Saturated‐cascade similitude theory of gravity wave spectra

Dewan, E. M.

doi:10.1029/97jd02151

Cited by 107 publications

(118 citation statements)

References 76 publications

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“…Such approaches have been adopted by VanZandt (1982), Lovejoy (1985, 1987), Fritts et al (1988), Tsuda et al (1989), Gardner et al (1993), Gardner (1994), Hostetler and Gardner (1994), Lazarev et al (1994) and Dewan (1997), although they do not predict identical scaling exponents; see below. We note that Eady (1950) made some incisive remarks about the causative role of turbulence in the atmospheric general circulation that seem to have been largely ignored in the numerical model era.…”

Section: Brief Review Of Theories Of Atmospheric Turbulencementioning

confidence: 99%

From molecules to meteorology via turbulent scale invariance

Tuck

2010

Quart J Royal Meteoro Soc

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This review attempts to interpret the generalized scale invariance observed in common atmospheric variables -wind, temperature, humidity, ozone and some trace species -in terms of the computed emergence of ring currents (vortices) in simulations of populations of Maxwellian molecules subject to an anisotropy in the form of a flux. The data are taken from 'horizontal' tracks of research aircraft and from 'vertical' trajectories of research dropsondes. It is argued that any attempt to represent the energy distribution in the atmosphere quantitatively must have a proper basis in molecular physics, a prerequisite to accommodate the observed longtailed velocity probability distributions and the implied effects on radiative transfer, atmospheric chemistry, turbulent structure and the definition of temperature itself. The relationship between fluctuations and dissipation is discussed in a framework of non-equilibrium statistical mechanics, and a link between maximization of entropy production and scale invariance is hypothesized.

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Section: Brief Review Of Theories Of Atmospheric Turbulencementioning

confidence: 99%

From molecules to meteorology via turbulent scale invariance

Tuck

2010

Quart J Royal Meteoro Soc

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“…Studies by Smith et al [9], Weinstock [130], Hines [119], Gardner [131] and Dewan [132] emphasized the importance of nonlinear interactions for obtaining a universal power law spectrum. Weinstock [130] discussed the connection between the saturation amplitude of each wave and the collective dissipation caused by all other waves.…”

Section: Energy and Temperature Spectra (A) Vertical Spectrum Of The mentioning

confidence: 99%

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Sukoriansky

Galperin

2013

Phil. Trans. R. Soc. A.

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The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data.

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“…In comparison, the original 23/9 D model of anisotropic scaling turbulence (Schertzer and Lovejoy, 1985b) in which the horizontal is dominated by the energy flux (ε, m 2 s −3 ) and the vertical by buoyancy variance flux (φ, m 2 s −5 ) is obtained with ϕ h =ε 1/3 , ϕ v =φ 1/5 , H h =1/3, H v =3/5. Similarly, the popular quasi-linear gravity wave models (Dewan and Good, 1986;Dewan, 1997;Gardner, 1994;Gardner et al, 1993) typically take ϕ h =ε 1/3 , ϕ v =N (the Brunt Väisälä frequency; this is not a turbulent flux, a fact which is a serious weakness of that theory) so that H h =1/3, H v =1. (Interestingly, Van Zandt, 1982 was a forerunner of these quasi-linear gravity wave theories and proposed -purely empirically -a vertical spectral exponent of −2.4, in accord with our results below).…”

Section: Understanding the Effects Of Vertical Aircraft Motion On Thementioning

confidence: 99%

“…However, if on the contrary the turbulence is anisotropic with different turbulent exponents in the horizontal and vertical directions (H h =H v ) then the interpretation may be quite different. Indeed such scaling anisotropy is essentially the mainstream position of the experimentalists who have examined the vertical structure with "Jimspheres", radar, radiosondes or drop sondes (Adelfang, 1971;Endlich et al, 1969;Van Zandt, 1982;Fritts and Chou, 1987;Schertzer and Lovejoy, 1985b;Dewan and Good, 1986;Dewan, 1997;Lazarev et al, 1994;Tsuda et al, 1989;Gardner et al, 1995;Lovejoy et al, 2007Lovejoy et al, , 2009c; see the review in Lovejoy et al, 2008;Radkevitch et al, 2008). For example, in the ER-2 case, the fractality of the trajectories leads to anomalous turbulent exponents while the existence of small nonzero slopes can lead to spurious transitions from the true horizontal exponents (H h ) at small scales to the different vertical exponent (H v ) at large horizontal scales with the two separated by a spurious scale break.…”

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confidence: 99%

Reinterpreting aircraft measurements in anisotropic scaling turbulence

Lovejoy

Tuck

Schertzer³

et al. 2009

Atmos. Chem. Phys.

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Abstract. Due to both systematic and turbulent induced vertical fluctuations, the interpretation of atmospheric aircraft measurements requires a theory of turbulence. Until now virtually all the relevant theories have been isotropic or "quasi isotropic" in the sense that their exponents are the same in all directions. However almost all the available data on the vertical structure shows that it is scaling but with exponents different from the horizontal: the turbulence is scaling but anisotropic. In this paper, we show how such turbulence can lead to spurious breaks in the scaling and to the spurious appearance of the vertical scaling exponent at large horizontal lags.We demonstrate this using 16 legs of Gulfstream 4 aircraft near the top of the troposphere following isobars each between 500 and 3200 km in length. First we show that over wide ranges of scale, the horizontal spectra of the aircraft altitude are nearly k −5/3 . In addition, we show that the altitude and pressure fluctuations along these fractal trajectories have a high degree of coherence with the measured wind (especially with its longitudinal component). There is also a strong phase relation between the altitude, pressure and wind fluctuations; for scales less than ≈40 km (on average) the wind fluctuations lead the pressure and altitude, whereas for larger scales, the pressure fluctuations leads the wind. At the same transition scale, there is a break in the wind spectrum which we argue is caused by the aircraft starting to accurately follow isobars at the larger scales. In comparison, the temperature and humidity have low coherencies and phases and there are no apparent scale breaks, reinforcing the hypothesis that it is the aircraft trajectory that is causally linked to the scale breaks in the wind measurements.Correspondence to: S. Lovejoy (lovejoy@physics.mcgill.ca) Using spectra and structure functions for the wind, we then estimate their exponents (β, H ) at small (5/3, 1/3) and large scales (2.4, 0.73). The latter being very close to those estimated by drop sondes (2.4, 0.75) in the vertical direction. In addition, for each leg we estimate the energy flux, the sphero-scale and the critical transition scale. The latter varies quite widely from scales of kilometers to greater than several hundred kilometers. The overall conclusion is that up to the critical scale, the aircraft follows a fractal trajectory which may increase the intermittency of the measurements, but doesn't strongly affect the scaling exponents whereas for scales larger than the critical scale, the aircraft follows isobars whose exponents are different from those along isoheights (and equal to the vertical exponent perpendicular to the isoheights). We bolster this interpretation by considering the absolute slopes (| z/ x|) of the aircraft as a function of lag x and of scale invariant lag x/ z 1/H z .We then revisit four earlier aircraft campaigns including GASP and MOZAIC showing that they all have nearly identical transitions and can thus be easily explained by the propose...

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Saturated‐cascade similitude theory of gravity wave spectra

Cited by 107 publications

References 76 publications

From molecules to meteorology via turbulent scale invariance

From molecules to meteorology via turbulent scale invariance

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Reinterpreting aircraft measurements in anisotropic scaling turbulence

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