【摘要】 本文首先根据间隙湍流结构的自相似性和KdV—Burgers方程的鞍—焦异宿轨道行波解,求得了间隙湍流的分数维D与波数比b以及D与自相似结构尺度R的关系;其次,模拟了在不同R下的D—b关系以及不同b下的D—R关系;最后,还求得了湍流能谱和分数维以及能谱指数与D的关系。模拟结果表明,(d|β|/dD)>0,这和A.J.Chorin的结论是一致的。更多还原

【Abstract】 Finst. the relations of fractal dimension D with (K1/K0), and D with the scale of self-similar structure are discovered and simulated based on the seif-simiiarity of turbulance and the analytic solution of saddle-focus heteroclinic orbit. Finally, the relations of D With the spectrum of turbulence and the D with the universal inertial exponent | Β | are analyzed, the result of simulation shows that (d| Β | /dD)>0 which is of the same view of A. J.Chorin.更多还原