A refinement of the previous hypothesis of turbulent energy spectrum |
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| Authors: | Tosio Nan-niti |
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| Institution: | (1) Tokyo University of Mercantile Marine, 2-1-6 Etchujima, Kotoku, 135 Tokyo, Japan |
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| Abstract: | To refine the previous hypothesis of turbulent energy spectrum (Nan-niti, 1970), further theoretical consideration and a simple
experiment using electric fans was carried out. From the hypothesis ofq=δε/δk andεq=const., the following relations are derived for the spectrumF, and the autocorrelation functionR:F(k)∼k
−(5−2α)/3 andR(t)∼1−(t/τ)2(1−α)/3, whereq is the local energy supply,ε the energy dissipation rate, andk the wavenumber,t the time,τ the lifetime of the largest eddy. The following further relations are also obtained:ε∼l
−α,v∼l
β,v∼τ
γ andγ=(1−α)/(2+α)=β/(1−β), wherel is the length scale of the phenomenon,v turbulent velocity,α=1/2,β=1/6, andγ=1/5. The experimental results support these relations. |
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