A Multifractal Representation of the Small-Scale Structure in a Turbulent Plume

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  • 1 ARAP Group, Titan Research and Technology Division, Titan Corporation, Princeton, New Jersey
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Abstract

An improved method for representing the small-scale structure of a turbulent scalar field using fractal recursion techniques is described. The model generalizes the fractal successive refinement method described by Sykes and Gabruk to include a more realistic description of the pseudodissipation field. that is, the square of the scalar gradient. Turbulent dissipation fields are known to be multifractal, so a multifractal generation technique has been incorporated into the fractal refinement model to yield a scalar field with isosurfaces but with a multifractal pseudodissipation field.

The model fields are compared with realizations from large-eddy simulations of turbulent scalar dispersion and shown to provide improved agreement with the small-scale structure. The simple combination of fractal and multifractal properties employed in the model also provides insight into the structure of the random scalar field. Finally, the generation technique is completely localized in physical space and is therefore applicable to inhomogeneous fields.

Abstract

An improved method for representing the small-scale structure of a turbulent scalar field using fractal recursion techniques is described. The model generalizes the fractal successive refinement method described by Sykes and Gabruk to include a more realistic description of the pseudodissipation field. that is, the square of the scalar gradient. Turbulent dissipation fields are known to be multifractal, so a multifractal generation technique has been incorporated into the fractal refinement model to yield a scalar field with isosurfaces but with a multifractal pseudodissipation field.

The model fields are compared with realizations from large-eddy simulations of turbulent scalar dispersion and shown to provide improved agreement with the small-scale structure. The simple combination of fractal and multifractal properties employed in the model also provides insight into the structure of the random scalar field. Finally, the generation technique is completely localized in physical space and is therefore applicable to inhomogeneous fields.

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