Tempoeral Development of the Plane Poiseuille Turbulence

Abstract

First of all, turbluence was investigated by Reynolds on the physical basis in 1883. His poioneering work revealed the importance of Reynolds number R = Ua/v, where U and a are the representative values of velocity and length characterizing the flow and v the kinematic viscosity. Above some value of R, i.e. critical Reynolds number, the flow would become Turbulent. Theory concerning the onset of turbulence was established by Orr (1906) and Sommerfeld (1908) on the basis of the linear stability theory of infinitesimal disturbance. Transport theories or mixing length theories were made based on the analogy between momentum and energy transports among molecules in kinetic theory of gases and those among fluid particles in turbulent motion, by Prandtl, Taylor, Karman and others. Statistical theory of isotropic turbulence of Taylor (1935) seems to have set turbulence theories on a firm path. The spectrum of turbulence was also due to Taylor (1938), and Kolmogoroff’s 5/3 power law was derived purely from the dimensional analysis (1941).