Vortex Stretching and Relative Diffusion in Grid Turbulence

概要

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The relative diffusion of a pair of probe particle in grid turbulence at high Reynolds numbers is treated as the most clear-cut manifestation of the vortex stretching. The diffusion law obtained is different from Richardson's 4/3 law and t^3 law for steady turbulence. Let L_*(t) be the root-mean-square of the relative distance of the pair at time t and L_t the length scale of the largest eddies in the inertial range at time t. Then there exist two characteristic regimes: [I] L_*(t)<L_t and [II] L_*(t)>L_t. In [I], the eddy diffusion rate turns out to be dL_*^2/dt~L^<(4+2μ)/3>/(1+pt)^x, where μis the intermittency exponent x an exponent characterizing the decay of turbulence with 1≧x>(2+μ)/3, and p a decay constant. If L_*(t)≫L_*(0), then L_*^2(t)~[(1+pt)^<1-x>-1]^<3/(1-μ)> for x≠1 and L_*^2(t)~[1n(1+pt)]^<3/(1-μ)> for x=1. The crossover from [I] to [II] occurs at a time t_c of the order of the mean turnover time τ_0 of the eddies of size L_0 at t=0. Then L_*^2(t)-L_*^2(t_c)~[(1+p_cs)^<1-z>-1] for z≠1 and 1n(1+p_cs) for z=1, where s≡t-t_c>0, p_c=p/(1+pt_c) and z=(3x-2-μ)/(1-μ). The overall behavior of L_*(t) from t/τ_0=0 to 10^4 is illustrated for initial Reynolds number R_0=10^5.
理論物理学刊行会の論文
1983-03-25