Reprinted from the Proceedings of the Conference 

 Applying Research to Hydraulic Practice 

 ASCEIJackson, Mississippi! August 17-20, 19S2 



Hydraulic Applications of a Second-Order Closure 

 Model of Turbulent Transport 



By 



Y. Peter Sheng 



INTRODUCTION 



Eddy-viscosity models have been widely used for the hydraulic 

 analyses of turbulent transport phenomena in oceans, lawes, and 

 estuaries. If sufficient data is available to establish the validity 

 of the required parameters in the subject models, then the predictions 

 of the models in that particular application give reasonably acceptable 

 results. However, when sufficient data are not available and tne 

 parameters for a specific application must be extrapolated from much 

 different situations, the resulting predictions are highly speculative. 



For example, sediment transport in coastal waters usually occurs 

 in highly oscillatory flow with appreciable density stratification. 

 The flow may also cause bed forms which in turn affect tne flow. In 

 such a situation, large errors could result from the use of standard 

 eddy-viscosity models since these models do not contain the accurate 

 physics describing: (1) the time lag between the mean flow gradients 

 and the turbulent transport; (2) the time-dependent damping of tne 

 turbulent transport due to stable density gradients and tne 

 counter-gradient turbulent transport due to unstable density gradients; 

 and (3) the partitioning between skin friction drag and profile drag in 

 the vicinity of an arbitrary roughness element. 



This paper highlights a turbulent transport model developed to 

 make accurate predictions in turbulent flows where data is unavailaole 

 or hard to obtain, using as its strength modeling constants evaluated 

 in situations far-removed from the flow of application. Tne basic 

 turbulent transport model, originally developed by Donaldson and his 

 associates at A.R.A.P. (1,11,12), involves the retention of the 

 second-order turbulent correlation equations that affect the mean flow 

 variables. The added physics contained in the second-order closure 

 model permit one to directly calculate the phenomena mentioned in the 

 previous paragraph, without resorting to some ad-hoc eddy viscosity 

 fixes. 



In the following, I will first give a brief description of the 

 turbulent transport model. I will then discuss three example hydraulic 

 applications of this model to (1) an oscillatory turoulent Doundary 

 layer, (2) the transport of momentum, heat, and species witnin a 

 vegetation canopy, and (3) coastal currents driven by tide, wind, or 



^Consultant, Aeronautical Research Associates of Princeton, Inc., 

 P.O. Box 2229, Princeton, N.J. 085^40. 



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