Two-Dimensional " Poor Man' s Navier -Stokes Equation" Model of Turbulent Flows

Aspartofacontinuing effortto construct“ syntheticvelocity” subgrid-scale (SGS)modelsforlarge-eddysimulation (LES)techniquesutilizing Kolmogorov scaling and discretedynamic systems (chaotic maps ), focusiscentered on constructing the chaotic maps from experimental data to demonstrate consistency of the modeling approach with basic physics. Although such efforts have been made previously, all of them used a linear combination of logistic maps to e t one-dimensional experimental data. A two-dimensional chaotic map derived directly from the Navier‐Stokes equations is employed, and the bifurcation parameters of this map are determined to best e t twodimensional experimental velocity data. A genetic algorithm is used as the optimization tool to obtain the required least-squares e t of the time series for a point in a two-dimensional e ow behind a turbulator. Results compare reasonably well with the experimental time series, implying that two-dimensional chaotic maps provide viable candidates for producing temporal e uctuations in synthetic-velocity SGS models for LES and additionally as part of real-time control mechanisms.