Evidence far a<i>k</i><sup>−5/3</sup>Law Inertial Range in Mesoscale Two-Dimensional Turbulence

Gage, K. S.

doi:10.1175/1520-0469(1979)036<1950:efalir>2.0.co;2

Cited by 272 publications

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“…The slopes in this portion of the spectra for these fields are comparable to other models and agree with observations (Tulloch and Smith, 2006). Specific humidity has a much shallower slope of (1.6 in this wavenumber range, close to , indicative of the dominance of mesoscale activity (Gage, 1979). Above wavenumber 200, the spectral slopes increase to near (6.6 for temperature and wind, and (3.4 for specific humidity.…”

Section: Forecast Error Spectrasupporting

confidence: 87%

Spectral analysis of forecast error investigated with an observing system simulation experiment

Privé¹,

Errico

2015

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C TThe spectra of analysis and forecast error are examined using the observing system simulation experiment framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office. A global numerical weather prediction model, the Global Earth Observing System version 5 with Gridpoint Statistical Interpolation data assimilation, is cycled for 2 months with once-daily forecasts to 336 hours to generate a Control case. Verification of forecast errors using the nature run (NR) as truth is compared with verification of forecast errors using self-analysis; significant underestimation of forecast errors is seen using self-analysis verification for up to 48 hours. Likewise, self-analysis verification significantly overestimates the error growth rates of the early forecast, as well as mis-characterising the spatial scales at which the strongest growth occurs. The NR-verified error variances exhibit a complicated progression of growth, particularly for low wavenumber errors. In a second experiment, cycling of the model and data assimilation over the same period is repeated, but using synthetic observations with different explicitly added observation errors having the same error variances as the control experiment, thus creating a different realisation of the control. The forecast errors of the two experiments become more correlated during the early forecast period, with correlations increasing for up to 72 hours before beginning to decrease.

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Section: Forecast Error Spectrasupporting

confidence: 87%

Spectral analysis of forecast error investigated with an observing system simulation experiment

Privé¹,

Errico

2015

Tellus A: Dynamic Meteorology and Oceanography

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“…This is in agreement with the prediction of two-dimensional turbulence theory for a downscale enstrophy-cascading inertial subrange [Batchelor, 1969;Kraichnan, 1967] One hypothesis is that the k -•/• regime is a two-dimensional inertial subrange in which KE cascades upscale from a relatively small scale source associated with moist convective processses [Gage, 1979]. The results of certain modelling studies support this view [Lilly, 1969[Lilly, , 1983 …”

Section: Introductionsupporting

confidence: 86%

Simulation of the κ^−5/3 mesoscale spectral regime in the GFDL SKYHI General Circulation Model

Koshyk

Hamilton

Mahlman

1999

Geophysical Research Letters

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“…This is a situation of interest both for experiments [5,6] and in the atmosphere [7,8]. The flow realizes the type of turbulence theoretically postulated by A.N.…”

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confidence: 56%

Statistical Geometry in Scalar Turbulence

Celani

Vergassola

2001

Phys. Rev. Lett.

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A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized by strong clustering. The quantitative counterpart is the existence of special functions of particle configurations which are statistically invariant under the flow. These are the statistical integrals of motion controlling the scalar statistics at small scales and responsible for the breaking of scale invariance associated to intermittency. PACS number(s) : 47.10.+g, 47.27.-i, 05.40.+j Scalar fields transported by turbulent flow occur in many physical situations, ranging from the dynamics of the atmosphere and the ocean to chemical engineering (see, e.g., Ref.[1]). Specific examples are provided by pollutant density, temperature or humidity fields and the concentration of chemical or biological species. The advection-diffusion equation governing the transport of the scalar field θ is :where v(r, t) is the incompressible advecting flow and κ is the molecular diffusivity. Two broad cases are distinguished : active scalars, where v depends on θ, e.g. by an explicit relation v = v (θ), and passive scalars, where the statistics of v is independent of θ. Here, we shall be concerned with the latter, although we conjecture that the physical mechanisms presented in the following are quite general and relevant also for the active cases. The Fokker-Planck equation (1) is associated to the Lagrangian dynamics of tracer particles whose position ρ(t) obeys dρ(t) = v(ρ(t), t) dt + √ 2κ dβ(t), where β(t) is the isotropic Brownian motion [2]. The equation (1) governs the evolution of the probability density of particles at position r and time t.Scalar turbulence is typically generated by maintaining a mean scalar gradient θ = g·r, e.g. by heating/cooling devices in temperature field experiments. The notation • denotes the average with respect to the velocity statistics, which is in principle arbitrary. We shall be interested in flows with correlations having a nontrivial power law behavior in the inertial range of scales r ≪ L, where L is the velocity correlation length. Examples are provided by the two and three dimensional Navier-Stokes turbulent flow (see, e.g., Ref.[3]). A very robust feature of scalar turbulence is its strong intermittency : rare strong events (such as the sharp cliffs observed in Fig. 1) dominate the scalar statistical properties. More quantitatively, intermittency reflects in the anomalous scaling of the correlations. In the inertial range, the scalar structure functions S n (r) = (θ(r, t) − θ(0, t)) n take the form S n (r) ∝ r ζ dim n

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Evidence far ak^−5/3Law Inertial Range in Mesoscale Two-Dimensional Turbulence

Cited by 272 publications

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Spectral analysis of forecast error investigated with an observing system simulation experiment

Spectral analysis of forecast error investigated with an observing system simulation experiment

Simulation of the κ^−5/3 mesoscale spectral regime in the GFDL SKYHI General Circulation Model

Statistical Geometry in Scalar Turbulence

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Evidence far ak−5/3Law Inertial Range in Mesoscale Two-Dimensional Turbulence

Cited by 272 publications

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Spectral analysis of forecast error investigated with an observing system simulation experiment

Spectral analysis of forecast error investigated with an observing system simulation experiment

Simulation of the κ−5/3 mesoscale spectral regime in the GFDL SKYHI General Circulation Model

Statistical Geometry in Scalar Turbulence

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Evidence far ak^−5/3Law Inertial Range in Mesoscale Two-Dimensional Turbulence

Simulation of the κ^−5/3 mesoscale spectral regime in the GFDL SKYHI General Circulation Model