2006 年 62 巻 4 号 p. 437-446
A roughness and time dependent mixing length equation is developed from an extension of von Kármán’s similarity hypothesis, based on local equilibrium (turbulent energy production balanced by the dissipation), with an algebraic equation for the shape of the turbulent kinetic energy. Our vertical mixing length profile and the related mean velocities approach the experimental data well. We show that our equation follows Prandtl’s mixing length equation only near a smooth wall. The use of the proposed time-dependent mixing length equation in a turbulent oscillatory boundary layer shows, like the k-ε model, an increase in the mixing length and the eddy viscosity near flow reversal.
