2.4 Laminar and Turbulent Flow
37
Time
b
Time
Fig. 2.11: Steady and unsteady random fluctuations
Mean velocity, ii, may be a function of time (see Fig. 2.11 b). Even if velocity
ii is constant (see Fig. 2.11a), the real velocity u is a function of time. This
means that the turbulence is always unsteady. A similar representation is valid
for other velocity components and pressure. Thus, we have:
v
w
p
v + Vi }
w+w l .
p+pl
It should be noted that mean values of u l , Vi, Wi and pi are zero, i.e.:
(2.38)
(2.39)
A bar over each quantity denotes an averaging of the particular quantity over
a time interval T. Thus, for u l and u:
- lio T I
u l = -
u dt = 0
T o '
(2.40)