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Transition from supercritical to subcritical regime in free surface flow of yield stress fluids
Author(s) -
Ugarelli Rita,
Di Federico Vittorio
Publication year - 2007
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2007gl031487
Subject(s) - supercritical flow , laminar flow , hydraulic jump , mechanics , herschel–bulkley fluid , bingham plastic , flow (mathematics) , shear stress , supercritical fluid , shear flow , mathematics , materials science , thermodynamics , physics , rheology
Characteristics of the transition from supercritical to subcritical regime (hydraulic jump) in laminar flow of a Herschel‐Bulkley fluid on an horizontal plane are examined. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid. The determination of the flow conditions downstream, given those upstream, involves solution of a nonlinear algebraic system in three unknowns; an approximate analytical formula for conjugate depths is derived since no exact solution can be obtained in closed form. The relative error thus introduced is then evaluated numerically; its maximum value is shown to be less than a few percent. The behavior of flow depth, bottom shear stress and critical depth are established and illustrated as function of the flow behavior index; the critical depth and the ratio of conjugate depths increase with the behavior index and until the bottom shear stress exceeds a certain value, and then decrease afterwards.