NDLI: The similarity solution for turbulent mixing of two-layer stratified fluid

Content Provider	Springer Nature Link
Author	Whitehead, J. A.
Copyright Year	2008
Abstract	Experiments are reviewed in which a two-layer salt-stratified tank of water was mixed by turbulence. The density profile began as a single step and evolved to a smooth mixed profile. The turbulence was generated by many excursions of a horizontally moving vertical rod with Richardson number Ri > 0.9 and Reynolds Number Re > 600. There was almost perfect collapse of all the profiles to one universal profile as a function of a similarity variable. We develop a theoretical model for a simple mixing law with a buoyancy flux that is a function of internal Richardson number Rii. A similarity equation is found. A flux law that increases with small Rii and decreases with large Rii is considered next. Since no analytical solution is known, the similarity concept is tested by numerically integrating the equations in space and time. With buoyancy flux monotonically increasing with internal Richardson number, the similarity approach is valid for a profile starting from a slightly smoothed step. However, a shock forms for a mixing law with higher initial Rii (so that buoyancy flux decreases with Richardson number) and the similarity approach is invalid for those initial conditions.
Starting Page	551
Ending Page	560
Page Count	10
File Format	PDF
ISSN	15677419
Journal	Environmental Fluid Mechanics
Volume Number	8
Issue Number	5-6
e-ISSN	15731510
Language	English
Publisher	Springer Netherlands
Publisher Date	2008-06-19
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Turbulence Mixing Stratified Similarity solution Layered fluid Oceanography Meteorology/Climatology Hydrogeology Mechanics Environmental Physics
Content Type	Text
Resource Type	Article
Subject	Environmental Chemistry Water Science and Technology

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