Modelling circulations in depth-integrated flows Part 1: The accumulation of the evidence

A considerable body of experimental evidence has accumulated that suggests that the circulations generated in numerical models of free-surface Hows that are two-dimensional in plan may be realistic physically even though none ofthe numerical experiments described in the literature have explicitely utilized realistic lateral shear stresses. On the other hand, it is easily shown by analytical means that not only is it impossible to generate realistic circulations without the introduction of correspondingly realistic shear stresses but that, in the absence of such shear stresses, no circulation at all should have arisen in the experiments described. The first part ofthe study is given over to a review ofthe evidence already available both for and against accepting the physical realism of circulations induced in numerical models of free-surface flows that are twodimensional in plan. In a separate second part ofthe study an attempt is made to reconcile this evidence. An appendix outlining some ofthe concepts introduced in this work has been added to this first part, together with some introductory references, at the request ofthe reviewers.