The impact of the turbulence scale effect depends on the relative magnitudes
of the turbulence in the horizontal and vertical planes. The smallest turbulence
scale effect will occur in situations where the turbulence is manifested primarily
in either the horizontal or vertical plane. As an example, numerous observations
of plane turbulent jets exiting a channel of width 2 bo between two vertical edges
have shown that the downstream mean horizontal velocity um along the jet center
line is well represented by a self-similar empirical formula such as:
bo
um = 3.5 U o
(17)
x
where Uo is the exit velocity and x is the distance downstream. This relationship
is valid for both geometrically distorted and undistorted flow models at any depth
in the jet, which indicates that the turbulence is primarily in the horizontal plane
with only weak fluctuations in the vertical plane. In other words, for the case of
a plane jet exiting a channel with vertical sidewalls, the turbulence terms that are
not in similitude in distorted models have only minor influence because the
vertical velocity fluctuations are small compared to the horizontal fluctuations.
A similar jet exiting a channel with sloping edges will have vertical velocity
fluctuations on the same order as (or even greater than) the horizontal
fluctuations. Do not expect self-similar behavior in the downstream jet
at different water depths because the induced vertical velocities impact the
entrainment rate and transport mass vertically. In a distorted model the sloping
edges of the channel creating the jet will be steeper. This will decrease the
vertical velocity fluctuations, making the jet structure appear more like that of a
plane jet with vertical channel walls.
The magnitude of the turbulence scale effect in distorted models will vary
with each situation and the amount of model distortion. For some studies the
effect may be negligible so long as the major flow features are reasonably
reproduced. For example, if there is a region of flow separation in the lee of a
headland, expect the distorted model to reproduce the geometry of the flow
separation downstream of the headland (particularly on the surface), and the
maximum velocity magnitudes and directions caused by flow accelerations along
the line of separation should scale reasonably correct. Within the area of reduced
flow adjacent to the line of flow separation, velocity vectors may not be in
similitude with the prototype, but this might not be as important so long as it
recognized that this might be an area where sedimentation could take place.
Any observed vertical velocities are likely to be more pronounced in the distorted
model, but on the other hand, the steeper slopes in the distorted model will
produce smaller vertical velocities so this could help balance the disparity.
Flow around a vertical cylinder represents an interesting case because of the
well-known horseshoe vortex responsible for scour. This vortex has strong
vertical velocity and acceleration components that will not be well represented in
a distorted model. In some physical models of inlets and harbors, vertical piles
obstruct the flow, and it is important to establish how well this flow reduction
is simulated in distorted models. Vortices are shed in the wake of the pile, but
31
Chapter 4 Turbulence Scale Effect in Distorted Models
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