An Alternative to Shell-Models: More Complete and Yet Simple Models of Intermittency

Chigirinskaya, Y.; Schertzer, D.; Lovejoy, S.

doi:10.1007/978-94-011-5118-4_65

Cited by 3 publications

(3 citation statements)

References 2 publications

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“…(1a) on either DNS or geophysical numerical simulations. The closest is perhaps the multifractal characterization of time signals in turbulent shell models (Biferale, 2003) or in "scaling cascade of gyroscopes" models (Chigirinskaya and Schertzer, 1996;Chigirinskaya et al, 1998). While the former discretizes the NS equations in Fourier space keeping a small and fixed number of degrees of freedom per octave in scale, the latter more realistically discretizes the equations on a dyadic tree structure such that the number of degrees of freedom increases with wavenumber.…”

Section: Discussionmentioning

confidence: 99%

The stochastic multiplicative cascade structure of deterministic numerical models of the atmosphere

Stolle

Lovejoy

Schertzer³

2009

Nonlin. Processes Geophys.

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Abstract.By direct statistical analysis we show that over almost all their range of scales and to within typically better than ±1%, atmospheric fields obtained from analyses and numerical integrations of atmospheric models have the multifractal structure predicted by multiplicative cascade models. We quantify this for the horizontal wind, temperature, and humidity fields at 5 different pressure levels for the ERA40 reanalysis, the Canadian Meteorological Centre Global Environmental Multiscale (CMC, GEM) model, as well as the National Oceanographic and Atmospheric Administration Global Forecasting System (NOAA, GFS). We investigate the additional prediction that the cascade belongs to a universal multifractal basin of attraction. By demonstrating a "Levy collapse" of the statistical moments to within ±2 to ±5% over most of the range of scales, we conclude that there is good evidence for this. Finally, we discuss how this stochastic multiplicative cascade structure can be exploited in improving ensemble forecasts.

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Section: Discussionmentioning

confidence: 99%

The stochastic multiplicative cascade structure of deterministic numerical models of the atmosphere

Stolle

Lovejoy

Schertzer³

2009

Nonlin. Processes Geophys.

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“…With the viewpoint of working with intermittent vector fields, is it possible to use Fourier space beyond the conventional shell models for isotropic turbulence? A first answer was given by Chiriginskaya et al (1998) [33], from a seminal model by Chiriginskaia and Schertzer (1997) [34], who introduced a cascade of gyroscopes. With respect to the very old analogy of the cascade of eddies as the fragmentation of (scalar) grains, with, for instance, the log-normal distribution inspired by Kolmogorov and Obhukov, this approach is based on a dyadic network of triads of vector interactions between a parent eddy and two children eddies, from the largest scale down to the dissipation (in the molecular sense).…”

Section: Recent Progresses Towards Stochastic Fields and Multifractal...mentioning

confidence: 99%

“…This analogy was perhaps pushed to its best form by Waleffe [5] with his principle of triad instability, where the Euler equations for fluid are expanded in terms of helical modes [4]. Needless to say, it seems to be worthwhile to continue in this direction, as well as to clarify the mutual links with the general approach defining multifractal operators acting on vector fields [33].…”

Section: Recent Progresses Towards Stochastic Fields and Multifractal...mentioning

confidence: 99%

Modal Projection for Quasi-Homogeneous Anisotropic Turbulence

Zhu

Cambon

2023

Atmosphere

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This article, or essay, addresses the anisotropic structure and the dynamics of quasi-homogeneous, incompressible turbulence. Modal projection and expansions in terms of spherical harmonics in three-dimensional Fourier space are in line with a seminal study by Jack Herring, around the so-called Craya–Herring frame of reference, with a large review of the related approaches to date. The research part is focused on structure and dynamics of rotating sheared turbulence, including a description of both directional and polarization anisotropy with a minimal number of modes. Effort is made to generalize expansions in terms of scalar spherical harmonics (SSHs) to vector spherical harmonics (VSHs). Looking at stochastic fields, for possibly intermittent vector fields, some directions are explored to reconcile modal projection, firstly used for smooth vector fields, and multifractal approaches for internal intermittency but far beyond scalar correlations, such as structure functions. In order to illustrate turbulence from Earth to planets, stars, and galaxies, applications to geophysics and astrophysics are touched upon, with generalization to coupled vector fields (for kinetic, magnetic, and potential energies), possibly dominated by waves (Coriolis, gravity, and Alfvén).

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Pandora Box of Multifractals: Barely Open?

Schertzer

Tchiguirinskaia

2017

Advances in Nonlinear Geosciences

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An Alternative to Shell-Models: More Complete and Yet Simple Models of Intermittency

Cited by 3 publications

References 2 publications

The stochastic multiplicative cascade structure of deterministic numerical models of the atmosphere

The stochastic multiplicative cascade structure of deterministic numerical models of the atmosphere

Modal Projection for Quasi-Homogeneous Anisotropic Turbulence

Pandora Box of Multifractals: Barely Open?

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