In this case the vertical convective accelerations due to horizontal gradients of
the vertical velocity (vz ) are less in the distorted model than in the prototype.
It is difficult to assess definitively the impact of the nonsimilar convective
acceleration terms in bend flows. Thorne and Abt (1993) overviewed numerical
modeling approaches based on the cylindrical form of the Navier-Stokes
equations. A basic assumption is that vertical velocities in the uniform flow are
small, allowing the use of depth-integrated flow equations. This assumption
implies that the nonsimilar convective accelerations of Equation 32 are also
Thorne and Abt (1993) discussed two major schools of thought regarding
the horizontal convective accelerations. Early work by Engelund (1974) argued
that in the cross-stream (r-direction) momentum equation the centrifugal
acceleration (vθ /r) is balanced by the pressure gradient and cross-stream bottom
shear stress. All other convective accelerations are negligible. In the
downstream (θ-direction) momentum equation the water-surface slope is
balanced only by downstream bed shear stress, thus ignoring any influence of
convective accelerations. If Engelund's simplifying assumptions are reasonable,
then correct similitude of bottom friction will be far more important in a distorted
model than the dissimilar convective acceleration terms.
The second school of thought maintains that the horizontally directed
convective accelerations are important, but recognizes very severe field
requirements for validating numerical models because it requires measuring
cross-channel water-surface elevations to millimeter accuracy (Thorne and Abt
1993). However, even in this case the emphasis is placed on those horizontal
convective accelerations which are shown to be in similitude in a distorted
physical model. Because of the assumption that vertical velocities are small, the
nonsimilar convective accelerations given in Equation 4-31 must also be
considered negligible in the numerical model development. Thorne and Abt
(1993) recommended adopting models following the thesis of Engelund (1974)
because they have been shown to give reasonable results.
A geometrically distorted physical model with proper attention to bottom
surface roughness includes more of the physics than depth-integrated numerical
models despite having convective acceleration terms that exhibit a scale effect.
The four convective accelerations that contain a scale effect in a distorted
physical model of river bends are considered inconsequential in most practical
numerical modeling. This provides some level of comfort in using a distorted
physical model to simulate flow around bends.
Chapter 4 Turbulence Scale Effect in Distorted Models