Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T07:16:56.572Z Has data issue: false hasContentIssue false
  • English
  • Français

Internal waves, turbulence and mixing in stratified flows: a report on Euromech Colloquium 339

Published online by Cambridge University Press:  26 April 2006

C. Staquet  and
J. Sommeria
C. Staquet
Affiliation:
Laboratoire de physique, Ecole Normale Supérieure de Lyon, 46 allée d’Italie, 69364 Lyon Cédex 07, France
J. Sommeria
Affiliation:
Laboratoire de physique, Ecole Normale Supérieure de Lyon, 46 allée d’Italie, 69364 Lyon Cédex 07, France
Get access Rights & Permissions [Opens in a new window]

Abstract

Euromech colloquium 339 was organized by C. Staquet in Lyon (France) from September 6 to 9, 1995. It involved seventy-six participants from fourteen countries. Papers were presented on various aspects of stably stratified flows: (i) internal waves, their generation mechanisms, propagation and reflection properties, their instabilities leading to breaking; (ii) vortex structures in stably stratified fluids, which can be slow layerwise structures, or small intense vortices, appearing for instance in shear flow instabilities; (iii) statistical properties of random wave fields or stratified turbulence; (iv) mixing properties resulting from internal wave fields and stratified turbulence. These quite different dynamical regimes are often closely connected in actual flow problems, and one purpose of this colloquium was to better understand these connections. Participants were interested in fundamental aspects or in more specific applications, in engineering, geophysics and astrophysics. The colloquium was a rare opportunity to gather together scientists with these different points of view, to compare approaches and results, and to highlight general problems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 314 , 10 May 1996 , pp. 349 - 371
Copyright
© 1996 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

Abramyan, T. O. & Kudine, A. M. 1983 A laboratory study of the interaction of patches of mixed liquid spreading in a stratified medium. Izv. Atmos. Ocean Phys. 19, 670–673.Google Scholar
Andreassen, O., Wasberg, C. E., Fritts, D. C. & Isler, J. R. 1994 Gravity wave breaking in two and three dimensions. 1. Model description and comparison of two-dimensional evolutions. J. Geophys. Res. 99 D4, 8095–8108.Google Scholar
Barenblatt, G. I. 1978 Dynamics of turbulent spots and intrusions in a stably stratified fluid. Izv. Atmos. Ocean. Phys. 14, 139–145.Google Scholar
Bayly, B., Holm, D. & Lifschitz, A. 1996 Three-dimensional stability of elliptical vortex columns in external strain flows. Phil. Trans. R. Soc. Lond. (to appear).Google Scholar
Benielli, D. & Sommeria, J. 1996 Excitation of internal waves by parametric instability and stratified turbulence. Dyn. Atmos. Oceans 23, 335–343.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
Bonneton, P., Roux, N. & Perrier, M. 1995 Etude expérimental de la dynamique des ondes de relief. Notes du Centre National de Recherches Météorologiques 12, Mai 1995.
Boubnov, B. M., Gledzer, E. B. & Hopfinger, E. J. 1995 Stratified circular Couette flow: instability and flow regimes. J. Fluid Mech. 292, 333–358.Google Scholar
Bouruet-Aubertot, P., Sommeria, J. & Staquet, C. 1995 Breaking of standing internal gravity waves through two-dimensional instabilities. J. Fluid Mech. 285, 265–301.Google Scholar
Bouruet-Aubertot, P., Sommeria, J. & Staquet, C. 1996 Stratified turbulence produced by internal wave breaking: two-dimensional numerical experiments. Dyn. Atmos. Oceans 23, 371–378.Google Scholar
Brown, A. R., Derbyshire, S. H. & Mason, P. J. 1994 Large eddy simulation of stable atmospheric boundary layers with a revised stochastic subgrid scale model. Q. J. R. Met. Soc. 120, 1485–1512.Google Scholar
Bühler, O. 1995 Waves and balanced mean flows in the atmosphere. PhD thesis, Cambridge University.
Cambon, C. 1989 Spectral approach to turbulence in a stratified fluid. In Advances in Turbulence 2 (ed. H.-H. Fernholz & H. E. Fiedler). Springer.
