Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-05T21:50:07.444Z Has data issue: false hasContentIssue false
  • English
  • Français

Layers and internal waves in uniformly stratified fluids stirred by vertical grids

Published online by Cambridge University Press:  16 March 2016

S. A. Thorpe
S. A. Thorpe*
Affiliation:
School of Ocean Sciences, Bangor University, Menai Bridge, Anglesey LL59 5AB, UK
*
†Address for correspondence: 1A, Green Edge, Beaumaris, Anglesey LL58 8BY, UK. Email address for correspondence: oss413@bangor.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Laboratory experiments in which uniformly stratified fluids are stirred by horizontally moving vertical grids, or arrays of vertical rods, are reviewed to examine their consistency and to compare their findings, particularly those relating to the generation of layers. Selected experiments are of three types, those in which (a) turbulence spreads from a horizontally confined region where it is continuously generated by an oscillating grid; (b) grid stirring is maintained throughout a rectangular tank; or (c) a ‘cloud’ of turbulence decays after a short period of horizontally localized grid mixing. In all the experiments turbulence is generated over the full vertical extent of the tank. In the experiments of types (a) and (c) layers of comparable scale are observed to intrude into the ambient fluid from the turbulent region. In the type (b) experiments, layers form only when the time interval between the passage of the grid through the stratified fluid is sufficiently long, allowing turbulence to decay substantially between grid strokes. Two mechanisms are found to be dominant in the production of layers. In experiments of type (a) and (c) overturning eddies in the turbulent region of scale significantly larger than the Ozmidov length scale collapse and spread, intruding and forming layers in the adjoining laminar region. Internal shear waves propagating ahead of the intrusions have a vertical wavelength that is approximately twice the layer height. In type (b) experiments, layers are formed through a process described by Holford & Linden (Dyn. Atmos. Oceans, vol. 30, 1999a, pp. 173–198): the bending of vortices shed by the grid bars. The height of the layers is approximately half the vertical wavelength of internal shear waves that travel at the speed of the grid. It is proposed that the flow field of the shear waves bends the vortices, resulting in diapycnal mixing that forms the layers. The relationship of layers and internal shear waves in the experiments is therefore as follows: in type (a) and (c) experiments internal waves are generated by layers intruding from the turbulent region into the quiescent stratified region, but in experiments of type (b) internal waves drive and dictate the height of the layers; layers are generated as a consequence of vortex bending by internal waves. There is insufficient evidence to establish whether zigzag instability, either of vortex pairs or of vortex streets shed by a moving grid, accounts for the layers in any of the three types of grid experiments. The Phillips and Posmentier instability may reinforce layers formed by other processes. The generation of pancake vortices or vortical mode motion is left for later review.

JFM classification

Turbulent Flows: Stratified turbulence Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 793 , 25 April 2016 , pp. 380 - 413
Check for updates
Copyright
© 2016 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

