Turbulent drag reduction in one and two dimensions

Theo Odijk

Physica A: Statistical Mechanics and its Applications, 2001, vol. 298, issue 1, 140-154

Abstract: Drag reduction is investigated in one- and two-dimensional turbulent flows that are stationary and homogeneous. In the two-dimensional case, the polymer chains are deformed though advected passively through the Kraichnan cascades within a scaling analysis. The typical rate of shear must then be larger than the time of deformation of a chain. Ultimately, elastic forces compete with Reynolds stresses at an elastic cut-off similar to that defined in the Tabor–de Gennes scenario in three dimensions. There are several regimes in two dimensions because there are two cascades. In the one-dimensional case, a Burgers-type equation is coupled to a frame-indifferent equation for the viscoelastic Maxwell stress together with a stochastic force. Dissipation arises within viscoelastic shocks. The (effectively longitudinal) speed of the elastic waves is a cut-off for the shocks. This elastic cut-off shows up in velocity correlations. The implications for soap film and wire experiments are discussed.

Keywords: Turbulence; Drag reduction; Polymers; Elastic waves; Elasticity; Rheology (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:298:y:2001:i:1:p:140-154

DOI: 10.1016/S0378-4371(01)00215-1

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