Turbulence and Combustion Group

Stochastic modeling of acceleration in turbulent flows

The goal of this research is the development of Lagrangian stochastic models of acceleration in homogeneous turbulence (with and without mean deformations) that agree with the available data from DNS and experiments. We have identified a class of second-order Markovian stochastic models (conditional on a log-normal representation for the Lagrangian dissipation) that are exactly consistent with Gaussian (one-point, one-time) velocity statistics and conditionally Gaussian acceleration statistics (the Reynolds (2003) model belongs to this class). Preliminary calculations of two-time cross-correlations (below) using the Reynolds (2003) model and a cubic acceleration model (an easily identifiable nonlinear model in the class) show that the former has an unphysical cusp at the origin (as opposed to smooth behavior generated by the latter). DNS data are going to be used as a discriminator among different stochastic models in the class.

Selected publications
	A.G. Lamorgese, S.B. Pope, P.K. Yeung and B.L. Sawford (2007) ``A conditionally cubic-Gaussian stochastic lagrangian model for acceleration in isotropic turbulence'', Journal of Fluid Mechanics 582, 423--448
	P.K. Yeung, S.B. Pope, A.G. Lamorgese and D.A. Donzis (2006) ``Acceleration and dissipation statistics of numerically simulated isotropic turbulence'', Physics of Fluids 18, 065103
	A.G. Lamorgese, D.A. Caughey and S.B. Pope (2005) ``Direct numerical simulation of homogeneous turbulence with hyperviscosity,'' Physics of Fluids 17,015106
	S.B. Pope (2002) "A Stochastic Lagrangian Model for Acceleration in Turbulent Flows," Physics of Fluids 14(7), 2360--2375
	P.R. Van Slooten and S.B. Pope (1997) "PDF Modeling for Inhomogeneous Turbulence with Exact Representation of Rapid Distortions," Physics of Fluids 9(4), 1085--1105