of interest are strongly influenced by turbulence, a scale effect will be present in
a distorted model.
If distorted physical models of turbulent flow regions are to be a viable
alternative, the turbulence scale effect must be assessed, and a determination
must be made on how the scale effect will modify model results that are scaled
up to full-size. This understanding could expand the utility of physical
hydrodynamic models for simulating real-world coastal engineering problems.
Turbulence Similitude in Geometrically Distorted
Models
Strict similitude criteria for hydrodynamic modeling are found by casting the
Navier-Stokes equations into nondimensional form and requiring that all
dimensionless coefficients retain the same value in the model as in the prototype.
Following the derivation provided by Hughes (1993), the four govening
equations for incompressible, free surface flow are given by the continuity
equation and the Navier-Stokes equations, i.e.,
∂u ∂v ∂w
+
+
=0
(1)
∂x ∂y ∂z
x-direction momentum
∂2u ∂2u ∂ 2u
∂u
∂u
∂u
∂u
1 ∂p
+u
+v
+w
=-
+ v 2 + 2 + 2
ρ ∂x
∂t
∂x
∂y
∂z
∂x
∂y
∂z
acceleration terms
pressure term
viscous shear terms
(2)
() () ( )
∂
∂
∂
u '2 +
-
u 'v ' +
u 'w'
∂x
∂y
∂z
turbulence terms
1
Scale effects are differences between the prototype and model response that arise from the
inability to simulate all relevant forces in the model at the proper scale dictated by the scaling
criteria.
25
Chapter 4 Turbulence Scale Effect in Distorted Models
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