The representation of small-scale turbulence in numerical simulation experiments

Abstract

Analysis of previous attempts at numerical simulation of turbulent flows indicates that the models lacked suitable mechanisms for simulating the development and maintenance of a three dimensional turbulent energy cascade. The future practicality of such computations seems to require development of equations describing the transport of turbulent energy into and through the inertial range. It would also be desirable to simulate some of the effects of three dimensionality in a two dimensional model. Deardorff has attacked the latter problem, while for the former two models are described here. The first order model, originally suggested by Smagorinsky, is cast in the form of a variable eddy viscosity coefficient. It is shown to be consistent with the existence of the Kolmogoroff inertial range eddy spectrum function at the smallest resolvable scale. The second order model requires solving initial value equations for local stress components and variances, but is expected to be suitable for use with coarser spatial resolution, perhaps even within the energy containing range.