A sampling-based data-driven estimator closes the conditional average in invariance-derived PDF transport equations for 2D vorticity, producing PDFs that match direct DNS evaluations in decaying and forced HIT.
Weiss,The dynamics of enstrophy transfer in two-dimensional hydrodynamics, Physica D48 (1991), 273–294
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A data-driven approach for 2D vorticity PDF equations by a new conditional average estimation
A sampling-based data-driven estimator closes the conditional average in invariance-derived PDF transport equations for 2D vorticity, producing PDFs that match direct DNS evaluations in decaying and forced HIT.