Alford, M. H. & Gregg, M. C. 2001 Near-inertial mixing: modulation of shear, strain and microstructure at low latitude. J. Geophys. Res. 106, 16947–16968.CrossRefGoogle Scholar
Augier, P. & Billant, P. 2011 Onset of secondary instabilities on the zigzag instability in stratified fluids. J. Fluid Mech. 682, 120–131.CrossRefGoogle Scholar
Baines, P. G. 1995 Topographic Effects in Stratified Flows. p. 482. Cambridge University Press.Google Scholar
Baines, P. G. 2001 Mixing by flows down gentle slopes into stratified environments. J. Fluid Mech. 443, 237–270.CrossRefGoogle Scholar
Balmforth, N. J., Llewellyn Smith, S. G. & Young, W. R. 1998 Dynamics of interfaces and layers in a stratified turbulent fluid. J. Fluid Mech. 355, 329–358.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.CrossRefGoogle Scholar
Bolster, D., Hang, A. & Linden, P. F. 2008 The front speed of intrusions into a continuously stratified medium. J. Fluid Mech. 594, 369–377.CrossRefGoogle Scholar
Bosco, M. & Meunier, P. 2014 Three-dimensional instabilities of a stratified cylinder wake. J. Fluid Mech. 759, 149–180.CrossRefGoogle Scholar
Britter, R. E., Hunt, J. C. R., Marsh, G. L. & Snyder, W. H. 1983 The effects of stable stratification on turbulent diffusion and the decay of grid turbulence. J. Fluid Mech. 127, 27–44.CrossRefGoogle 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
Deloncle, A., Billant, P. & Chomaz, J.-M. 2008 Nonlinear evolution of the zigzag instability in stratified fluids: a shortcut on the route to dissipation. J. Fluid Mech. 599, 229–230.CrossRefGoogle Scholar
Deloncle, A., Billant, P. & Chomaz, J.-M. 2011 Three-dimensional stability of vortex arrays in a stratified and rotating fluid. J. Fluid Mech. 678, 482–510.CrossRefGoogle 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.CrossRefGoogle Scholar
Diamessis, P. J. & Nomura, K. K. 2004 The structure and dynamics of overturns in stably stratified homogeneous turbulence. J. Fluid Mech. 499, 197–229.CrossRefGoogle Scholar
Dickey, T. D. & Mellor, G. L. 1980 Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 99, 13–32.CrossRefGoogle Scholar
Dillon, T. M. 1982 Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J. Phys. Oceanogr. 87, 9601–9613.Google Scholar
Ferron, B., Mercier, H., Speer, K., Gargett, A. & Polzin, K. 1998 Mixing in the Romanche fracture zone. J. Phys. Oceanogr. 28, 1929–1945.2.0.CO;2>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.CrossRefGoogle Scholar
Gargett, A., Osborn, T. R. & Nasmyth, P. W. 1984 Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech. 144, 231–280.CrossRefGoogle Scholar
Gibson, C. H. 1980 Fossil temperature, salinity, and vorticity turbulence in the pcean. In Marine Turbulence (ed. Nihoul, J.), Elsevier Oceanography Series, pp. 221–257. Elsevier.Google Scholar
Holford, J. M. & Linden, P. F. 1999a Turbulent mixing in a stratified fluid. Dyn. Atmos. Oceans 30, 173–198.CrossRefGoogle Scholar
Holford, J. M. & Linden, P. F. 1999b The development of layers in a stratified fluid. In Mixing and Dispersion in Stably Stratified Flows. Proceedings of 5th IMA Conference on Statified Flows, University of Dundee, Scotland, pp. 165–179. Oxford University Press.Google Scholar
Hopfinger, E. J. & Linden, P. F. 1982 Formation of thermocline in zero-mean-shear turbulence subjected to a stabilizing buoyancy flux. J. Fluid Mech. 114, 157–173.CrossRefGoogle Scholar
Hopfinger, E. J. & Toly, J. A. 1976 Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78, 155–175.CrossRefGoogle Scholar
Inall, M. 2009 Internal wave induced dispersion and mixing on a sloping boundary. Geophys. Res. Lett. 36, L05604.CrossRefGoogle Scholar
Itsweire, E. C. 1984 Measurements of vertical overturns in a stably stratified turbulent flow. Phys. Fluids 27, 764–766.CrossRefGoogle Scholar
Itsweire, E. C., Helland, K. N. & van Atta, C. W. 1986 The evolution of grid-generated turbulence in a stably stratified fluid. J. Fluid Mech. 162, 299–338.CrossRefGoogle Scholar
Ivey, G. N. & Corcos, G. M. 1982 Boundary mixing in a stratified fluid. J. Fluid Mech. 121, 1–26.CrossRefGoogle Scholar
Lazier, J. N. R. 1973 Temporal changes in some fresh water temperature structures. J. Phys. Oceanogr. 3, 226–229.2.0.CO;2>CrossRefGoogle 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
Maffioli, A., Davidson, P. A., Dalziel, S. B. & Swaminathan, N. 2014 The evolution of a stratified turbulent cloud. J. Fluid Mech. 739, 229–253.CrossRefGoogle Scholar
Manins, P. C. 1976 Intrusions into a stratified fluid. J. Fluid Mech. 74, 547–560.CrossRefGoogle Scholar
