Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-25T15:20:24.225Z Has data issue: false hasContentIssue false
  • English
  • Français

The evolution of a stratified turbulent cloud

Published online by Cambridge University Press:  17 December 2013

Andrea Maffioli ,
P. A. Davidson ,
S. B. Dalziel  and
N. Swaminathan
Andrea Maffioli*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
P. A. Davidson
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
S. B. Dalziel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
N. Swaminathan
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
†Email address for correspondence: aplm2@cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Localized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Turbulent Flows: Stratified turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 739 , 25 January 2014 , pp. 229 - 253
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abdilghanie, A. M. & Diamessis, P. J. 2013 The internal gravity wave field emitted by a stably stratified turbulent wake. J. Fluid Mech. 720, 104–139.CrossRefGoogle Scholar
Armi, L. 1978 Some evidence for boundary mixing in the deep ocean. J. Geophys. Res. 83 (C4), 1971–1979.CrossRefGoogle Scholar
Basak, S. & Sarkar, S. 2006 Dynamics of a stratified shear layer with horizontal shear. J. Fluid Mech. 568, 19–54.CrossRefGoogle Scholar
Billant, P. & Chomaz, J.-M. 2000 Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid. J. Fluid Mech. 418, 167–188.Google Scholar
Billant, P. & Chomaz, J.-M. 2001 Self-similarity of strongly stratified inviscid flows. Phys. Fluids 13 (6), 1645–1651.Google Scholar
Bonneton, P., Chomaz, J.-M. & Hopfinger, E. J. 1993 Internal waves produced by the turbulent wake of a sphere moving horizontally in a stratified fluid. J. Fluid Mech. 254, 23–40.Google Scholar
Brethouwer, G., Billant, P., Lindborg, E. & Chomaz, J.-M. 2007 Scaling analysis and simulation of strongly stratified turbulent flows. J. Fluid Mech. 585, 343–368.Google Scholar
Browand, F. K., Guyomar, D. & Yoon, S.-C. 1987 The behaviour of a turbulent front in a stratified fluid: experiments with an oscillating grid. J. Geophys. Res. 92 (C5), 5329–5341.Google Scholar
Caldwell, D. R., Brubaker, J. B. & Neal, V. T. 1978 Thermal microstructure on a lake slope. Limnol. Oceanogr. 23, 372–374.Google Scholar
Dalziel, S. B. 1992 Decay of rotating turbulence: some particle tracking experiments. Appl. Sci. Res. 49, 217–244.CrossRefGoogle Scholar
Davidson, P. A. 2004 Turbulence. An Introduction For Scientists and Engineers. Oxford University Press.Google Scholar
Davidson, P. A. 2011 The minimum energy decay in quasi-isotropic grid turbulence. Phys. Fluids 23 (8), 085108.Google Scholar
Davidson, P. A., Staplehurst, P. J. & Dalziel, 2006 On the evolution of eddies in a rapidly rotating system. J. Fluid Mech. 557, 135–144.Google Scholar
De Silva, I. P. D. & Fernando, H. J. S. 1998 Experiments on collapsing turbulent regions in stratified fluids. J. Fluid Mech. 358, 29–60.Google Scholar
Diamessis, P. J., Domaradzki, J. A. & Hesthaven, J. S. 2005 A spectral multidomain penalty method model for the simulation of high Reynolds number localized incompressible stratified turbulence. J. Comput. Phys. 202 (1), 298–322.Google Scholar
Dohan, K. & Sutherland, B. R. 2003 Internal waves generated from a turbulent mixed region. Phys. Fluids 15 (2), 488–498.CrossRefGoogle Scholar
Fincham, A. M., Maxworthy, T & Spedding, G. R. 1996 Energy dissipation and vortex structure in freely decaying stratified grid turbulence. Dyn. Atmos. Oceans 23, 155–169.Google Scholar
Fortuin, J. M. H. 1960 Theory and application of two supplementary methods of constructing density gradient columns. J. Polym. Sci. 44 (144), 505–515.Google Scholar
