Anomalous Diffusion of Vorticity in Fully-Developed Turbulence

概要

論文の詳細を見る
It is found on the basis of vortex-stretching physics that the spatial spread of a ribbon-like active region of vorticity in the inertial range increases with time as σ(t)≡<|R(t)-R_0|^2>∝1/[t_∞-t]^<2η>,(t<t_∞) where σ(t) is the mean square of the linear dimension of the spatial spread and η is a positive number of order unity, given by η=3[(3-μ)ν-1]/(2+μ) with μ being the intermittency exponent and ν an exponent characterizing the degree of randomness of the spatial configuration of the thin ribbonlike active region. As t→t_∞,σ(t) increases anomalously, where t_∞ is the mean lifetime of the active region. A crossover to the dissipation range occurs at a time t_c(<t_∞), where σ(t) attains a maximum value σ(t_c)∝R^<2bη>≫1 with b≡(2+μ)/(4-μ) and R being the Reynolds number. In the dissipation range t>t_c, the active region disappears due to viscosity. If μ=0, ν=1/2, then η=2bη=3/4. If μ=1/3, ν=3/5, then η=0.77, bη=0.49. This anomalous diffusion is a remarkable manifestation of the self-similarity of the energy cascade. The singularity of σ(t) arises from the fact that the expansion rate of the length of a ribbon-like active region depends on its cross-section diameter l and diverges logarithmically asl→0.
理論物理学刊行会の論文
1981-06-10