UID:
almafu_9959245608002883
Format:
1 online resource (xv, 475 pages) :
,
digital, PDF file(s).
Edition:
1st ed.
ISBN:
1-107-23548-0
,
1-139-62534-9
,
1-139-60884-3
,
1-139-61232-8
,
1-139-09381-9
,
1-139-61604-8
,
1-299-40570-3
,
1-139-62162-9
Content:
Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modelling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. By generalizing the classical turbulence laws, emergent higher-level laws of atmospheric dynamics are obtained and are empirically validated over time-scales of seconds to decades and length-scales of millimetres to the size of the planet. In generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modelling and understanding the atmosphere. This synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs. This is an important resource for atmospheric science researchers new to multifractal theory and is also valuable for graduate students in atmospheric dynamics and physics, meteorology, oceanography and climatology.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Contents; Preface; Acknowledgments; Acronyms and abbreviations; Chapter 1 Introduction; 1.1 A new synthesis; 1.1.1 Two (irreconcilable?) approaches to understanding the atmosphere; 1.1.2 Which chaos for geophysics, for atmospheric science: deterministic or stochastic?; 1.2 The Golden Age, resolution, revolution and paradox: an up-to-date empirical tour of atmospheric variability; 1.2.1 The basic form of the emergent laws and spectral analysis; 1.2.2 Atmospheric data in a Golden Age; In-situ networks; In-situ measurements: aircraft, sondes; Remote sensing; Reanalyses
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1.2.3 The horizontal scaling of atmospheric fields1.2.4 The atmosphere in the vertical; 1.2.5 The smallest scales; 1.2.6 Temporal scaling, weather, macroweather and the climate; 1.2.7 The scaling of the atmospheric boundary conditions; 1.3 The phenomenological fallacy; Chapter 2 Classical turbulence, modern evidence; 2.1 Complexity or simplicity? Richardson ́s dreams and the emergence of the laws of turbulence; 2.1.1 Numerical weather prediction and statistical theories of turbulence; 2.1.2 The nonlinear revolution: complex or simple?
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2.2 The equations of the atmosphere and their scale symmetries2.2.1 The cascade alternative; 2.2.2 Scaling; 2.2.3 Conservation of turbulent fluxes from one scale to another; 2.3 Extensions to passive scalars, to the atmospheric primitive equations; 2.3.1 Passive scalars, conservation of passive scalar variance flux; 2.3.2 The scale invariance of the equations of the atmosphere: an anisotropic scaling analysis of the ``primitive equations ́ ́; 2.4 Classical isotropic 3D turbulence phenomenology: Kolmogorov turbulence and energy cascades
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2.4.1 Fourier locality, energy transfer and cascade phenomenology2.4.2 The Kolmogorov-Obukhov spectrum; 2.4.3 Vortex stretching, the break-up of eddies and the cascade direction; 2.4.4* The vorticity spectrum; 2.5 The special case of 2D turbulence; 2.5.1 Comparing two- and three-dimensional turbulence; 2.5.2 Two-dimensional enstrophy cascades; 2.6 Atmospheric extensions; 2.6.1 Applying isotropic turbulence to the atmosphere: the Gage-Lilly model; 2.6.2 The real transition is from k-5/3 to k-2.4 and it is spurious: a review of the classical aircraft campaigns and a new one (TAMDAR)
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2.6.3 The classical approach: conclusions from analyses and reanalyses2.6.4 Evidence from satellite altimeter winds over the ocean; 2.6.5 The continuing difficulties with the classical model and inferences from numerical simulations; 2.6.6 Empirical determination of the direction of the cascade; 2.7 Summary of emergent laws in Chapter 2; Appendix 2A: Spectral analysis in arbitrary dimensions; Appendix 2B: Cascade phenomenology and spectral analysis; Term (I); Term (III); Term (II); Appendix 2C: Spectral transfers; Chapter 3 Scale-by-scale simplicity: an introduction to multiplicative cascades
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3.1 Cascades as conceptual models
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English
Additional Edition:
ISBN 1-108-44601-9
Additional Edition:
ISBN 1-107-01898-6
Language:
English
URL:
https://doi.org/10.1017/CBO9781139093811
