Turbulence origination initial stage analysis for plane-parallel straight fluid flow, the rheological model of which takes into account the threshold “addition” of the transverse viscosity factor

Abstract

A plane-parallel straight fluid flow is considered, the rheological model of which takes into account the threshold “addition” of the transverse viscosity factor. For the case of the velocity profile power dependence on the transverse coordinate in a small neighborhood of the flow region point in question, the conditions for “generating” and, possibly, the subsequent unlimited increase in the transverse velocity component are obtained. The simultaneous fulfillment of these two conditions is proposed to be interpreted as the laminar-turbulent transition initial stage. The analysis of the fulfillment of these conditions for the simplest special cases with linear, parabolic and cubic velocity profiles has been carried out. It is shown that the beginning of the transition in the inflection point vicinity on the cubic velocity profile is determined by the strain rate tensor second invariant modulus exceedance in this point of the threshold level corresponding to the transverse viscosity factor addition.