Author(s): M. B. Abbott; M. P. Vlum

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Abstract: In almost all classical hydraulics, problems are posed in terms of determining what happens at given places and times. It is possible, however, to pose these problems "the other way around", so to speak, by asking at which place a given event occurs at a given time. In quantitative terms, the problem is posed of determining those values of the independent variables at which given values of the dependent variables occur at given times. This alternative view has certain advantages over that traditionally used, and also disadvantages. The traditional approach can be used most efficiently when, roughly speaking, the same order of variation occurs in the dependent variables over most of the domain during most of the time. In a large number of real-life situations, however, nothing much happens in most of the domain during most of the time but the areas of interest are concentrated in small regions that may move across the domain in time. Examples are the spillage, transport and dispersion of pollutants in watercourses, the propagation of Tsunamis waves, halocline and thermocline decay, bio-chemical process at air-water and bed-water interfaces and haloclines and also the transport of short wave energy. The alternative methods provide a generally superior resolution in these situations, as compared with the traditional ones, but this advantage is bought at the cost of an increased complexity of the numerical scheme or code. Applications are shown to the transport processes, dispersion process and conservation (propagation) processes of hydraulics, so covering most common applications. The transport applications are shown to be related to an existing method, which is then generalised, the dispersion applications appear to be new in hydraulics while the conservation applications generalise on the one side to a method so far only outlined in gas dynamics and on the other side to the method of characteristics. The study concludes with an outline of the problem of best descriptions.

DOI: https://doi.org/10.1080/00221687709499651

Year: 1977