From molecules to meteorology via turbulent scale invariance

Tuck, A. F.

doi:10.1002/qj.644

Cited by 34 publications

(59 citation statements)

References 99 publications

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“…However, examination of the apparently calm regions shows that they also have embedded regions of high activity, and as we zoom into smaller and smaller regions this strong heterogeneity continues in a scaling manner until we reach the dissipation scale (Tuck, 2010). This explains why aircraft measurements of the wind invariably find roughly k −5/3 (i.e.…”

Section: Introductionmentioning

confidence: 78%

Atmospheric waves as scaling, turbulent phenomena

Pinel

Lovejoy

2014

Atmos. Chem. Phys.

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Abstract. It is paradoxical that, while atmospheric dynamics are highly nonlinear and turbulent, atmospheric waves are commonly modelled by linear or weakly nonlinear theories. We postulate that the laws governing atmospheric waves are in fact high-Reynolds-number (Re), emergent laws so that -in common with the emergent high-Re turbulent lawsthey are also constrained by scaling symmetries. We propose an effective turbulence-wave propagator which corresponds to a fractional and anisotropic extension of the classical wave equation propagator, with dispersion relations similar to those of inertial gravity waves (and Kelvin waves) yet with an anomalous (fractional) order H wav /2. Using geostationary IR radiances, we estimate the parameters, finding that H wav ≈ 0.17 ± 0.04 (the classical value = 2).

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Section: Introductionmentioning

confidence: 78%

Atmospheric waves as scaling, turbulent phenomena

Pinel

Lovejoy

2014

Atmos. Chem. Phys.

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“…Intensive research efforts undertaken over the recent decades have provided with robust evidence for the existence statistical scale-invariance (scaling) properties in the complex structure of atmospheric winds (see, e.g., [1, 2, 3] for reviews). Typically, near-surface wind time-series display power-law scaling behavior with a ubiquitous high-frequency inertial range, with a 5/3 scaling exponent in close agreement with Kolmogorov [4] predictions.…”

Section: Introductionmentioning

confidence: 99%

Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind

Nogueira

2017

PLoS ONE

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The equivalency between the power law behavior of Multiscale Entropy (MSE) and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing) scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1–10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the underlying scaling behavior, with both periodic and fractal terms playing an important role in the observed wind time-series.

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“…I am also grateful to all three reviewers of the initial version of my manuscript for Entropy. I thank the first reviewer of the initial version of my manuscript for a very helpful list of references, from among which are References [2,24,42,43,75,76] cited in this revised version thereof. (Reference [76] by extension requires also citing Reference [77].)…”

Section: Synopsismentioning

confidence: 99%

“…I thank the first reviewer of the initial version of my manuscript for a very helpful list of references, from among which are References [2,24,42,43,75,76] cited in this revised version thereof. (Reference [76] by extension requires also citing Reference [77].) I also thank Technical Support at Mackichan Software, especially John MacKendrick and George Pearson, for their extensive help with putting the initial version of my manuscript into the correct computer format, into which I could paste early drafts of this revised version thereof.…”

Section: Synopsismentioning

confidence: 99%

“…This contributes, along with radiational cooling from high atmospheric altitudes to space, to lapse rates above the surface inversion layer in Antarctica in winter that can reach the dry adiabatic [78,79], although on the average they are perhaps about half that large [80]. It has been pointed out that the atmosphere, being a highly complex system far from thermodynamic equilibrium, may have a fractal structure that repeats on ever-smaller scales (scale invariance) [75][76][77]. (See also Reference [24], Chapters 2-5, especially Chapter 4, and most especially pp.…”

Section: Appendix a Horizontal Temperature Gradientsmentioning

confidence: 99%

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Condensation: Passenger Not Driver in Atmospheric Thermodynamics

Denur¹

2016

Entropy

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Abstract:The second law of thermodynamics states that processes yielding work or at least capable of yielding work are thermodynamically spontaneous, and that those costing work are thermodynamically nonspontaneous. Whether a process yields or costs heat is irrelevant. Condensation of water vapor yields work and hence is thermodynamically spontaneous only in a supersaturated atmosphere; in an unsaturated atmosphere it costs work and hence is thermodynamically nonspontaneous. Far more of Earth's atmosphere is unsaturated than supersaturated; based on this alone evaporation is far more often work-yielding and hence thermodynamically spontaneous than condensation in Earth's atmosphere-despite condensation always yielding heat and evaporation always costing heat. Furthermore, establishment of the unstable or at best metastable condition of supersaturation, and its maintenance in the face of condensation that would wipe it out, is always work-costing and hence thermodynamically nonspontaneous in Earth's atmosphere or anywhere else. The work required to enable supersaturation is most usually provided at the expense of temperature differences that enable cooling to below the dew point. In the case of most interest to us, convective weather systems and storms, it is provided at the expense of vertical temperature gradients exceeding the moist adiabatic. Thus, ultimately, condensation is a work-costing and hence thermodynamically nonspontaneous process even in supersaturated regions of Earth's or any other atmosphere. While heat engines in general can in principle extract all of the work represented by any temperature difference until it is totally neutralized to isothermality, convective weather systems and storms in particular cannot. They can extract only the work represented by partial neutralization of super-moist-adiabatic lapse rates to moist-adiabaticity. Super-moist-adiabatic lapse rates are required to enable convection of saturated air. Condensation cannot occur fast enough to maintain relative humidity in a cloud exactly at saturation, thereby trapping some water vapor in metastable supersaturation. Only then can the water vapor condense. Thus ultimately condensation is a thermodynamically nonspontaneous process forced by super-moist-adiabatic lapse rates. Yet water vapor plays vital roles in atmospheric thermodynamics and kinetics. Convective weather systems and storms in a dry atmosphere (e.g., dust devils) can extract only the work represented by partial neutralization of super-dry-adiabatic lapse rates to dry-adiabaticity. At typical atmospheric temperatures in the tropics, where convective weather systems and storms are most frequent and active, the moist-adiabatic lapse rate is much smaller (thus much closer to isothermality), and hence represents much more extractable work, than the dry-the thermodynamic advantage of water vapor. Moreover, the large heat of condensation (and to a lesser extent fusion) of water facilitates much faster heat transfer from Earth's surface to the tropopause than is possible...

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From molecules to meteorology via turbulent scale invariance

Cited by 34 publications

References 99 publications

Atmospheric waves as scaling, turbulent phenomena

Atmospheric waves as scaling, turbulent phenomena

Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind

Condensation: Passenger Not Driver in Atmospheric Thermodynamics

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