Simulation of entrainment near a density stratified layer: Laboratory experiment and LIDAR observation

Author

Abstract

In this paper a simple qualitative model of the growth of a mixed layer adjacent to a uniform layer with a stably stratified layer is presented. The depth variations of mixed layer can be estimated from direct measurements. The Entrainment of a stably stratified layer into a turbulent mixed layer in a confined region was studied in laboratory for different Richardson numbers. The internal waves generated at the interface propagate into the stratified fluid.
The experiments on entrainment near a density stratified layer have shown that the rate of entrainment is a weaker function of Ri than the case with a two layer case. It was also shown that the internal waves in the stratified region, with typical buoyancy period of about 10 s may interact with turbulence near the interface and create a non-uniform entrainment rate as an oscillatory behavior with a typical time scale of 150 s. The process is qualitatively consistent with processes associated with the way internal waves interact with turbulence and create a momentarily buoyancy flux with different signs. The modal structure of these waves appears to interact with the turbulence processes near the interface creating a non-uniform entrainment rate usually in steps. This may be related to the vertical wave number of the dominant wave which is dependent on the depth of the stratified layer as well as the horizontal cross section of the tank. The results show that the dominant mixing mechanisms are different for different Richardson number Ri ranges, the dominant entrainment mechanism was the impingement of the eddies on the interface and splashing of heavier fluid into the mixed layer.
Also applicability of this work for the atmospheric boundary layer, its growth and the entrainment zone was considered as the aerosol backscattering from the convective boundary layer shows spatial variations due to non-uniform mixing of the naturally occurring aerosol near the entrainment zone. For considering the applicability of this method for the atmospheric boundary layer, we used lidar measurements of this layer. Aerosol backscattering from the convective boundary layer shows spatial variations due to non-uniform mixing of the naturally occurring aerosol. Lidar measurements of the thickness of the entrainment zone show reasonable agreement with laboratory results. Both lidar and tank results show that simple parcel theory does not properly predict entrainment-zone thickness. The internal waves with the non-uniform entrainment of the mixed layer and free atmosphere with the amplitude of around 100 meters and a period of 15 minutes, is formed. Results show that the oscillation of aerosol layer is probably due to non-uniform entertainment in the interface between the mixed layer and free atmosphere with an increasing range resolution of LIDAR in entrainment zone. It can be shown, results in experiments has some consistency with growth and aerosol layer oscillations in atmospheric boundary layer. Although it seems to be a qualitative similarity between entrainment behavior at the top of the atmospheric mixed layer and laboratory experiments "mixing box", but the two are quite different as lab experiments are in an enclosure without mean flow, while the top of the mixed layer is a free solid boundary flow which may be associated with mean flow shear.

