Multiscale And Multiresolution Approaches In Turbulence PDF Download

The properties of turbulent jet scalar interfaces are investigated using a high-resolution experimental database of fully-developed turbulent scalar fields and interfaces in jets. The database was recorded at the UC Irvine turbulence atmospheric pressure flow facility using laser-induced fluorescence of disodium fluorescein in water, with the Reynolds number of the jet Re ∼ 2 x 104, and the Schmidt number Sc ∼ 2 x 103. The probability density function (pdf) of turbulent jet scalar fields is examined with emphasis on the extent to which the pdf depends on resolution scale effects. Coarse graining is conducted by a two-step method consisting of applying an averaging filter and performing quadratic B-spline interpolation. The scalar pdf is examined as the product of the interfacial area-volume ratio, or perimeter-area ratio for two-dimensional data, and the interfacial thickness quantified as the averaged inverse magnitude of the scalar gradient across each interface. It is demonstrated that because the area-volume ratio decreases with reduced resolution, whereas the interfacial thickness increases with reduced resolution, the scalar pdf exhibits significant, robustness to resolution scale effects over a wide range of resolution scales as well as scalar thresholds. It is demonstrated that the observed robustness arises from the dual self-similarity of the interfacial perimeter and thickness which are found to exhibit two self-similarity exponents of opposite signs and approximately equal magnitudes for the present jet conditions. In other flows, the degree of the multiresolution robustness can be expected to depend on the extent of the dual self-similarity and the relative magnitudes of the corresponding exponents. Significant robustness to reduction in resolution scale is found for the enclosed volume as well and is attributed to the dual self-similarities exhibited by the interfacial protrusions and indentations with similar scaling exponents. The interfacial protrusions and indentations provide nearly-opposite positive and negative contributions respectively to the volume enclosed by the turbulent scalar interface, in contrast to the interfacial surface area for which the protrusions and indentations both generate additive contributions. In order to improve the understanding of the turbulent interfaces, the multifractal aspects of scalar dissipation field conditional on the outer fluid interface are examined using multifractal analysis. The singularity exponents are calculated for every point on the outer fluid interface. The singularity exponent field is then analyzed by computing the generalized dimensions of iso sets using standard box-counting method as well as recently developed meshless M3 method. Examination of the generalized dimensions of the iso sets indicates strong dependence on scale. The average generalized dimension of iso set is found to depend strongly on the value of the singularity exponent of the iso set, with the highest average generalized dimension achieved for singularity exponent corresponding to the average generalized dimension of the interface. The present study is expected to be useful for comparison to higher Reynolds numbers and different Schmidt numbers, as a high-resolution reference case.