In this case the vertical convective accelerations due to horizontal gradients of

the vertical velocity (*v*z ) 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

negligible.

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 (*v*θ /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.

36

Chapter 4 Turbulence Scale Effect in Distorted Models

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