Atmospheric Predictability and Two-Dimensional Turbulence

Leith, C. E.

doi:10.1175/1520-0469(1971)028<0145:apatdt>2.0.co;2

Cited by 448 publications

(340 citation statements)

References 0 publications

Supporting

Mentioning

325

Contrasting

Unclassified

Order By: Relevance

“…It is therefore useful to know that the DIA has a Langevin representation (Leith, 1971;Kraichnan, 1970a). Consider the primitive amplitude equation…”

Section: Langevin Representation Of the Diamentioning

confidence: 99%

“…Heuristically (Leith, 1971), one can estimate η nl k as the rms value of an eddy turnover rate estimated from Kolmogorov arguments. In the absence of wave physics, one has that the contribution from one wave-number band k of width ∆k is…”

Section: The Eddy-damped Quasinormal Markovian (Edqnm) Approximationmentioning

confidence: 99%

“…Insight into the catastrophic failure of the EDQNM in the presence of wave phenomena can be gained by considering a Langevin representation due to Leith (1971) and Kraichnan (1970a): Here w(t) is a Gaussian white-noise process of unit amplitude; its presence ensures the Markovian nature of the resulting approximation. The random auxiliary field ξ is, as in the Langevin 202 representation (239) of the DIA, constrained to have variance identical to that of ψ k .…”

Section: Langevin Representation Of the Edqnmmentioning

confidence: 99%

“…For homogeneous turbulence, for which angular integrations can be performed analytically, that was first done by Leith (1971) and Leith and Kraichnan (1972). The procedure introduces effective, bin-averaged mode-coupling coefficients.…”

Section: Decimating Smooth Wave-number Spectramentioning

confidence: 99%

“…The procedure introduces effective, bin-averaged mode-coupling coefficients. Leith (1971) called their computation a "complex exercise in solid geometry and computer logic"; however, Bowman (1992) found a simple and efficient analytical procedure 244 that also generalized naturally to anisotropic turbulence. In his practical calculations of 2D anisotropic plasma turbulence, Bowman used a cylindrical-polar k-space geometry with bins spaced logarithmically in wave-number magnitude and linearly in wave-number angle.…”

Section: Decimating Smooth Wave-number Spectramentioning

confidence: 99%

See 4 more Smart Citations

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

263

397

View full text Add to dashboard Cite

A pedagogical review of the historical development and current status (as of early 2000) of systematic statistical theories of plasma turbulence is undertaken. Emphasis is on conceptual foundations and methodology, not practical applications. Particular attention is paid to equations and formalism appropriate to strongly magnetized, fully ionized plasmas. Extensive reference to the literature on neutral-fluid turbulence is made, but the unique properties and problems of plasmas are emphasized throughout. Discussions are given of quasilinear theory, weak-turbulence theory, resonance-broadening theory, and the clump algorithm. Those are developed independently, then shown to be special cases of the direct-interaction approximation (DIA), which provides a central focus for the article. Various methods of renormalized perturbation theory are described, then unified with the aid of the generating-functional formalism of Martin, Siggia, and Rose. A general expression for the renormalized dielectric function is deduced and discussed in detail. Modern approaches such as decimation and PDF methods are described. Derivations of DIA-based Markovian closures are discussed. The eddy-damped quasinormal Markovian closure is shown to be nonrealizable in the presence of waves, and a new realizable Markovian closure is presented. The test-field model and a realizable modification thereof are also summarized. Numerical solutions of various closures for some plasmaphysics paradigms are reviewed. The variational approach to bounds on transport is developed. Miscellaneous topics include Onsager symmetries for turbulence, the interpretation of entropy balances for both kinetic and fluid descriptions, self-organized criticality, statistical interactions between disparate scales, and the roles of both mean and random shear. Appendices are provided on Fourier transform conventions, dimensional and scaling analysis, the derivations of nonlinear gyrokinetic and gyrofluid equations, stochasticity criteria for quasilinear theory, formal aspects of resonance-broadening theory, Novikov's theorem, the treatment of weak inhomogeneity, the derivation of the Vlasov weak-turbulence wave kinetic equation from a fully renormalized description, some features of a code for solving the direct-interaction approximation and related Markovian closures, the details of the solution of the EDQNM closure for a solvable three-wave model, and the notation used in the article.

show abstract

“…It is therefore useful to know that the DIA has a Langevin representation (Leith, 1971;Kraichnan, 1970a). Consider the primitive amplitude equation…”

Section: Langevin Representation Of the Diamentioning

confidence: 99%

Section: The Eddy-damped Quasinormal Markovian (Edqnm) Approximationmentioning

confidence: 99%

Section: Langevin Representation Of the Edqnmmentioning

confidence: 99%

Section: Decimating Smooth Wave-number Spectramentioning

confidence: 99%

Section: Decimating Smooth Wave-number Spectramentioning

confidence: 99%

See 3 more Smart Citations

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

263

397

View full text Add to dashboard Cite

show abstract

Characteristics of Tropical-Cyclone Turbulence and Intensity Predictability

Kieu

Rotunno

2021

Preprint

View full text Add to dashboard Cite

The tropical cyclone (TC) is a multiscale nonlinear system in which any small-scale perturbation could amplify and progressively influence larger scales, resulting in T-C intensity variability. This type of upscale-error growth, termed the "real butterfly effect" (Palmer et al., 2014), exists in various fluid-flow systems and determines their intrinsic predictability. Unlike deterministic systems whose predictability is governed by Lyapunov exponents and attractor invariants (e.g.,

show abstract

Untitled

1999

J. Geophys. Res.

View full text Add to dashboard Cite

Data from several middle-atmosphere general circulation models are used to calculate kinetic energy spectra as a function of total horizontal wavenumber n. The horizontal and vertical resolution between models varies but all have upper. boundaries at heights • 80 km. Tropospheric spectra show power-law behavior with slopes slightly shallower than-3 for wavenumbers n • 10 (horizontal wavelengths • 4000 km) and are dominated by the rotational part of the flow. These spectra agree well with those calculated using data obtained from a global assimilation model and with the results of previous observational studies. Stratospheric spectra have larger amplitudes than tropospheric ones at planetary scales and smaller amplitudes at smaller scales. Mesospheric spectra are characterized by enhanced spectral amplitudes at all wavenumbers compared to the stratosphere and spectral slopes in the wavenumber range n • 10 are generally shallower. Stratospheric and mesospheric spectra include approximately equal contributions from the rotational and divergent parts of the flow for n • 20 in all models. These features appear to be independent of model resolution. The divergent part of the flow, presumably associated with explicitly resolved inertiogravity waves in the models, increases more rapidly with height above the lower stratosphere than the rotational part. The divergent part is fairly insensitive to season, whereas the rotational part changes considerably between January and July in the middle-atmosphere region. Spectral amplitudes and vertical growth rates of both parts vary widely between models for a given season. The horizontal diffusion schemes used by the models are compared in an attempt to explain some of these differences. Nellsen, 1978; Koshyk and Boer, 1995; Nastrom et al., 1984]. On scales between about 4000 and 400 km, the spectra show slopes of •0-3, are dominated by the rotational part of the flow, and are associated with downscale enstrophy fluxes [Boer and Shepherd, 1983], all

show abstract

Atmospheric Predictability and Two-Dimensional Turbulence

Cited by 448 publications

References 0 publications

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Characteristics of Tropical-Cyclone Turbulence and Intensity Predictability

Untitled

Contact Info

Product

Resources

About