Derivation of the equation of change for the Reynolds stresses. At the end of S5.2 it was pointed out that there is an equation of change for the Reynolds stresses. This can be derived by 

(a) Multiplying the i^th component of the vector form of Eq. 5.2-5 by vj and time smoothing, 

(b) Multiplying the j^th component of the vector form of Eq. 5.2-5 by v’ and time smoothing, and 

(c) Adding the results of (a) and (b) Show that one finally gets Equations 5.2-10 and 11 will be needed in this development.   

Transcribed Image Text:

v'v' = -p\v'v' · Vv} – plv'v' · Vvj* – plV v'v'v' Dt v'Vp'} – (v'Vp']* + µ (v'V°v'}*