Testing velocity profiles in turbulent jets for self
similarity  a practical guide
1. Defining a coordinate system
First, let us clearly define a sensible coordinate system for this flow.
D
y
x
U
Fig. 1:
Coordinate system (axes in blue) for turbulent jet flow.
This is the usual way of doing it, and it is worth noting why this is so.
First, in this model
of the flow, only two spatial dimensions are considered.
This includes both planar jets
and axisymmetric jets.
Whenever there is a mean flow, or most dominant flow
component (in this case, the flow along the jet axis), it is common to assign the
x
coordinate, and corresponding
u
velocity component parallel to that direction.
The flow
measured is a timeaveraged component (owing to the relatively large time constant of
the pitot tube/manometer system), and so it is denoted
U
, rather than
u
.
x
is defined
parallel to the mean flow and the long axis of the jet exit nozzle, beginning at the nozzle
exit.
Positive
x
moves in the direction of the flow, with positive
U
.
The remaining
coordinate,
y
, should be perpendicular to
x
.
It has its origin at the centerline, which is the
line of symmetry of the jet.
Note how the coordinate system is fixed with respect to the
jet flow itself, and not to some arbitrary laboratory reference.
2. The mean velocity profile in a turbulent jet
The evolution of the jet flow at x > 56D is thought to occur in a selfsimilar fashion
because turbulent velocity fluctuations have had sufficient time to rearrange the initial
flow that further flow evolution occurs with only preexisting turbulence as its precursor.
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 Spring '08
 Spedding
 Jet, Umax, turbulent jet

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