4.2. SHORT-WAVE HYDRODYNAMIC MODELS
107
100 = K
0.3 m X
0.008 m/
or
K = 2.66
Final Note: The A'-values found by the two methods should now be averaged to get
a value of A at)e = 2.93.
Surface Tension. The scale effect due to surface tension forces not being
in proper proportion in a Froude-scaled model becomes important when the
water waves are very short or the water depth is very shallow. Usual “rules
of thumb” are that surface tension effects must be considered when wave
periods are less than 0.35 seconds and when water depth is less than 2 cm
(Le Méhauté 1976). At these small parameter values, the restoring force of
surface tension begins to be significant and the model will experience wave
motion damping that does not occur in the prototype. Also, wave celerity
is a function of surface tension, so phenomena such as wave refraction will
not be in similitude when surface tension effects are significant.
The relative magnitude of surface tension forces can be evaluated using the linear wave theory expression for wave celerity that includes the
influence of surface tension, i.e.,
or
C2
qL
2tto-\
----- 1 ------- tank
2tt
pL J
2irh
~T
gL
, /2tt/z\
2ttct
= — tank —— + ——tanh
2%
\ L J
pL
(4-43)
(4.44)
gravity term
surface tension term
where
C - wave celerity
L - wavelength
g
- gravity
p
- fluid density
h - water depth
The relative contribution of the surface tension term can be expressed
as a fraction by dividing the surface tension term by the gravity term to
get
(¥)
(4.45)