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A SIMPLE-MODEL OF ROSSBY-WAVE HYDRAULIC BEHAVIOR

HAYNES, PH; JOHNSON, ER; HURST, RG; (1993) A SIMPLE-MODEL OF ROSSBY-WAVE HYDRAULIC BEHAVIOR. J FLUID MECH , 253 359 - 384. 10.1017/S0022112093001831. Green open access

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Abstract

This paper considers hydraulic control and upstream influence in systems where the only wave propagation mechanism arises from the variation of vorticity or potential vorticity. These systems include two-dimensional shear flows as well as many simple paradigms for large-scale geophysical flows. The simplest is a flow in which the vorticity or potential vorticity is piecewise constant. We consider such a flow confined to a rotating channel and disturbed by a topographic perturbation. We analyse the behaviour of the system using steady nonlinear long-wave theory and demonstrate that it exhibits behaviour analogous to open-channel hydraulics, with the possibility of different upstream and downstream states. The manner by which the system achieves such states is examined using time-dependent long-wave theory via integration along characteristics and using full numerical solution via the contour-dynamics technique.The full integrations agree well with the hydraulic interpretation of the steady-state theory. One aspect of the behaviour of the system that is not seen in open-channel hydraulics is that for strong subcritical flows there is a critical topographic amplitude beyond which information from the control cannot propagate far upstream. Instead flow upstream of the topographic perturbation adjusts until the long-wave speed is zero, the control moves to the leading edge of the obstacle and flow downstream of the control is supercritical, with a transition from one supercritical branch to another on the downstream slope of the obstacle.

Type: Article
Title: A SIMPLE-MODEL OF ROSSBY-WAVE HYDRAULIC BEHAVIOR
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112093001831
Publisher version: http://dx.doi.org/10.1017/S0022112093001831
Language: English
Additional information: © 1993 Cambridge University Press
Keywords: DEEP PLANETARY CIRCULATION, UPSTREAM INFLUENCE, BOTTOM TOPOGRAPHY, COASTAL FLOWS, SEPARATION, CHANNEL, SHELF
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/1325351
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