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Self-similarity and Reynolds number invariance in Froude modelling

Author(s): Valentin Heller

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Keywords: Froude similarity; laboratory studies; Reynolds number invariance; scale effect; scale invariance; self-similarity; similarity (scaling) theory

Abstract: This review aims to improve the reliability of Froude modelling in fluid flows where both the Froude number and Reynolds number are a priori relevant. Two concepts may help to exclude significant Reynolds number scale effects under these conditions: (i) self-similarity and (ii) Reynolds number invariance. Both concepts relate herein to turbulent flows, thereby excluding self-similarity observed in laminar flows and in non-fluid phenomena. These two concepts are illustrated with a wide range of examples: (i) irrotational vortices, wakes, jets and plumes, shear-driven entrainment, high-velocity open channel flows, sediment transport and homogeneous isotropic turbulence; and (ii) tidal energy converters, complete mixing in contact tanks and gravity currents. The limitations of self-similarity and Reynolds number invariance are also highlighted. Many fluid phenomena with the limitations under which self-similarity and Reynolds number invariance are observed are summarized in tables, aimed at excluding significant Reynolds number scale effects in physical Froude-based models.


Year: 2017

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