D322 拡散する渦管に巻き込まれたらせん渦層におけるエネルギー散逸

概要

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Energy dissipation around a diffusing straight vortex tube aligned with a uniform shear flow of a shear rate S is investigated analytically. When the tube starts with a vortex filament of circulation Γ at time St=0,it wraps and stretches vorticity lines of the uniform shear flow around itself to form double spiral vortex layers with high azimuthal vorticity. The contribution of the tube to total dissipation is expressed as (Γ^2/8π)t^<-1>, while that of the layers is evaluated to be 3^<-2/3>πΓ(1/3)υ^2S^2(Γ/2πυ)^<4/3>t at a large Reynolds number Γ/υ≫1,where υ is the kinematic viscosity of fluid. The contribution of the layers is, therefore, greater than that of the tube at St>0.623 (Γ/2πυ)^<1/3>. The scaling of energy dissipation for vortex tubes and layers in turbulence by a Taylor-microscale Reynolds number is discussed based on the present analysis and recently reported DNS data.
2000-07-25