The similarity solution for turbulent mixing of two-layer stratified fluid
Whitehead, John A.
MetadataShow full item record
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.
© 2008 The Author. This is an open-access article distributed under the terms of the Creative Commons Attribution Noncommercial License. The definitive version was published in Environmental Fluid Mechanics 8 (2008): 551-560, doi:10.1007/s10652-008-9076-5.
Suggested CitationEnvironmental Fluid Mechanics 8 (2008): 551-560
The following license files are associated with this item:
Except where otherwise noted, this item's license is described as Attribution-NonCommercial 4.0 International
Showing items related by title, author, creator and subject.
Park, Young-Gyu (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1993-09)A turbulent mixing experiment was conducted to observe the dynamics and the energetics of layer formation along with the region of layer formation in the Reynolds number (Re) and the overall Richardson number (Rio) space. ...
Scaling for turbulent viscosity of buoyant plumes in stratified fluids : PIV measurement with implications for submarine hydrothermal plume turbulence Zhang, Wei; He, Zhiguo; Jiang, Houshuo (2017-10-07)Time-resolved particle image velocimetry (PIV) has been used to measure instantaneous twodimensional velocity vector fields of laboratory-generated turbulent buoyant plumes in linearly stratified saltwater over extended ...
Manucharyan, Georgy E.; Caulfield, C. P. (2014-12)We consider experimentally an initially quiescent and linearly stratified fluid with buoyancy frequency NQ in a cylinder subject to surface-stress forcing from a disc of radius R spinning at a constant angular velocity Ω. ...