English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The field theoretic renormalization group and operator product expansion areapplied to the model of a passive scalar quantity advected by a non-Gaussianvelocity field with finite correlation time. The velocity is governed by theNavier--Stokes equation, subject to an external random stirring force with thecorrelation function $\propto \delta(t-t') k^{4-d-2\epsilon}$. It is shown thatthe scalar field is intermittent already for small $\epsilon$, its structurefunctions display anomalous scaling behavior, and the corresponding exponentscan be systematically calculated as series in $\epsilon$. The practicalcalculation is accomplished to order $\epsilon^{2}$ (two-loop approximation),including anisotropic sectors. Like for the well-known Kraichnan's rapid-changemodel, the anomalous scaling results from the existence in the model ofcomposite fields (operators) with negative scaling dimensions, identified withthe anomalous exponents. Thus the mechanism of the origin of anomalous scalingappears similar for the Gaussian model with zero correlation time andnon-Gaussian model with finite correlation time. It should be emphasized that,in contrast to Gaussian velocity ensembles with finite correlation time, themodel and the perturbation theory discussed here are manifestly Galileancovariant. The relevance of these results for the real passive advection,comparison with the Gaussian models and experiments are briefly discussed.Comment: 25 pages, 1 figur

Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: Two-loop approximation