TM NO. 377 



Both -^O/' and^ttVr in (A-68) aad (A-69) have units of dynes per square 



centimeter or force per unit area*, The former term is identified as a dyanmic 

 or turbvilent pressure^, and the latter as a turbulent (or shear) stress. 



Momentum Equations for Turbiolent Velocities «=■=■ To appreciate how the eddy 

 stresses can "be interpreted as real physical quantities ^ let us consider the 

 Navier-Stokes equations for an incompressible fluid in two dimensions in the 

 vertical XI plane » These equations are; 



^ ^-i^^W^tL (A-71) 



and ^ «.^- Cr-^^VV W ^ (A.Y2) 



where p = pressure (dyne cm"^) 



■V ~ kinematic viscosity (cm^ sec"-'-) 

 Q s gravitational acceleration (980) cm sec~2 

 \/'^= laplaciatj operator ( -^1.+ ^-r, ) ^^ 



i ~ measured positively tipwardo 



Note that; 



dt- dt da ^ dim 



The two-dimensional continuity equation for an incompressible fliiid can also 



be used 2 



Substituting the Reynolds formulations (A-62) and also the pressure relation 



into equations (A-7I) and (A'=72)^ and taking time averages in accordance with 

 equation (A-63)^ gives 1 



^-^■w^^'u!^^m^^J^^-i^i^f^^i:^) (A-75) 



and 



-f fili? f7i'i^VaF^i^t^'cb'-J^-6>^/^^u^w) (A-76) 



did 



A-l4 



