CLOSURE THEORIES WITH NON-GAUSSIAN RESTARTS FOR TRUNCATED 2-DIMENSIONAL TURBULENCE

NonMarkovian closure theories, with and without non-Gaussian restarts, are compared with ensemble averaged direct numerical simulations (DNS ) for severely truncated two-dimensional Navier-Stokes flows. Both the closures and DNS are formulated for discrete spectra relevant to flow s on the doubly periodic domain allowing unambiguous comparisons betwe en the closure and DNS results. We examine the performance of the dire ct interaction approximation (DIA), self-consistent field theory (SCFT ) and local energy-transfer theory (LET) closures and are particularly interested in the reliability of cumulant update versions of these cl osures (CUDIA, CUSCFT, and CULET). In the latter, the potentially long time-history integrals are periodically truncated and the closures ar e restarted using a three-point cumulant as the new non-Gaussian initi al conditions, thus yielding computationally much more efficient closu res. In 80-day integrations, the DIA replicates the DNS results most f aithfully in inviscid, viscous decay and forced dissipative experiment s. With an update time of T=10 days, the CUDIA is particularly promisi ng performing nearly as well but with some extra oscillations at inter mediate times. The SCFT and particularly LET, have spurious oscillatio ns in inviscid and viscous decay experiments; this is also the case, b ut to a greater degree, for the CUSCFT and CULET closures.