2002/02/24 by Victor S. L’vov, Victor S. L'vov, Anna Pomyalov +1 · 4 citations
Environmental Science · Physics and Astronomy · #Climate variability and models #Hydrology and Drought Analysis #Plant Water Relations and Carbon Dynamics #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1103/physrevlett.89.064501
published as Phys. Rev. Lett., 89 , 064501 (2002) · PRL, submitted, REVTeX 4, 4 pages
arxiv created 2002/02/24 · openalex publication_date 2002/07/18 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The statistics of two-dimensional turbulence exhibit a riddle: the scaling exponents in the regime of inverse energy cascade agree with the K41 theory of turbulence far from equilibrium, but the probability distribution functions are close to Gaussian-like in equilibrium. The skewness S\ensuremath≡S3(R)/S23/2(R) was measured as Sexp\ensuremath≈0.03. This contradiction is lifted by understanding that two-dimensional turbulence is not far from a situation with equipartition of enstrophy, which exists as true thermodynamic equilibrium with K41 exponents in space dimension of d=(4)/(3). We evaluate the skewness S(d) for (4)/(3)\ensuremath≤d\ensuremath≤2, showing that S(d)=0 at d=(4)/(3), and that it remains as small as Sexp in two dimensions.