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
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
2
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,