consequence of a general (mass, tracer, energy) conservation problem. The wave equation is derived from this fundamental conservation principle. The ... More


The Discontinuous Galerkin Method

Heiner Igel

in Computational Seismology: A Practical Introduction

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198717409
eISBN:
9780191835070
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198717409.003.0009
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

The discontinuous Galerkin method is introduced as a special type of finite-element method in which the solution fields are allowed to be discontinuous at the element boundaries. This requires the ... More


Advection–Diffusion Models

Matthieu Roy-Barman and Catherine Jeandel

in Marine Geochemistry: Ocean Circulation, Carbon Cycle and Climate Change

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198787495
eISBN:
9780191829604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198787495.003.0006
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

Advection–diffusion models provide a continuous description of tracers in the ocean. The advection–diffusion equation is obtained by combining the conservation equation for an infinitely small box ... More


Solute Transport in Soils

Marco Bittelli, Gaylon S. Campbell, and Fausto Tomei

in Soil Physics with Python: Transport in the Soil–Plant–Atmosphere System

Published in print:
2015
Published Online:
August 2015
ISBN:
9780199683093
eISBN:
9780191763175
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199683093.003.0013
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

This chapter deals with solute transport, which is a very important part of the study of soil physics, describing the movement of nutrients, salts and contaminants. Its application is particularly ... More


Vector Fields

S. G. Rajeev

in Fluid Mechanics: A Geometrical Point of View

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805021
eISBN:
9780191843136
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805021.003.0001
Subject:
Physics, Soft Matter / Biological Physics, Condensed Matter Physics / Materials

The velocity of a fluid at each point of space-time is a vector field (or flow). It is best to think of it in terms of the effect of fluid flow on some scalar field. A vector field is thus a first ... More


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