Theoretical Interpretation of Atmospheric Wavenumber Spectra of Wind and Temperature Observed by Commercial Aircraft During GASP

Gage, K. S.; Nastrom, G. D.

doi:10.1175/1520-0469(1986)043<0729:tioaws>2.0.co;2

Cited by 192 publications

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“…Within the independent-source model, spectral universality can be ascribed to that of the inversecascade [4]. In [14,16] it was also hypothesized that oppositely directed cascades could not coexist without a sink between the forcing scales. Lilly [15], using closure theories, showed that there is no need of such sink.…”

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confidence: 99%

Nonlinear Superposition of Direct and Inverse Cascades in Two-Dimensional Turbulence Forced at Large and Small Scales

2011

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We inquire about the properties of 2d Navier-Stokes turbulence simultaneously forced at small and large scales. The background motivation comes by observational results on atmospheric turbulence. We show that the velocity field is amenable to the sum of two auxiliary velocity fields forced at large and small scale and exhibiting a direct-enstrophy and an inverse-energy cascade, respectively. Remarkably, the two auxiliary fields reconcile universal properties of fluxes with positive statistical correlation in the inertial range.PACS numbers: 47.27.ETurbulence represents a tantalizing nonequilibrium system characterized by cascade processes which, as typical in statistical physics, strongly depends on space dimensionality. In d= 3, kinetic energy, injected at large scales, goes toward smaller ones with positive and constant flux (≈ energy-injection rate ǫ), until is dissipated by molecular diffusion [1]. Between the injection and dissipative scales, the energy spectrum behaves as a powerlaw E(k) ≈ ǫ 2/3 k −5/3 . In d = 2, ideal (inviscid and unforced) fluids preserve both energy ≺ v 2 ≻/2 and square vorticity (enstrophy) ≺ ω 2 ≻ /2 (ω=∇×v). On this basis, Kraichnan [2] predicted that sustaining the flow at a single scale ℓ f (∼ k −1 f ), with energy (enstrophy) injection rate ǫ (η = ǫk 2 f ), generates a double cascade of enstrophy downscale (< ℓ f ) and of energy upscale (> ℓ f ). He also predicted two power laws for the energy spectrum: E(k) ≈ η 2/3 k −3 (but for log-corrections [3]) in the direct enstrophy cascade range; E(k) ≈ ǫ 2/3 k −5/3 for the inverse energy cascade. The direct cascade, with a positive enstrophy flux (≈ η), ends at the dissipative scale. Whilst, in an unbounded domain, the inverse cascade proceeds undisturbed, with a negative energy flux (≈−ǫ), unless large-scale friction stops it at a scale≫ ℓ f [4]. For a recent numerical study of the dual cascade see [5].In 3d-layers, as the atmosphere, both 3d and 2d-phenomenology can be relevant depending on the aspect ratio, the injection and observation scales [6][7][8]. Aircraft measurements [9, 10] of atmospheric-winds revealed that horizontal energy spectra at the troposphere end (at ≈ 10Km altitude) display two power-laws: E(k) ∝ k −5/3 at wave-numbers in the mesoscales (≈10−500Km); E(k) ∝ k −3 at synoptic scales (≈500 − 3, 000Km). Though, 2d phenomenology should dominate at scales larger than the troposphere thickness [11], measured spectra display the steeper and shallower power-laws in reverse order with respect to Kraichnan's scenario. To complicate the picture, the energy flux seems to be positive at 10−100Km [12], suggesting a 3d-like direct energy cascade, though the involved scales may be too large.In the 2d-framework, on which we focus here, several explanations for the observed spectra have been proposed. Interpreting the synoptic −3 spectrum as an enstrophy cascade, forced by instabilities of the horizontal motion at the planetary scale (∼10 4 Km) [11], the −5/3 mesoscales spectrum may result: from a 2d-inverse energy cascade forced b...