Canuto, V. M. & Dubovikov, M. S. 1996 A dynamical model for turbulence: I. General formalism. Phys. Fluids 8, 571–586.Google Scholar
Caulfield, C. P. & Peltier, W. R. 1994 Three-dimensionalization of the stratified mixing layer. Phys. Fluids 6, 3803–3805.Google Scholar
Chagelishvili, G. D. 1995 Onto peculiar evolution of internal gravity waves in high shear winds. J. Fluid Mech (submitted).Google Scholar
Christie, D. R. 1992 The morning glory of the Gulf of Carpentaria: a paradigm for nonlinear waves in low atmosphere. Austral. Met. Mag. 41, 21–60.Google Scholar
Cortesi, A. B. 1995 Direct numerical simulations of the temporally developing, stably-stratified mixing layer for a wide range of Richardson and Prandtl numbers. PhD dissertation, ETH Zurich.
Craik, A. D. D. & Criminale, W. O. 1986 Evolution of wavelike disturbances in shear flows: a class of exact solutions of the Navier-Stokes equations. Proc. R. Soc. Lond. A 406, 13–26.Google Scholar
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179.Google Scholar
Daubner, S. & Zeitlin, V. 1996 On the stationary energy spectra for unidirectionally propagating internal waves. Phys. Lett. A (submitted).Google Scholar
Dávalos-Orozco, L. A. 1996 Rayleigh-Taylor instability of a two-fluid system under a general rotation field. Dyn. Atmos. Oceans 23, 247–255.Google Scholar
Dörnbrack, A., Gerz, T. & Schumann, U. 1995 Turbulent breaking of overturning gravity waves below a critical level. Appl. Sci. Res. 54, 163–176.Google Scholar
Drazin, P. G. 1977 On the instability of an internal gravity wave. Proc. R. Soc. Lond. A 356, 411–432.Google Scholar
Dunkerton, T. J. 1984 Inertio-gravity waves in the stratosphere. J. Atmos. Sci. 41, 3396–3404.Google Scholar
Dupont, P. & Voisin, V. 1996 Internal waves generated by a translating and oscillating sphere. Dyn. Atmos. Oceans 23, 289–298.Google Scholar
Fernando, H. J. S. 1991 Turbulent mixing in stratified fluids. Ann. Rev. Fluid Mech. 23, 455–493.Google 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
Fincham, A. M. & Spedding, G. R. 1996 Low cost, high resolution DPIV for turbulent flows. Exps. Fluids (submitted).Google Scholar
Forster, G. K. & Craik, A. D. D. 1996 The stability of three-dimensional time-periodic flows with elliptical streamline. J. Fluid Mech. (submitted).Google Scholar
Fritts, D. C., Isler, J. R., Thomas, G. E. & Andreassen, O. 1993 Wave breaking signatures in noctilucent clouds. Geophys. Res. Lett. 20, 2039.Google Scholar
Fritts, D. C., Isler, J. R. & Andreassen, O. 1994 Gravity wave breaking in two and three dimensions. 2. Three-dimensional evolution and instability structure. J. Geophys. Res. 99 D4, 8109–8123.Google Scholar
Fritts, D. C. & Rastogi, P. K. 1985 Convective and dynamical instabilities due to gravity wave motions in the lower and middle atmosphere: Theory and observations. Radio Sci. 20, 1247–1277.Google Scholar
Garrett, C. & Munk, W. 1979 Internal waves in the ocean. Ann. Rev. Fluid Mech. 11, 339–369.Google Scholar
Gerz, T. & Yamazaki, H. 1993 Direct numerical simulations of buoyancy driven turbulence in stably stratified fluid. J. Fluid Mech. 249, 415–440.Google Scholar
Godeferd, F. S., Staquet, C. & Cambon, C. 1995 Stably stratified turbulence: a statistical two-point closure vs. direct numerical simulations. Proc. Xth Symp. on Turbulent Shear Flows.
Gregg, M. 1987 Diapycnal mixing in the thermocline: a review. J. Geophys. Res. 92 C5, 5249–5286.Google Scholar
Gregg, M. C. 1989 Scaling turbulent dissipation in the thermocline. J. Geophys. Res. 94 C7, 9686–9698.Google Scholar
Gurvich, A. S. 1995 Model of three-dimensional spectrum of locally axisymmetric temperature inhomogeneities in stably stratified atmosphere. Izv. Atmos. Ocean. Phys. 31, 211–216.Google Scholar
Hacker, J., Linden, P. F. & Dalziel, S. B. 1994 Mixing in lock-release gravity currents. Proc. Fourth Intl Symp. Stratified Flows, Grenoble, France vol. 4, B6.
