Statistical Equilibrium Computations of Coherent Structures in Turbulent Shear Layers

• Published in: SIAM journal on scientific computing Vol. 17; no. 6; pp. 1414 - 1433
• Main Authors: Turkington, Bruce, Whitaker, Nathaniel
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.11.1996
• Subjects: Algorithms; Applied mathematics; Boundary conditions; Boundary layer and shear turbulence; Classical and quantum physics: mechanics and fields; Classical mechanics of continuous media: general mathematical aspects; Computational methods in fluid dynamics; Entropy; Equilibrium; Exact sciences and technology; Fluid dynamics; Fluid mechanics: general mathematical aspects; Fundamental areas of phenomenology (including applications); Inviscid flows with vorticity; Laminar flows; Numerical analysis; Physics; Probability distribution; Reynolds number; Turbulent flows, convection, and heat transfer; Vortices; Statistical method; Statistical equilibrium; Turbulent shear layer; Optimization method; Coherent structure; Maximum entropy method; Two dimensional turbulence
• ISSN: 1064-8275; 1095-7197
• DOI: 10.1137/S1064827593251708

A numerical method is developed to treat the statistical equilibrium model of coherent structures in two-dimensional turbulence. In this model the vorticity, which fluctuates on a microscopic scale, is described macroscopically by a local probability distribution. A coherent vortex is identified with a most probable macrostate, which maximizes entropy subject to the constraints dictated by the complete family of conserved quantities for incompressible, inviscid flow. Attention is focused on the special case corresponding to vortex patches, and a simple, robust, and efficient algorithm is proposed in this case. The form of the iterative algorithm and its convergence properties are derived from the variational structure of the statistical equilibrium problem. Solution branches are computed for the shear layer configuration, and the results are interpreted in terms of the dynamical phenomena of rollup and coalescence.