Wave-Number Spectrum of Drift-Wave Turbulence

Abstract

A simple model for the evolution of turbulence fluctuation spectra, which includes neighboring interactions leading to the usual dual cascade as well as disparate scale interactions corresponding to refraction by large scale structures, is derived. The model recovers the usual Kraichnan-Kolmogorov picture in the case of exclusively local interactions and midrange drive. On the other hand, when disparate scale interactions are dominant, a simple spectrum for the density fluctuations of the form |nk|2 proportional to k(-3)/(1+k2)2 is obtained. This simple prediction is then compared to, and found to be in fair agreement with, Tore Supra CO2 laser scattering data.

Spectrum of Kinetic-Alfvén Turbulence

“…At such sub-proton scales, the shear-Alfvén cascade is expected to transform into the cascade of strongly anisotropic kinetic-Alfvén modes with a different linearized dispersion relation ω ∝ k z k ⊥ . Sub-range, micro-scale plasma turbulence attracts considerable interest due to its importance in solar wind heating, magnetic reconnection in a variety of astrophysical systems, and laboratory experiments with strongly magnetized plasmas (e.g., Biskamp et al 1999;Cho & Lazarian 2004;Kiyani et al 2009;Gürcan et al 2009;Chandran et al 2010;Kletzing et al 2010;Howes 2010;Salem et al 2012). Such turbulence has been understood to a much lesser extent compared to its Alfvénic or MHD counterpart.…”

Logarithmic discretization and systematic derivation of shell models in two-dimensional turbulence

“…34, suggesting that the model is useless as it is, for a direct study of turbulence in 2D fluids. While this is rather discouraging, such models are being used as underlying elements in various more complex models, such as multi-shell models [35] or hierarchical tree models [36], as well as models that rely mainly on disparate scale interactions [21]. The derivation and the numerical implementation given here, is therefore very useful for the development of such tools in cases where anisotropy may be an important feature.…”

“…The model is somewhat reminiscent of the one discussed in Ref. [21], and assuming h is potential vorticity, it conserves potential enstrophy between disparate scale interactions. However, it is flawed in that it excludes interactions between h 0 and small enough scales for which µ m becomes negative.…”

“…In its basic form, it is a differential approximation model with built in logarithmic discretization and arbitrary coefficients multiplying the interaction terms. In fact, one can recover smooth differential approximation models in the continuum limits of these models [20][21][22]. A shell model usually takes only a subset of the total number of possible interactions into account, but by choice of the interaction coefficients, it respects the conservation laws of the fluid system it represents.…”

The role of phase dynamics in a stochastic model of a passively advected scalar

“…ω k are the natural frequencies of the flow assumed random and distributed according to a Gaussian distribution with zero mean, f (ω) = exp(−ω 2 /2)/ √ 2π, and ζ k are the natural frequencies of the forcing, also assumed random and distributed according to a Gaussian distribution, but the mean is prescribed by a spectrum defined through a dispersion relation similar to that of the DWs (see Refs. [29,30]):…”