Time Evolution of Fully-Developed Turbulence

概要

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A mathematical model is used to analyze the time evolution of three-dimensional homogeneous isotropic turbulence in order to clarify how the convective nonlinearity brings about the inertial-range similarity law and the power law of decay. It is shown that in the inviscid limit the enstrophy Ω_1 diverges at a finite time t_∞ as Ω_1〜(t_∞-t)^<γ_1> with γ_1=(4-μ)/(2+μ), where μ is the intermittency exponent. If the viscosity is nonzero, then the above divergence is suppressed and the enstrophy decays in time after a time of the order of t_∞ as Ω_1〜t^<-(2+z)>. It is shown that the decay exponent z is independent of μ and is written as z=(σ-1)/(σ+3), where σ is the exponent for the large-scale structure of the initial energy spectrum, E(k, 0)〜K^σ. The decay of the total energy, the Reynolds number and the energy dissipation rate are also written in terms only of z. Results obtained are compared with numerical simulations of the Navier-Stokes equations.
理論物理学刊行会の論文
1983-10-25