model's vertical and horizontal length scales are the same...in other words the
model is "geometrically similar."
Undistorted physical models can accurately reproduce the macro-scale
features of turbulent processes, and these physical models are the preferred tools
for studying turbulence-influenced flows provided the region of interest is small
enough and the modeling facility is large enough to accommodate undistorted
Froude scaling. When undistorted models are not feasible because of area
restrictions, an alternative might be a geometrically distorted physical model,
provided the flow conditions meet the necessary criteria.
Geometrically Distorted Models
In the context of free-surface hydrodynamic physical models, a
"geometrically distorted" model is a physical model having a vertical length
scale that is different than the horizontal length scale. Geometric distortion,
in general, invalidates the necessary scaling criteria; but under very specific
conditions the impact of geometric distortion is minimized to the point that
model results can be reliably scaled to prototype dimensions. Specifically,
situations where the vertical components of flow velocities and accelerations
are very small in comparison to the horizontal components can be modeled in
distorted models (Hughes 1993). This implies that water pressure is hydrostatic
throughout the inviscid flow region. Flow conditions that meet this specific
criterion include "long-wave models" (tidal flows) and unidirectional flow
models. However, there are certain restrictions that must be observed.
The main advantage of geometrically distorted physical models is the
flexibility in choosing the horizontal scale so that large horizontal areas can
be modeled in existing model facilities. Without geometric distortion, model
water depths would be very small, and model results could be severely affected
by surface tension effects and bottom friction. Distorted models allow greater
water depths, require less horizontal area, exhibit less frictional losses, and
facilitate more accurate vertical measurements (water-surface elevations).
The main drawback to geometrically distorted models is the inability to
simulate short waves (wind waves) in addition to long waves. Also, boundary
slopes are steeper in distorted models so how this might influence the particular
flow situation being modeled must be considered.
In geometrically undistorted models, macro-scale features of turbulence
are in similitude with the prototype, so overall characteristics of hydrodynamic
processes like breaking waves, hydraulic jumps, and regions of flow separation
are faithfully reproduced by the model. Conversely, in geometrically distorted
models, turbulent processes are not in strict theoretical similitude.
For most distorted physical models, this is generally not a problem either
because the modeled flow situation does not have significant large-scale
turbulence, or because the turbulent processes that do occur have little impact on
the flow features being simulated. However, if flow patterns in the main region
Chapter 4 Turbulence Scale Effect in Distorted Models