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CHAPTER 4. HYDRODYNAMIC MODELS
Short-wave models must be geometrically undistorted.
The geometric similarity requirement for short-wave models is an essential part for dynamic similarity. In terms of the nondimensional equations of motion, geometric similarity means that nondimensional boundary
conditions and initial conditions are also the same between prototype and
model.
Having accepted the fact that short-wave models must be undistorted,
we can replace Nx and Nz with the undistorted length scale, Nf., and we
can let both horizontal and vertical velocity scales be represented by Ny.
This simplifies the nondimensional equations of motion to the following
form.
Continuity
dû dv dw n
dx dy
dz
x-Direction
f L \ dû ~dû „dû
~dû
( P \ dp
\vt) ~dî+udï + vdï + w'dî = ~ \pv^) aï
+
dI 2û d2û
d2û
I / \ d2v d2v d2v
\LV/ dx2 dÿ2 dz2
dx2 dy2 + dz2
y-Direction
L \
vt)
dv
dv
dv
~dv
/ P \ dp
+
+ w— = - —- ) —dt
dx
dy
dz
\PV2 ) dy
(4.15)
(4.16)
(4.17)