ERDC/CHL CETN-IV-26
June 2000
where the subscripts p and m refer to prototype and model, respectively.
Equation 13 can be rearranged into ratios of prototype values of a variable over the
corresponding model value. These are termed "scale factors," and they are denoted by an upper
case N. For example, the scale factor for depth-averaged velocity is:
Vp
NV =
Vm
Replacing all the prototype-to-model ratios with scale factors, and recognizing that gravity will
be the same in the model as in the prototype, results in the following scaling relationship:
NV
=1
(14)
1/2
bg
N d /8 N 1/8
3
N S -1
L
s
e
or
1/2
bg
N d /8 N 1/8
3
NV = N S -1
(15)
L
s
e
with NL = (he)p /(he)m representing the length scale of the model. If the model sediment has the
same density as the prototype sediment, then N(Ss-1) = 1, resulting in a simplified scaling
relationship of:
NV = N d /8 N 1/8
3
(16)
L
e
10
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