STUDY OF THE POOR MAN\u27S NAVIER-STOKES EQUATION TURBULENCE MODEL

The work presented here is part of an ongoing effort to develop a highly accurate and numerically efficient turbulence simulation technique. The paper consists of four main parts, viz., the general discussion of the procedure known as Additive Turbulent Decomposition, the derivation of the synthetic velocity subgrid-scale model of the high wavenumber turbulent fluctuations necessary for its implementation, the numerical investigation of this model and a priori tests of said models physical validity. Through these investigations we have demonstrated that this procedure, coupled with the use of the Poor Mans Navier-Stokes equation subgrid-scale model, has the potential to be a faster, more accurate replacement of currently popular turbulence simulation techniques since: 1. The procedure is consistent with the direct solution of the Navier-Stokes equations if the subgrid-scale model is valid, i.e, the equations to be solved are never filtered, only solutions. 2. Model parameter values are set by their relationships to N.S. physics found from their derivation from the N.S. equation and can be calculated on the fly with the use of a local high-pass filtering of grid-scale results. 3. Preliminary studies of the PMNS equation model herein have shown it to be a computationally inexpensive and a priori valid model in its ability to reproduce high wavenumber fluctuations seen in an experimental turbulent flow

A data-fitting procedure for chaotic time series

In this paper the authors introduce data characterizations for fitting chaotic data to linear combinations of one-dimensional maps (say, of the unit interval) for use in subgrid-scale turbulence models. They test the efficacy of these characterizations on data generated by a chaotically-forced Burgers` equation and demonstrate very satisfactory results in terms of modeled time series, power spectra and delay maps