TURBULENCE AS A NONEQUILIBRIUM PHASE-TRANSITION

The transition from laminar to turbulent flow is studied on the basis of an exact equation for the averaged velocity and an approximate nonl inear equation for the Reynolds stress tau. The stationary state can b e determined from the condition of minimum of a functional that is ana logous to the Landau functional in the theory of phase transitions. Th e Reynolds stress plays the role of a parameter. It is shown that a no ntrivial solution for tau corresponding to a steady turbulent regime e xists only for Reynolds numbers R that exceed a certain critical value R(cr). The results of a numerical calculation of the profile of the a veraged velocity, the friction coefficient, and the Reynolds stress in a wide range of values of R agree well with experimental data for cha nnel flow.