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confidence: 99%

Nonlinear Superposition of Direct and Inverse Cascades in Two-Dimensional Turbulence Forced at Large and Small Scales

2011

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“…In the case of the modulation of Ω 2 (t) near the transition to turbulence, spectra with a slope in the range between -5/3 and -3 are observed. At an increase in the amplitude, the spectra are modified to the form qualitatively corresponding to the spectra of atmospheric turbulence [1] with a slope -3 at frequencies below 0.1 Hz and -5/3 at higher frequencies (0.1-0.31 Hz) (figure 3a). A further increase in the amplitude can result in spectra with a constant slope between -5/3 and -3.…”

Section: Resultsmentioning

confidence: 99%

“…In particular, spectra of turbulence with a slope of -3 begin at scales larger than 700 km and are limited by a strong peak at a scale of 10 4 km. Spectra with a slope -5/3 were detected at scales smaller than 500 km [1]. Analysis of third order structure functions in [2] showed that only one of these regions with the slope of -3, corresponds to two-dimensional turbulence.…”

Section: Introductionmentioning

confidence: 97%

“…This indicates the direct energy transfer cascade in both spectral regions under consideration. Despite the existing explanations [1,8,9]reasons for the inverse position of spectral regions, as well as the possibility of reproducing this phenomenon under laboratory conditions, are as yet unclear. Both viscous dissipation [10]and vertical motions that are components of large scale circulation [6] prevent two-dimensional turbulent flows in the atmosphere.…”

Section: Introductionmentioning

confidence: 97%

“…Large scale flows in the atmosphere occur in the presence of fast rotation of the Earth, and their properties are usually explained within the concept of "two-dimensional" turbulence [1,2]. In twodimensional turbulence, two inertial intervals are usually identified corresponding to energy transfer at low wave numbers and enstrophy transfer at high wave numbers [3].…”

Section: Introductionmentioning

confidence: 99%

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The Different Types of Turbulence in Rotating Spherical Layers

Zhilenko

Krivonosova

Gritsevich

2018

J. Phys.: Conf. Ser.

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Abstr act. Turbulent flows of a viscous incompressible fluid in a layer between rotating concentric spheres under the action of the modulation of the velocity of one of the spheres have been studied experimentally and numerically. The form of spectra of turbulent pulsations of the azimuthal velocity depends on the sphere whose rotational velocity is modulated, as well as on the amplitude and frequency of modulation. The possibility of the formation of turbulence with spectra qualitatively similar to spectra obtained in measurements in the upper atmosphere is established: with the slope close to -3 at low frequencies and close to -5/3 at high frequencies and with the negative longitudinal velocity structure function of the third order. It has been shown that such spectra are formed in the regions of a flow that are strongly synchronized under the action of the modulation of the rotational velocity.

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The spatial scale dependence of water vapor variability inferred from observations from a very tall tower

2014

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Recent studies have established that atmospheric water vapor fields exhibit spatial spectra that take the form of power laws and hence can be compactly characterized by scaling exponents. The power law scaling exponents have been shown to exhibit substantial vertical variability. In this work, Taylor's frozen turbulence hypothesis is used to infer the first‐order spatial structure function and generalized detrended fluctuation function scaling exponents for scales between 1 km and 100 km. Both methods are used to estimate the Hurst exponent (H) using 10 Hz time series of water vapor measured at 396 m altitude from an Ameriflux tower in Wisconsin. Due to the diurnal cycle in the boundary layer height at the 396 m observational level, H may be estimated for both the daytime convective mixed layer and the nocturnal residual layer. Values of H≈13 are obtained for the convective mixed layer, while values of H>12 apply in the nocturnal residual layer. The results are shown to be remarkably consistent with a similar analysis from satellite‐based observations as reported in Pressel and Collins (2012).

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Theoretical Interpretation of Atmospheric Wavenumber Spectra of Wind and Temperature Observed by Commercial Aircraft During GASP

Cited by 192 publications

References 0 publications

Nonlinear Superposition of Direct and Inverse Cascades in Two-Dimensional Turbulence Forced at Large and Small Scales

Nonlinear Superposition of Direct and Inverse Cascades in Two-Dimensional Turbulence Forced at Large and Small Scales

The Different Types of Turbulence in Rotating Spherical Layers

The spatial scale dependence of water vapor variability inferred from observations from a very tall tower

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