Gilreath, H. E. & Brandt, A. 1985 Experiments on the generation of internal waves in a stratified fluid. AIAA J. 23 (5), 693–700.Google Scholar
Grant, H. L., Moilliet, A. & Vogel, W. M. 1968 Some observations of the occurrence of turbulence in and above the thermocline. J. Fluid Mech. 34 (3), 443–448.Google Scholar
Gregg, M. C. 1987 Diapycnal mixing in the thermocline: a review. J. Geophys. Res. 92 (C5), 5249–5286.Google Scholar
Hogg, C. A. R., Marti, C. L., Huppert, H. E. & Imberger, J. 2013 Mixing of an interflow into the ambient water of Lake Iseo. Limnol. Oceanogr. 58 (2), 579–592.Google Scholar
Ivey, G. N & Corcos, G. M. 1982 Boundary mixing in a stratified fluid. J. Fluid Mech. 121, 1–26.Google Scholar
Kimura, Y. & Herring, J. R. 1996 Diffusion in stably stratified turbulence. J. Fluid Mech. 328, 253–269.CrossRefGoogle Scholar
Kundu, P. K. & Cohen, I. M. 2004 Fluid Mechanics, 3rd edn. Elsevier.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Lilly, D. K. 1983 Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40, 749–761.Google Scholar
Lin, J. T. & Pao, Y. H. 1979 Wakes in stratified fluids. Annu. Rev. Fluid Mech. 11, 317–338.Google Scholar
Lin, Q., Boyer, D. L. & Fernando, H. J. S. 1993 Internal waves generated by the turbulent wake of a sphere. Exp. Fluids 15, 147–154.Google Scholar
Lindborg, E. 2006 The energy cascade in a strongly stratified fluid. J. Fluid Mech. 550, 207–242.Google Scholar
Linden, P. F. 1975 The deepening of a mixed layer in a stratified fluid. J. Fluid Mech. 71, 385–405.Google Scholar
Liu, Y. N., Maxworthy, T. & Spedding, G. R. 1987 Collapse of a turbulent front in a stratified fluid. 1 Nominally two-dimensional evolution in a narrow tank. J. Geophys. Res. 92 (C5), 5427–5433.Google Scholar
Mahrt, L. 1989 Intermittency of atmospheric turbulence. J. Atmos. Sci. 46, 79–95.Google Scholar
Manins, P. C. 1976 Intrusion into a stratified fluid. J. Fluid Mech. 74 (3), 547–560.CrossRefGoogle Scholar
Maurer, B. D. 2011 Gravity-driven intrusions in stratified fluids. PhD thesis, University of California, San Diego.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Praud, O., Fincham, A. M. & Sommeria, J. 2005 Decaying grid turbulence in a strongly stratified fluid. J. Fluid Mech. 522, 1–33.CrossRefGoogle Scholar
Riley, J. J. & de Bruyn Kops, S. M. 2003 Dynamics of turbulence strongly influenced by buoyancy. Phys. Fluids 15 (7), 2047–2059.Google Scholar
Riley, J. J. & Lelong, M.-P. 2000 Fluid motions in the presence of strong stable stratification. Annu. Rev Fluid Mech. 32, 613–657.Google Scholar
Savaş, Ö 1985 On flow visualization using reflective flakes. J. Fluid Mech. 152, 235–248.CrossRefGoogle Scholar
Spedding, G. R. 2002 Vertical structure in stratified wakes with high initial Froude number. J. Fluid Mech. 454, 71–112.CrossRefGoogle Scholar
Spedding, G. R., Browand, F. K. & Fincham, A. M. 1996 Turbulence, similarity scaling and vortex geometry in the wake of a towed sphere in a stably stratified fluid. J. Fluid Mech. 314, 53–103.Google Scholar
Staplehurst, P. J. 2007 Structure formation in rotating turbulence. PhD thesis, University of Cambridge.Google Scholar
Taylor, J. R. & Sarkar, S. 2007 Internal gravity waves generated by a turbulent bottom Ekman layer. J. Fluid Mech. 590, 331–354.CrossRefGoogle Scholar
Thorpe, S. A. 1982 On the layers produced by rapidly oscillating a vertical grid in a uniformly stratified fluid. J. Fluid Mech. 124, 391–409.CrossRefGoogle Scholar
Waite, M. L. & Bartello, P. 2004 Stratified turbulence dominated by vortical motion. J. Fluid Mech. 517, 281–308.Google Scholar
Yeung, P. K. 2001 Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations. J. Fluid Mech. 427, 241–274.Google Scholar
Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.Google Scholar