One-dimensional turbulence: vector formulation and application to free shear flows

One-dimensional turbulence is a stochastic simulation method representing t he time evolution of the velocity profile along a notional line of sight th rough a turbulent flow. In this paper, the velocity is treated as a three-c omponent vector, in contrast to previous formulations involving a single ve locity component. This generalization allows the incorporation of pressure- scrambling effects and provides a framework for further extensions of the m odel. Computed results based on two alternative physical pictures of pressu re scrambling are compared to direct numerical simulations of two time-deve loping planar free shear flows: a mixing layer and a wake. Scrambling based on equipartition of turbulent kinetic energy on an eddy-by-eddy basis yiel ds less accurate results than a scheme that maximizes the intercomponent en ergy transfer during each eddy, subject to invariance constraints. The latt er formulation captures many features of free shear flow structure, energet ics, and fluctuation properties, including the spatial variation of the pro bability density function of a passive advected scalar. These results demon strate the efficacy of the proposed representation of vector velocity evolu tion on a one-dimensional domain.