风沙湍流的间隙性、稳定性分布及分形特征

The Intermitteny, Stable Distribution and Fractal Characteristic for the Wind—Sand Turbucent Flow

根据风沙湍流本身的不均匀性、间隙性,用稳定性分布研究了含沙量M随高度h的变化得M(h)∝h^(-D),求得分维D=2.36(h>10cm),D=1.465(h<10cm),速度分布W(|u|)=a_2|u|^((-D)/(2-1))。沙粒扩散<|x(t)|>∝t^(2/D);结合Kdv-Burgers方程的行波解,得风沙流的标度律(υ/β)ξ+Dlnh=A,揭示了耗散性υ、弥散性β、风速ξ和高度h之间的一种本质联系。被空气湍流吹动的沙粒起始半径r_e=(c’/(5-D)ρ)[(β/υ)In(E_1/E_2)]^((5-D)/3),起动风速V_1=V_(2exp)[(υ/2β)γ_c^3ρ~3(2.65/c’)~3],最后讨论了风沙流的多重分形特征。

Based on the heterogeneity and intermittency of wind - sand turbulent flow. the relationships be tween the sand percent and the height are studied, and the formula M (h) ∞h-Dis derived by the stable distribution theory, obtaining the fracbol dimensions D = 2. 36 (h>10cm), D=l. 465 (h<10cm) as well as the velocity distribution w (|u|) = q2|u|-D/2-1the sand particle diffusiom<|x(t)| >∞t2/D. According to the tra - veiling solutions of the Kdv -Burgers equation, the scaling law for wind-sand flow υ/βζ+DLnh=∧ is found. and it reveals the inherent relations among the dissipationυ, dispersionβ, wind velocityζ and height h. The starting radius of sand particle drived by wind turbulence is given by re =c'/(5-D)ρ[β/υLnE1/E2](5-D/) /3and the starting wind velocity V1 =V2exρ [υ/2βre3ρ3(2.65/c')3] Finally, the multifractal charateristicsof the wind-sand flow are discussed.