XV 

 SOME CURRENT PROBLEMS IN TURBULENT SHEAR FLOWS 



S. Corrsin 

 The Johns Hopkins University 



TABLE OF CONTENTS 



Page 



Introduction 373 



The Proximity of Boundaries in Turbulent Shear Flows 374 



Mean Stress and Strain-Rate 377 



Local Isotropy 379 



Shear Spectrum 386 



The Gradient Transport Postulate 387 



Shear Stress Fluctuations 389 



Wall Layer and Laminar Sublayer 392 



Fluctuations in Skin Friction and Surface Static Pressure 395 



Boundary Layer Thickness Fluctuations 396 



Introduction 



This paper is intended to be a heuristic account of several problems in the 

 dynamics of turbulent shear flow. More to formulate questions than to answer them, 

 it is in no sense a survey of the current research status in the field; the admirable new 

 monograph of Townsend [1] will fill this role for some time to come. Unfortunately, 

 it has not been possible to incorporate here the relevant contributions of his book, but 

 I have attempted to make some references to it. 



The turbulent transfer of a passive scalar contaminant in a mean gradient has 

 become partly clarified through the use of Lagrangian dispersion analysis (in the ideal 

 case, just by following indelibly tagged fluid) [2] instead of the Eulerian representation 

 more convenient for turbulence dynamics. In approaching the problem of turbulent 

 momentum transfer, it is therefore unavoidable that we ask the naive question of 

 whether an idealized problem analogous to the scalar case can be sensibly formulated. 

 Can we treat kinematically the turbulent dispersion of momentum from a "point 

 source", at least in some kind of "small perturbation" limit? 



An immediate difficulty is the conceptual one of visualizing a dispersing fluid 

 (or solid) particle indelibly tagged with a mean momentum increment. In the very 

 act of being convected by turbulent fluid the particle partakes of the general flow 

 dynamics. On the other hand, if this action can be described by a linear differential 

 equation, and if it does not affect the basic turbulence, there remains some hope for 

 the utility of this approach. If the interaction is essentially non-linear, not only will 

 the point-source dispersion be complex, but also the entire notion of synthesizing a 

 mean gradient by superposition of sources will be invalid. 



In a flowing isotropic turbulence [mean velocity U, turbulent velocity u { <^ U], 

 the possibility of an equation linear in v i? the perturbation velocity of a particle, 

 depends upon the negligibility of effects quadratic in v { . 



373 



