Abstract
Dynamic statistical equations for the turbulent fluxes of scalars and momentum in incompressible flows are derived after time wise integration of the equation for the oscillating transported property, decomposing the turbulent fluxes in terms representing distinct features of the main and fluctuating flow that influence the respective turbulent transport. These expressions provide a means for discussing the gradient diffusion hypothesis for the turbulent transport, for reconsidering the mixed length model in entirely continuous terms, and for seeking possible alternatives or corrections. Applying this methodology to the turbulent transport flux of kinetic energy, two dominating terms are found: one identified with a kinetic energy gradient model for shear layers; the other related to the main velocity gradient. Accordingly, a composed, Statistical Dynamic model is proposed for the turbulent transport of kinetic energy in shear layers, adding a velocity derivative term to Daly and Harlow’s generalized gradient model. This velocity derivative term is calibrated in a nearly homogeneous turbulent shear flow, and the resulting Statistical Dynamic model is proved superior to Daly and Harlow’s and other gradient models in channel and boundary layer flows.
Highlights
Forty-three years ago, Corrsin (1975) called attention to a paradox concerning the gradient assumption for the turbulent transport in fluid flows: it was virtually the only kind of model used for practical calculations serious objections to the assumption were known for a long time
Two possibly dominating terms are identified in the statistical dynamic equation for turbulent kinetic energy: the gradient term previously referred and a new term related to the velocity derivatives
Employing the statistical dynamic equations, the turbulent transport fluxes of scalars and momentum were decomposed into terms representing various aspects of the main and fluctuating flow that dynamically create such transports
Summary
Forty-three years ago, Corrsin (1975) called attention to a paradox concerning the gradient assumption for the turbulent transport in fluid flows: it was virtually the only kind of model used for practical calculations serious objections to the assumption were known for a long time. Two possibly dominating terms are identified in the statistical dynamic equation for turbulent kinetic energy: the gradient term previously referred and a new term related to the velocity derivatives.
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