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Costal Inlets Research Program
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> Flow at Bend cont'd - TR-03-60050
Flow at Bend cont'd - TR-03-60049
Flow at Bend cont'd - TR-03-60051
TR-03-6
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30
31
32
33
34
35
36
37
38
39
40
X
X
=
Z
(27)
prototype
Z
model
or
expressed
in
terms
of
scale
ratios
N
X
= N
Z
(28)
which
means
a
geometrically
undistorted
model.
From
Equations
23
through
26
the
following
can
be
concluded:
convective
acceleration
terms
in
similitude
2
∂
v v
∂
v v v
∂
v
r
v
θ
∂
v
r
v
θ
∂
v
; ;
v
r
θ
;
θ θ
;
r
θ
;
v
z z
;
v
r
(29)
∂
r r
∂
θ
r
∂
r r
∂
θ
∂
z
r
convective
acceleration
terms
not
in
similitude
∂
v
∂
v
r
∂
v v
∂
v
;
v
z
θ
;
v
r z
;
θ
z
v
z
(30)
∂
r r
∂
θ
∂
z
∂
z
The
two
nonsimilar
convective
accelerations
contained
in the
horizontal
direction
momentum equations
are
larger
in the
model
than
they
should
be by a
factor
equal
to the
geometric
distortion,
i.e.,
∂
v
∂
v
∂
v
∂
v
^
^
^
^
Ω
v
z r
;
v
z
θ
=
v
z r
;
v
z
θ
^
^
^
^
(31)
∂
z
∂
z
proto
∂
z
∂
z
model
^
^
^
^
where Ω =
N
x
/N
z
.
This
implies
that
horizontal
convective
accelerations
due
to
vertical
gradients of the
radial
and
tangential
velocities
(
v
r
,
v
θ
)
are
greater in the
distorted
model
than
in the
prototype.
Conversely,
the
two
nonsimilar
convective
accelerations
contained
in the
vertical
momentum
equation
are
smaller in the
model
than
they
should
be by a
factor
equal
to the
inverse
of the
geometric
distortion,
i.e.,
1 ∂
v
z
v
θ
∂
v
z
∂
v v
∂
v
^ ^ ^
^ ^ ^
=
v
r z
;
θ
z
^
^
;
v
r
(32)
Ω ∂
r r
∂
θ
^
proto
∂
r r
∂
θ
^
model
^^
^^
35
Chapter
4
Turbulence
Scale
Effect
in
Distorted
Models
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