Hanazaki, H. & Hunt, J. C. R. 1996 Linear processes in unsteady stably stratified turbulence. J. Fluid Mech. (to appear).Google Scholar
He, Y. & Moodie, T. B. 1991 The signalling problem in nonlinear hyperbolic wave theory. Stud. Appl. Maths 85, 343–372.Google Scholar
Henyey, F. S., Wright, J. & Flatté, S. 1986 Energy and action flow through the internal wavefield: an eikonal approach. J. Geophys. Res. 91, 8487–8495.Google Scholar
Holloway, G. 1988 The buoyancy flux from internal gravity wave breaking. Dyn. Atmos. Oceans 12, 107–125.Google Scholar
Holmboe, J. 1962 On the behavior of symmetric waves in stratified shear layers. Geofys. Publ. 24, 67–113.Google Scholar
Holton, J. R., Haynes, P. H., McIntyre, M. E., Douglass, A. R., Rood, R. B. & Pfister, L. 1995 Stratosphere–troposphere exchange. Rev. Geophys. 33, 403–439.Google Scholar
Hunt, J. C. R. & Carruthers, D. J. 1990 Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497–532.Google Scholar
Hunt, J. C. R., Stretch, D. D. & Britter, R. E. 1988 Length scales in stably stratified turbulent flows and their use in turbulence models. In Stably Stratified Flow and Dense Gas Dispersion (ed. J. S. Puttock), pp. 285–321. Clarendon.
Jacobitz, F., Sarkar, S. & Van Atta, C. W. 1995 Numerical simulation of a stratified turbulent shear flow. J. Fluid Mech. (submitted).Google Scholar
Kadri, Y., Bonneton, P., Chomaz, J. M. & Perrier, M. 1996 Stratified flow over three-dimensional topography. Dyn. Atmos. Oceans 23, 321–334.Google Scholar
Klostermeyer, J. 1990 On the role of parametric instability of internal gravity waves in atmospheric radar observations. Radio Sci. 25, 983.Google Scholar
Klostermeyer, J. 1991 Two and three-dimensional parametric instabilities in finite amplitude internal gravity waves. Geophys. Astrophys. Fluid Dyn. 61, 1–25.Google Scholar
Larson, M. & Jönsson, L. 1994 Mixing in a two-layer stably stratified fluid by a turbulent jet. J. Hydraul. Res. 32, 271–289.Google Scholar
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.
Linden, P. F., Boubnov, B. M. & Dalziel, S. B. 1995 Source-sink turbulence in a rotating stratified fluid. J. Fluid Mech. 298, 81–112.Google Scholar
Lombard, P. N. & Riley, J. J. 1996 On the breakdown into turbulence of propagating internal waves. Dyn. Atmos. Oceans 23, 345–355.Google Scholar
Lott, F. & Miller, M. J. 1996 A new subgrid scale orographic drag parametrization; its testing in the ECMWF model. Q. J. R. Met. Soc (to appear).Google Scholar
Lumley, J. L. 1964 The spectrum of nearly inertial turbulence in a stably stratified fluid. J. Atmos. Sci. 21, 99–102.Google Scholar
Maas, L. R. M. & Lam, F.-P. A. 1995 Geometric focusing of internal waves. J. Fluid Mech. 300, 1–41.Google Scholar
McComas, C. H. & Muller, P. 1981 The dynamic balance of internal waves. J. Phys. Oceanogr. 11, 970–989.Google Scholar
McIntyre, M. E. 1993 On the role of wave propagation and wave breaking in atmosphere–ocean dynamics. Proc. XVIII Intl Congr. Theor. Appl. Mech., Haifa, pp. 281–304. Elsevier.
McIntyre, M. E. 1994 The quasi-biennal oscillation (QBO): some points about the terrestrial QBO and the possibility of related phenomena in the solar interior. Proc. NATO Adv. Workshop on The Solar Engine and its Influence on the Terrestrial Atmosphere and Climate (ed. E. Nesme-Ribes). Springer.
McIntyre, M. E. & Norton, W. A. 1990 Dissipative wave-mean interactions and the transport of vorticity or potential vorticity. J. Fluid Mech. 212, 403–435.Google Scholar
Mied, R. P. 1976 The occurence of parametric instabilities in finite amplitude internal gravity waves. J. Fluid Mech. 78, 763–784.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.
