Permanent Waves in Slow Free-Surface Flow of a Herschel–Bulkley fluid |
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Authors: | Di Federico Vittorio |
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Institution: | (1) Università di Bologna, D.I.S.T.A.R.T.–Idraulica, Viale Risorgimento 2, Bologna, 40136, Italy |
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Abstract: | Unsteady flow of a viscoplastic fluid on an inclined plane is examined. The fluid is described by the three-parameter Herschel–Bulkley constitutive equation. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid and steady uniform motion. A permanent wave solution is then derived, and the relation between wave speed and flow depth is discussed. It is shown that more types of gravity currents are possible than in a Newtonian fluid; these include some cases of flows propagating up a slope. The speed of permanent waves is derived and the possible surface profiles are illustrated as functions of the flow behavior index. |
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Keywords: | Non-Newtonian fluids Free-surface flow Creeping flow Unsteady flow Fluid mechanics |
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