Energy Reversal in Turbulent Flows

Abstract

In turbulent shear flows, it is generally known from the mechanical energy equation that a production term of turbulent energy, normally implying a transfer of energy from the mean motion to the turbulence, contributes through a significant physical process to the permanence or quasisteady state of turbulence in the presence of convective, diffusive, and dissipative influences. It is shown that certain flows with asymmetric mean velocity distribution may display localized areas in which the production term is a loss in the energy balance and consequently of the same sign as the dissipation. For better terminology the phenomenon of negative production is here called energy reversal. The existence of zones of energy reversal also implies a concept of zones of opposing shear. In this localized region, the Reynolds stress and the viscous shear stress oppose each other unlike what is expected in normal boundary layer and pipe flows. A modified relationship, relating the Reynolds stress to the mean viscous stress, taking into account small- and large-scale effects, proposed by Hinze and Béguier is justified on the basis of experimental evidence.