Phillips, O. M. 1981 Wave interactions – the evolution of an idea. J. Fluid Mech. 106, 215–227.Google Scholar
Piccirillo, P. & Van Atta, C. W. 1996 The evolution of a uniformly sheared thermally stratified shear flow. J. Fluid Mech. (to appear).Google Scholar
Redondo, J. M., Sanchez, M. A. & Cantalapiedra, I. R. 1996 Turbulent mechanisms in stratified fluids. Dyn. Atmos. Oceans 24, 107–115.Google Scholar
Rees, J. M. & Mobbs, S. D. 1988 Studies of internal gravity waves at Halley Base, Antartica, using wind observations. Q. J. R. Met. Soc. 114, 939–966.Google Scholar
Riley, J. J., Metcalfe, R. W. & Weissman, M. A. 1981 Direct numerical simulations of homogeneous turbulence in density stratified fluids. In Nonlinear Properties of Internal Waves, AIP Conf. Proc. (ed. B. J. West), pp. 79–112.
Schär, C. 1993 A generalization of Bernoulli's theorem. J. Atmos. Sci. 50, 1437–1443.Google Scholar
Schatzman, E. 1993 Transport of angular momentum and diffusion by the action of internal waves. Astron. Astrophys. 279, 431.Google Scholar
Schowalter, D. G, Van Atta, C. W. & Lasheras, J. C. 1994 Baroclinic generation of streamwise vorticity in a stratified shear layer. Meccanica 20, 361–372.Google Scholar
Scinocca, J. & Shepherd, T. 1992 Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations. J. Atmos. Sci. 49, 5–27.Google Scholar
Shur, G. N. 1962 Experimental investigations of the energy spectrum of atmospheric turbulence. Trudy 43, pp. 79–90 (transl. AID. Rep. T63–55, Aerospace Information Division, Library of Congress).
Sidi, C. & Dalaudier, C. 1989 Temperature and heat flux spectra in the turbulent buoyancy range. Pure Appl. Geophys. 130, 547–569.Google Scholar
Slinn, D. N. & Riley, J. J. 1996 Turbulent mixing in the oceanic boundary layer due to internal wave reflection from sloping terrain. Dyn. Atmos. Oceans (in press).Google Scholar
Spedding, G. R., Browand, F. K. & Fincham, A. M. 1996 The long-time evolution of the initially-turbulent wake of a sphere in a stable stratification. Dyn. Atmos. Oceans 23, 171–182.Google Scholar
Staquet, C. 1995 Two-dimensional secondary instabilities in a strongly stratified shear layer. J. Fluid Mech. 296, 73–126.Google Scholar
Sutherland, B. R. 1996 Internal gravity wave radiation into weakly stratified fluid. Phys. Fluids 8, 430–441.Google Scholar
Sutherland, B. R. & Peltier, W. R. 1994 Turbulence transition and internal wave generation in density stratified jets. Phys. Fluids 6, 1267–1284.Google Scholar
Thomas, N. H. & Stevenson, T. N. 1972 A similarity solution for viscous internal waves. J. Fluid Mech. 54, 495–506.Google Scholar
Thorpe, S. A. 1977 Turbulence and mixing in a Scottish loch. Phil. Trans. R. Soc. Lond. 286, 125–181.Google Scholar
Townsend, A. A. 1957 Turbulent flow in a stably stratified atmosphere. J. Fluid Mech. 3, 499–523.Google Scholar
Weiss, R. F., Carmack, E. C. & Korpalov, V. M. 1991 Deep water renewal and biological production in Lake Baikal. Nature 349, 665–669.Google Scholar
Winters, K. B. & d'Asaro, E. A. 1994 Three-dimensional wave breaking near a critical level. J. Fluid Mech. 272, 255–284.Google Scholar
Winters, K. B., Lombard, P. N., Riley, J. J. & d'Asaro, E. A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289, 115–128.Google Scholar
Wu, J 1969 Mixed region collapse with internal wave generation in a density stratified medium. J. Fluid Mech. 35, 531–544.Google Scholar
Yoon, K. & Warhaft, Z. 1990 The evolution of grid generated turbulence under conditions of stable thermal stratification. J. Fluid Mech 215, 601–638.Google Scholar
Zakharov, V. E., L'Vov, V. S. & Falkovich, G. 1992 Kolmogoroff Spectra of Turbulence. Part 1. Wave Turbulence. Springer.
Zimmerman, W. B. & Velarde, M. G. 1994 Nonlinear waves in stably stratified dissipative media-solitary waves and turbulent bursts. Physica Scripta T55, 111–114.Google Scholar