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Non-linear Topographic Effects in Two-Layer Flows

Baines, PG; Johnson, ER; (2016) Non-linear Topographic Effects in Two-Layer Flows. Frontiers in Earth Science , 4 , Article 9. 10.3389/feart.2016.00009. Green open access

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Abstract

We consider the nature of non-linear flow of a two-layer fluid with a rigid lid over a long obstacle, such that the flow may be assumed to be hydrostatic. Such flows can generate hydraulic jumps upstream, and the model uses a new model of internal hydraulic jumps, which results in corrections to flows that have been computed using earlier models of jumps that are now known to be incorrect. The model covers the whole range of ratios of the densities of the two fluids, and is not restricted to the Boussinesq limit. The results are presented in terms of flow types in various regions of a Froude number-obstacle height (F0–Hm) diagram, in which the Froude number F0 is based on the initial flow conditions. When compared with single-layer flow, and some previous results with two layers, some surprising and novel patterns emerge on these diagrams. Specifically, in parts of the diagram where the flow may be supercritical (F0 > 1), there are regions where hysteresis may occur, implying that the flow may have two and sometimes three multiple flow states for the same conditions (i.e., values of F0 and Hm).

Type: Article
Title: Non-linear Topographic Effects in Two-Layer Flows
Open access status: An open access version is available from UCL Discovery
DOI: 10.3389/feart.2016.00009
Publisher version: http://dx.doi.org/10.3389/feart.2016.00009
Language: English
Additional information: © 2016 Baines and Johnson. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
Keywords: 2-layer flow, non-Boussinesq, topography, Froude number, hydraulic jump
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1474698
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