An investigation of mixing and transport at a sheared density interface

Citation

Sullivan, Gregory Daniel (1992) An investigation of mixing and transport at a sheared density interface. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/931s-r394. https://resolver.caltech.edu/CaltechETD:etd-08152007-082818

Abstract

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Scalar transport is investigated at a density interface imbedded in a turbulent shear flow. This problem is investigated first experimentally, and based on the experimental findings, a physical model for entrainment is developed.

Steady-state interfacial shear flows are generated in a laboratory water channel for layer Richardson numbers, Ri, between about 1 and 10. The flow field is made optically homogeneous, enabling the combined use of laser-Doppler velocimetry and laser-induced fluorescence with photodiode array imaging to measure the velocity and concentration fields at high resolution.

False-color images of the concentration field provide valuable insight into mixing and transport at the interface. The dominant interfacial mixing mechanism is found to depend on the local mean shear Richardson number, [...] for [...] less than about 0.40 to 0.45, local mixing is dominated by Kelvin-Helmholtz (K-H) instabilities; for somewhat larger values of [...], mixing is dominated by interfacial wave breaking. In both cases, vertical transport of mixed fluid into adjacent turbulent layers is accomplished by large-scale turbulent eddies which impinge on the interface and scour fluid from its outer edges.

Based on the experimental results, a model for interfacial mixing and entrainment is developed. A local equilibrium is assumed in which the rate of loss of interfacial fluid by eddy scouring is balanced by the rate of production (local mixing) by interfacial instabilities and molecular diffusion. In the case of one-sided entrainment, the model results are as follows: when interfacial mixing is diffusion dominated, [...] and [...], where [...] is the interface thickness, h is the boundary layer thickness, Pe is the Peclet number, and E is the normalized entrainment velocity; when mixing is wave breaking dominated, [...] and [...]; and when mixing is K-H dominated, [...] and [...]. In all cases the maximum concentration anomaly is [...]. The model for single-sided entrainment is simply extended to the case in which both layers are entraining. In the latter case it is found that entrainment depends on combinations of parameters from both layers.

The proposed entrainment model is supported by experimental results from this and previous studies. The data from this study are in agreement with [...] and are consistent with model results for [...]; results from previous studies support model predictions for E and [...].

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