*Adrian F. Tuck*

- Published in print:
- 2008
- Published Online:
- November 2020
- ISBN:
- 9780199236534
- eISBN:
- 9780191917462
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199236534.003.0011
- Subject:
- Earth Sciences and Geography, Atmospheric Sciences

In this chapter, we offer a summary of the book’s results and conclusions, ask what future developments might be contemplated, both theoretical and experimental, and provide some scientific ...
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In this chapter, we offer a summary of the book’s results and conclusions, ask what future developments might be contemplated, both theoretical and experimental, and provide some scientific quotations which seemed relevant. The quotations are collected here rather than dispersed through the text, because some of them apply at several junctures and one or two apply to the whole book. It is hoped that they will underline some important points in a memorable and even entertaining manner. Application of generalized scale invariance to large amounts of research quality in situ airborne observations of the free troposphere and lower stratosphere has shown that the atmosphere behaves as a random, non-Gaussian, Lévy stable process. The scaling exponents describing the resultant statistical multifractality are the conservation H1, the intermittency C1 and the departure from monofractality α, the Lévy exponent. They had average values of 0.55, 0.05, and 1.6 respectively as deduced from airborne time series of wind speed and temperature. Certain regimes, such as jet streams, however showed correlation within the mean; the value of H1(s) for horizontal wind speed s was positively correlated with the magnitude of the horizontal speed shear and the value of H1(T) for temperature was positively correlated with the meridional (equator-to-pole) temperature gradient. The value of H1(s) in the vertical showed clear correlation with vertical measures of jet stream strength, such as depth and maximum speed. The vertical scaling of temperature showed the paramount influence of gravity, having H1 close to unity, while horizontal wind speed and relative humidity were about 0.75. These results show that large scale ordered flow can be interpreted as emerging from less ordered smaller scale motions. At the same time, the smaller scale motions are never truly random in the atmosphere and the larger scale motions are never perfectly correlated, smooth flow. Ozone and water, while occasionally behaving as passive scalars, that is to say as tracers, more often showed the presence of sources and sinks: a numerical model-independent demonstration of the operation of photochemistry and precipitation respectively.
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In this chapter, we offer a summary of the book’s results and conclusions, ask what future developments might be contemplated, both theoretical and experimental, and provide some scientific quotations which seemed relevant. The quotations are collected here rather than dispersed through the text, because some of them apply at several junctures and one or two apply to the whole book. It is hoped that they will underline some important points in a memorable and even entertaining manner. Application of generalized scale invariance to large amounts of research quality in situ airborne observations of the free troposphere and lower stratosphere has shown that the atmosphere behaves as a random, non-Gaussian, Lévy stable process. The scaling exponents describing the resultant statistical multifractality are the conservation H1, the intermittency *C*_{1} and the departure from monofractality α, the Lévy exponent. They had average values of 0.55, 0.05, and 1.6 respectively as deduced from airborne time series of wind speed and temperature. Certain regimes, such as jet streams, however showed correlation within the mean; the value of *H*_{1}_{(s)} for horizontal wind speed s was positively correlated with the magnitude of the horizontal speed shear and the value of *H*_{1}(T) for temperature was positively correlated with the meridional (equator-to-pole) temperature gradient. The value of *H*_{1}(s) in the vertical showed clear correlation with vertical measures of jet stream strength, such as depth and maximum speed. The vertical scaling of temperature showed the paramount influence of gravity, having H1 close to unity, while horizontal wind speed and relative humidity were about 0.75. These results show that large scale ordered flow can be interpreted as emerging from less ordered smaller scale motions. At the same time, the smaller scale motions are never truly random in the atmosphere and the larger scale motions are never perfectly correlated, smooth flow. Ozone and water, while occasionally behaving as passive scalars, that is to say as tracers, more often showed the presence of sources and sinks: a numerical model-independent demonstration of the operation of photochemistry and precipitation respectively.

*Dmitry Budker and Alexander O. Sushkov*

- Published in print:
- 2015
- Published Online:
- April 2015
- ISBN:
- 9780199681655
- eISBN:
- 9780191761645
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199681655.003.0002
- Subject:
- Physics, Atomic, Laser, and Optical Physics, Particle Physics / Astrophysics / Cosmology

The problems in this chapter cover hydrostatics, nonviscous and viscous flow, surface gravity waves, bubbles, melting, the distribution of the Earth’s atmospheric temperature, and other topics. The ...
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The problems in this chapter cover hydrostatics, nonviscous and viscous flow, surface gravity waves, bubbles, melting, the distribution of the Earth’s atmospheric temperature, and other topics. The presentation takes into account the fact that many, if not most, students of physics in the United States will not have had a course on fluids in their undergraduate curriculum, so the presentation draws on analogies with electricity and magnetism. Many results will be found amusing and surprising even by practicing physicists.Less

The problems in this chapter cover hydrostatics, nonviscous and viscous flow, surface gravity waves, bubbles, melting, the distribution of the Earth’s atmospheric temperature, and other topics. The presentation takes into account the fact that many, if not most, students of physics in the United States will not have had a course on fluids in their undergraduate curriculum, so the presentation draws on analogies with electricity and magnetism. Many results will be found amusing and surprising even by practicing physicists.