Temporal behavior of a low-dimensional dynamical system proposed for construction of subgrid-scale models in LES of scalar transport J.
M. MCDONOUGH University of Kentucky, J. C. HOLLOWAY University of California, Los Angeles, M. G.
Chong, PowerLab, Irwindale, CA Temporal behavior
of a low-dimensional discrete dynamical system (DDS)
proposed as part of a subgrid-scale (SGS) model for LES
of scalar transport is examined. Following a brief review
of derivation of the DDS from the Navier–Stokes equations together with an equation for scalar transport via
application of the Galerkin procedure, representative bifurcation diagrams are presented to emphasize the wide
range of temporal behaviors and bifurcation sequences
accessible with this system. Direct comparisons between
time series generated with this DDS and those for velocity and temperature available in the extant literature
are then provided to demonstrate ability of the DDS to
mimic a broad range of physical and DNS behaviors, including replication of known bifurcation sequences and
qualitative appearance of time series. Finally, statistical properties of the time series will be reported to show
that the low-dimensional dynamical system being studied is capable of reproducing some, but not all, of the
quantitative observations from turbulent scalar transport. In particular, flatness, skewness and low-order
structure function results will be provided, along with
the usual power spectra and probability density functions.