This paper will introduce the basic principles associated with
hydraulic modelling of surface waters for geomorphological and
hydrological purposes and illustrate how these have been applied to
specific problems. The basic principles governing fluid flow are
derived from the principles of conservation of mass and momentum. In
the case of the shallow flow problems that typify most geomorphological
and hydrological contexts, these equations involve some modifications:
(i) as the boundary layer is likely to extend throughout the flow
depth, it is possible to assume a hydrostatic pressure distribution;
(ii) special conditions need to be determined for both the bottom and
water surface, including the possibility of horizontal gradients of
atmospheric pressure for large-scale applications, and wind stress; and
(iii) it is generally permissible to ignore the Coriolis terms. Direct
application of the resultant equations is complicated by the need to
Reynolds-average, which introduces additional terms but no additional
equations. These terms have to be determined through empirical or
semi-empirical transport equations, usually termed turbulence models.
Current applications of these equations to geomorphological and
hydrological applications are reviewed. Applications to river channels
have generally not made use of the full three-dimensional form of the
governing equations, and have either been one-dimensional, or, more
commonly, two-dimensional. The latter involves depth averaging of the
governing equations but requires parameterization of the effects of
secondary circulation upon the transport of momentum. This has
emphasized secondary circulation generated by curvature of the
depth-averaged streamlines, but has yet to address secondary
circulation associated with topographic discordance at river channel
confluences or diffluences or owing to anisotropic turbulence.
Applications to unsteady flows require special attention to be given to
the effects of spatial and temporal variation in the depth of
inundation, and the associated treatments are reviewed.