u
v
w
u=
v=
w=
^
^
^
;
;
V
V
W
x
y
z
x= ;
y= ;
z=
^
^
^
(5)
X
X
Z
^ t
p
t= ;
p=
^
T
P
where
V = characteristic nonturbulent horizontal velocity
W = characteristic nonturbulent vertical velocity
X = characteristic horizontal length
Z = characteristic vertical length
T = characteristic time
P = characteristic pressure
Different characteristic lengths and velocities were chosen for the horizontal and
vertical directions to accommodate geometrically distorted hydrodynamic
models. For convenience, the same characteristic velocities were used to
nondimensionalize the turbulent Reynolds stresses.
Making these substitutions into Equations 1 through 5, multiplying the
2