Author(s): A. G. Barnett
Linked Author(s): Alastair G. Barnett
Keywords: Unsteady Flow; Saint-Venant; CELL Integrals; Vector Graphics
Abstract: Following Saint-Venant, unsteady flow analysis is no different from steady flow analysis, except for an added term expressing local timewise variation in each equation. Where 3D steady flow analysis is feasible, 3D unsteady flow analysis is therefore a relatively simple extension. An outstanding example of practical 3D analysis is offered by boundary layer theory, where in flow regions near solid boundaries, kinematic limitations on flow directions allow significant simplification of steady 3D conservation balances. Although such flow regions have often been treated by 1D analysis, this has been as a matter of convenience rather than a requirement imposed by the nature of boundary layer flow. Indeed Saint-Venant himself had introduced 3D concepts such as wetted perimeter to his general theory, with excellent results supported by modern laboratory tests in 3D boundary layers formed in channels of compact cross-section shape. In such cases, analysis of variations of flow in the plane of a cross-section can be uncoupled from the longitudinal solution, which can then be computed separately as a first step. As well as the obvious value of full real-world dimensionality, such uncoupled 3D solutions have several advantages over conventional 2D models. First, the uncoupled longitudinal solution runs orders of magnitude faster than 2D solutions; second, the full lateral and depthwise solutions need only be completed by post-processing at selected points of interest; and third, solution mapping works on vector graphics, potentially providing horizontal channel resolution to within a few centimetres. 3D steady/unsteady analysis applies to all overland flow where Reynolds numbers are high enough for boundary layers to be fully turbulent, to ponding areas and to all reaches of channel except near those junctions where inflows fail to combine into a stable outflow pattern.