Keywords

Main Subjects

References

Bidokhti, A. A. and Britter, R. E., 2002, A large stratified shear flow water channel facility, Ex. in Fluids, 33, 281-287.
Bretherton, C. S., Macvean, M. K., Bechtold, P., Chlond, A., Cotton, W. R., Cuxart, J., Cluijpers, H., Khairoutdinov, M., Kosovic, B., Lewellen, D., Moeng, CH., Siebesma, P., Stevens, B., Stevens, D. E., Sykes, I. and Wyant, M.C., 1999, An intercomparison of radiatively driven entrainment and turbulence in a smoke cloud, as simulated by different numerical nodels, Q. J. R. Meteorol Soc., 125, 391-423.
Brooks, I. M., 2003, Finding boundary layer top, application of a wavelet covariance transformto Lidar Backscatter profiles, J. Atmos. Oceanic. Technol., 20, 1092-1105.
Cardoso, S. S. and Woods, A. W., 1993, Mixing by a turbulent plume in a confined stratified region, J. of Fluid Mech., 250, 277-305.
Da Silva, C. B., Hun,t J. C., Eames, I. and Westerweel, J., 2014, Interfacial layers between regions of different turbulence intensity, Annual Review of Fluid Mechanics, 46, 567-590.
Deardorff, J. W., Willis, G. E. and Stockton, B. H., 1980, Laboratory studies of the entrainment zone of a convectively mixed layer, J. of Fluid Mech., 100, 41-64.
De Rooy, W. C. and Siebesma, A. P., 2010, Analytical expressions for entrainment and detrainment in cumulus convection, Q. J. R. Meteorol. Soc., 136, 1216-1227.
De Rooy, W. C., Bechtold, P., Frohlich, K., Hohenegger, C., Jonker, H., Mironov, D., Siebesma, P., Teixeiraf, J. and Yanog, J., 2013, Entrainment and detrainment in cumulus convection, an overview, Q. J. R. Meteorol. Soc., 139, 1-19.
Fernando, H. J., 1988, The growth of a turbulent patch in a stratified fluid, J. of Fluid Mech., 190, 55-70.
Flamant, C., Pelon, J., Flamant, P. H. and Durand, P., 1997, Lidar determination of the entrainment zone thickness at the top of the unstable marine atmospheric boundary layer, Boundary-Layer Meteorol, 83, 247-284.
Garratt, J. R., 1992, The atmospheric boundary layer, Cambridge University Press, 316 pp.
Gill, A. E., 1982, Atmosphere-ocean dynamics, International Geophysics Series, 30, Acad. Press, 662pp.
Gryning, S. E. and Batchvarova, E., 1994, Parameterization of the depth of the entrainment zone above the daytime mixed layer, Q. J. R. Meteorol. Soc., 120, 47-58.
Hanna, S., 1982, A handbook on atmospheric diffusion, US Department of Commerce.
Itsweire, E. C., Helland, K. N. and Van Atta, C. W., 1986, The evolution of grid-generated turbulence in a stably stratified fluid, J. of Fluid Mech., 162, 299-338.
Jonker, H. J. and Jiménez, M. A., 2014, Laboratory experiments on convective entrainment using a saline water tank, Boundary-layer meteorology, 151, 479-500.
Kato, H. and Phillips, O., 1969, On the penetration of a turbulent layer into stratified fluid, J. of Fluid Mech., 37(04), 643-655.
Lin, Y. J. P. and Linden, P. F., 2005, The entrainment due to a turbulent fountain at a density interface, J. of Fluid Mech., 1-28.
Linden, P. F., 1980, Mixing across a density interface produced by grid turbulence, J. of Fluid Mech., 100, 691-703.
McGarth, J. I., Fernando, H. J. S. and Hunt, J. C. R., 1997, Turbulence, waves and mixing near free shear density interfaces, Part 2 Laboratory experiments, J. of Fluid Mech., 347, 197-234.
Moka, T. and Rudowicz, C., 2001, A lidar study of the atmospheric entrainment zone and mixed layer over Hong Kong, Atmospheric Research, 69, 147-163.
Pham, H. T. and Sarkar, S., 2010, Internal waves and turbulence in a stable stratified jet, J. of Fluid Mech., 648, 297-324.
Strang, E. and Fernando, H., 2001, Entrainment and mixing in stratified shear flows, J. of Fluid Mech., 428, 349-386.
Stull, R. B., 1988, An introduction to boundary layer meteorology, Kluwer Academic Publisher, 666 pp.
Thorpe, S. A., 1973, Turbulence in stably stratified fluids: a review of laboratory experiments, Boundary-Layer Meteorology, 5(1-2), 95-119.
Turner, J. E., 1973, Buoyancy effects in fluids, Cambridge University Press, 368pp.
Wong, A. B. S., Griffiths, R. W. and Hughes, G. O., 2001, Shear layer driven by turbulent plumes, J. of Fluid Mech., 434, 209-244.
 
 
Journal of the Earth and Space Physics
Volume 42, Issue 4
January 2017
Pages 27-34

Files

Share

How to cite

Statistics