Inclined gravity currents filling basins: The influence of Reynolds number on entrainment into gravity currents
Physics of Fluids
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Hogg, C., Dalziel, S., Huppert, H., & Imberger, J. (2015). Inclined gravity currents filling basins: The influence of Reynolds number on entrainment into gravity currents. Physics of Fluids, 27 (096602) https://doi.org/10.1063/1.4930544
Gravity currents of dense fluid feed basins in many important natural and industrial systems, such as lakes fed by dense rivers and auditoria supplied with cooled air by ventilation systems. The entrainment into these buoyancy driven currents can be influenced by viscous forces. Little work, however, has examined this viscous influence and how entrainment varies with the Reynolds number, Re. Using the idea of an entrainment coefficient, E, we derive a mathematical expression for the rise of the front at the top of the dense fluid ponding in a basin, where the horizontal cross-sectional area of the basin varies linearly with depth. We compare this expression to experiments on gravity currents with source Reynolds numbers, Re_s, covering the broad range 100 < Re_s < 1500. The form of the observed frontal rises was well approximated by our theory. By fitting the observed frontal rises to the theoretical form with E as the free parameter we find a linear trend for E (Re_s) over the range 350 < Re_s < 1100, which is in the transition to turbulent flow. In the experiments the entrainment coefficient, E, varied from 4 x 10^-5 to 7 x 10^-2. These observations show that viscous damping can be a dominant influence on gravity current entrainment in the laboratory and in geophysical flows in this transitional regime.
CARH gratefully acknowledges support by the Natural Environment Research Council and Arup. HEH is grateful for support from a Royal Society Wolfson Research Merit Award and a Leverhulme Emeritus Research Fellowship. This manuscript is Centre for Water Research reference 2674-CH.
External DOI: https://doi.org/10.1063/1.4930544
This record's URL: https://www.repository.cam.ac.uk/handle/1810/248963
Attribution-NonCommercial 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by-nc/2.0/uk/
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