A semi-analytical model for form drag of river bedforms

Bed resistance may consist of two components (e.g. Rouse, 1965; Yen, 2002):
(1) grain friction, and (2) form drag due to bedforms. The objective of the
present study is to develop a form drag model applicable to bedform-dominated
rivers under subcritical flow conditions.
A semi-analytical form drag model has been developed in the present study.
The model consists of two components: (1) an analytically-based reference form
drag model, accounting for the energy loss associated with a deceleration of the
flow due to a sudden expansion of a free surface flow, and (2) an empirical coef-
ficient taking into account effects due to deviations from the reference situation.
The empirical coefficient contains the following four effects relevant to form
drag:
1. the flow downstream of a bedform crest expands gradually rather than
abruptly,
2. the flow pattern over closely spaced bedforms differs from the pattern over
a solitary bedform,
3. the height of the flow separation zone may deviate from the bedform
height,
4. bedform geometry is irregular rather than regular.
In the semi-analytical form drag model these four effects are included; in the
so-called analytical form drag model they are not included. Both models are
applied to laboratory data of flow over uniform fixed and alluvial bedforms. The
results of the models are compared to those of existing bed resistance models
to analyze the performance of the analytical and semi-analytical models.
For the uniform fixed bedform data, it is found that the present semi-
analytical model yields better results than the analytical and empirical models
considered.
The form drag model of Yalin (1964) and Engelund (1966) yields the best
results for the alluvial flume data. However, from data of flow over bedforms
with small lee faces it appears that the semi-analytical form drag model yields
better predictions of form drag than the Yalin (1964) - Engelund (1966) form
drag model. Therefore, for bedforms in the field, which are usually gentler
than in the laboratory, the semi-analytical model is expected to yield better
predictions of bed resistance than the Yalin (1964) - Engelund (1966) model.