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THE EFFECTS OF OBSTACLE SHAPE AND VISCOSITY IN DEEP ROTATING FLOW OVER FINITE-HEIGHT TOPOGRAPHY

JOHNSON, ER; (1982) THE EFFECTS OF OBSTACLE SHAPE AND VISCOSITY IN DEEP ROTATING FLOW OVER FINITE-HEIGHT TOPOGRAPHY. J FLUID MECH , 120 359 - 383. 10.1017/S0022112082002808. Green open access

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Abstract

The limiting process introduced by Stewartson & Cheng (1979) is used to obtain solutions in the limit of vanishing Rossby number for deep rotating flows at arbitrary Reynolds number over cross-stream ridges of finite slope. Examination of inviscid solutions for infinite-depth flow shows strong dependence on obstacle shape of not only the magnitudes but also the positions of disturbances in the far field. In finite-depth flow there is present the Stewartson & Cheng inertial wave wake, which may be expressed as a sum of vertical modes whose amplitudes depend on the obstacle shape but are independent of distance downstream; the smoother the topography and the shallower the flow, the fewer the number of modes required to describe the motion. For abrupt topography the strength of the wake does not, however, decrease monoton- ically with decreasing container depth (or Rossby number). In very deep flows viscosity causes the wake to decay on a length scale of order the Reynolds number times the ridge width. In shallower flows, where only a few modes are present, the decay of the wake is more rapid. For Reynolds numbers and depths of the order of those in the experiments of Hide, Ibbetson & Lighthill (1968)) viscosity causes the disturbance to take on the appearance of a leaning column.

Type: Article
Title: THE EFFECTS OF OBSTACLE SHAPE AND VISCOSITY IN DEEP ROTATING FLOW OVER FINITE-HEIGHT TOPOGRAPHY
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112082002808
Publisher version: http://dx.doi.org/10.1017/S0022112082002808
Language: English
Additional information: © 1982 Cambridge University Press
UCL classification: 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: http://discovery.ucl.ac.uk/id/eprint/1325393
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