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Costal Inlets Research Program
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Anticipated Scale Effects cont'd
Flow at Bend cont'd - TR-03-60048
TR-03-6
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these
are
largely
manifested in the
horizontal
plane
over
most
of the
water
column.
It is expected
that
the
shed
vortices
will
be in
approximate
similitude
in a
geometrically
distorted
physical
model.
Experiments
conducted to
assess
potential
turbulence
scaling
effects in
distorted
models
are
discussed
in the
following
chapter.
Flow at Bend
Finally,
in
addition
to
scale
effects
related
to
generation
of
turbulence,
any
mechanism
that
creates
significant
vertical
velocities
or
accelerations
will
be
problematic
in a
geometrically
distorted
model.
For
example,
at
river
bends
centrifugal
forces
pile
water
up on the
outside
of the bend,
which
creates
a
lateral
slope in the
water
surface.
The
force
imbalance
results
in a
cross-channel
return
flow
toward
the
inside
of the
curve
along
the
bottom.
The
resulting
secondary
flow
resembles
a
helix
as it
moves
downstream. In a
distorted
model
the
curve
geometry
will
be
tighter
and
the
side
slopes
will
be
steeper.
The
same
phenomenon
occurs
where
flow
accelerates
as it
passes
a headland or
jetty
causing
a
lowering
of the
local
water
surface.
Similitude
requirements
are
formally
determined
as
before,
only
this
time
the
following
governing
equations
are
presented
in
cylindrical
coordinates
as
often
adopted
for
numerical
modeling
of
flow
around
river
bends.
Turbulence
terms
and viscous
shear
stress
terms
have
been
omitted
from
the momentum equations
to focus on the
distorted
model
scale
effects
associated
with
flow
acceleration
at
a
river
bend.
continuity
∂
v
r
v
r
1 ∂
v
θ
∂
v
z
++
+
=0
(18)
r r
∂
θ
∂
r
∂
z
r-direction
momentum
2
∂
v
r
∂
v
r
v
θ
∂
v
r
v
θ
∂
v
1 ∂
p
+
v
r
+
- +
v
z r
= -
(19)
r
∂
θ
ρ
∂
r
∂
t
∂
r
∂
z
r
acceleration
terms
pressure
term
θ
-direction
momentum
∂
v
θ
∂
v
v
∂
v
∂
v
1 ∂
p
vv
+
v
r
θ
+
θ θ
+
r
θ
+
v
z
θ
= -
(20)
r
∂
θ
ρ
r ∂
θ
∂
t
∂
r
∂
z
r
acceleration
terms
pressure
term
32
Chapter
4
Turbulence
Scale
Effect
in
Distorted
Models
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