Martin, J. E. & Rehmann, C. R. 2006 Layering in a flow with diffusively stable temperature and salinity stratification. J. Phys. Oceanogr. 36, 1457–1470.CrossRefGoogle Scholar
Martin, S., Simmons, W. & Wunsch, C. 1972 The excitation of resonant triads by single internal waves. J. Fluid Mech. 53, 17–44.CrossRefGoogle Scholar
Mater, B. D., Schaad, S. M. & Venayagamoorthy, S. K. 2013 Relevance of the Thorpe Lengthscale in stably stratified turbulence. Phys. Fluids 25, 076604.CrossRefGoogle Scholar
Maurier, B. D. & Linden, P. F. 2014 Intrusion-generated waves in a linearly stratified fluid. J. Fluid Mech. 752, 282–295.CrossRefGoogle Scholar
Maxworthy, T., Leilich, J., Simpson, J. & Meiburg, E. H. 2002 The propagation of a gravity current in a linearly stratified fluid. J. Fluid Mech. 453, 371–394.CrossRefGoogle Scholar
McEwan, A. D. & Baines, P. G. 1974 Shear fronts and an experimental stratified shear flow. J. Fluid Mech. 63, 257–272.CrossRefGoogle Scholar
Meunier, P. 2012 Stratified wake of a tilted cylinder. Part 1. Suppression of a von Kármán vortex street. J. Fluid Mech. 699, 174–197.CrossRefGoogle Scholar
Ostrovsky, L. A. & Zaborskikh, D. V. 1996 Damping of internal gravity waves by small-scale turbulence. J. Phys. Oceanogr. 26, 388–397.2.0.CO;2>CrossRefGoogle Scholar
Otheguy, P., Chomaz, J.-M & Billant, P. 2006 Elliptic and zigzag instabilities on co-rotating vertical vortices in a stratified fluid. J. Fluid Mech. 553, 253–272.CrossRefGoogle Scholar
Park, Y.-G., Whitehead, J. A. & Gnanadeskian, A. 1994 Turbulent mixing in stratified fluids: layer formation and energetic. J. Fluid Mech. 279, 279–311.CrossRefGoogle Scholar
Peters, H., Gregg, M. C. & Toole, J. M. 1988 On the parametrization of equatorial turbulence. J. Geophys. Res. 93, 1199–1218.CrossRefGoogle Scholar
Phillips, O. M. 1972 Turbulence in a strongly stratified fluid – is it unstable? Deep-Sea Res. 19, 79–81.Google Scholar
Posmentier, E. S. 1977 The generation of salinity finestructure by vertical diffusion. J. Phys. Oceanogr. 7, 298–300.2.0.CO;2>CrossRefGoogle 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
Riedinger, X., Le Dizès, S. & Meunier, P. 2011 Radiative instability of the flow around a rotating cylinder in a stratified fluid. J. Fluid Mech. 672, 130–146.CrossRefGoogle Scholar
Ruddick, B. R., Mcdougall, T. J. & Turner, J. S. 1989 The formation of layers in a uniformly stirred density gradient. Deep-Sea Res. 36, 597–609.CrossRefGoogle Scholar
Smyth, W. D., Zavialov, P. O. & Moum, J. N. 1997 Decay of turbulence in the upper ocean following sudden isolation from surface forcing. J. Phys. Oceanogr. 27, 810–822.2.0.CO;2>CrossRefGoogle Scholar
Snow, K. & Sutherland, B. R. 2014 Particle-laden flow down a slope in uniform stratification. J. Fluid Mech. 755, 251–273.CrossRefGoogle Scholar
Stansfield, K., Garrett, C. & Dewey, R. 2001 The probability distribution of the Thorpe displacement within overturns in Juan de Fuca Strait. J. Phys. Oceanogr. 31, 3421–3434.2.0.CO;2>CrossRefGoogle Scholar
Staquet, C. & Godeferd, F. S. 1998 Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Flow energetics. J. Fluid Mech. 360, 295–340.CrossRefGoogle Scholar
Thorpe, S. A. 1968 On the shape of progressive internal waves. Phil. Trans. R. Soc. Lond. A 263, 563–614.Google 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
Thorpe, S. A. 1998 Some dynamical effects of the sloping sides of lakes. In Physical Processes in Lakes and Oceans (ed. Imberger, J.), Coastal and Estuarine Studies, ch. 31, pp. 441–460. AGU.Google Scholar
Thorpe, S. A. 1999 On internal wave groups. J. Phys. Oceanogr. 29, 1085–1095.2.0.CO;2>CrossRefGoogle Scholar
Thorpe, S. A. 2010 The relation between the duration and shape of internal wave groups. J. Mar. Res. 68, 63–95.CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. p. 367. Cambridge University Press.CrossRefGoogle Scholar
Venayagamoorthy, S. K. & Stretch, D. D. 2006 Lagrangian mixing in decaying stably stratified turbulence. J. Fluid Mech. 564, 197–226.CrossRefGoogle Scholar
Waite, M. L. & Smolarkiewicz, P. K. 2008 Instability and breakdown of a vertical vortex pair in a strongly stratified fluid. J. Fluid Mech. 606, 239–273.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar
Wunsch, S. & Kerstein, A. 2001 A model for layer formation in stably stratified turbulence. Phys. Fluids 13 (3), 702–712.CrossRefGoogle Scholar
Xiang, X., Madison, T. J., Sellappan, P. & Spedding, G. R. 2015 The turbulent wake of a towed grid in a stratified fluid. J. Fluid Mech. 775, 149–177.CrossRefGoogle Scholar
Yim, E. & Billant, P. 2015 On the mechanism of the Gent-McWilliams instability of a columnar vortex in stratified rotating fluids. J. Fluid Mech. 780, 5–44.CrossRefGoogle Scholar