Author(s): C. Kranenburg

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Abstract: Laboratory experiments on mixed-layer deepening in a density-stratified fluid are known to be affected by side-wall friction, in particular when the overall Richardson number Ri* = B/u* 2 is large where B is the total mixed-layer buoyancy and u* the friction velocity. Finite aspect (depth to width)-ratio effects are calculated starting from a simple mathematical model based on the gradienttransport hypothesis. An asymptotic expansion for large Ri*, which covers almost the whole range of practical interest, yields good agreement with the entrainment rates observed by Kantha, Phillips and Azad (1977) and Deardorff and Willis (1982). At zero aspect-ratio the dimensionless entrainment rate E* = We/u*, where we is the entrainment rate, is found to vary as Ri* -1/2 for both two-layer fluid and an initial density distribution according to a power law, which result is in agreement with the Pollard, Rhines and Thompson (1973) model. A similar analysis of the experiments of Moore and Long (1971) shows that most of these experiments were controlled by side-wall friction.

DOI: https://doi.org/10.1080/00221688309499439

Year: 1983