Experiments in Fluids

, Volume 51, Issue 4, pp 1013–1028 | Cite as

Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge

  • Yuan Dossmann
  • Alexandre Paci
  • Francis Auclair
  • Jochem W. Floor
Research Article

Abstract

We present experimental results of internal wave generation by the oscillation of a two-dimensional topography in a linearly stratified fluid. Simultaneous synthetic schlieren and particle image velocimetry high-resolution measurements are made in a series of experiments with different forcing frequencies, all other parameters being kept constant. This setup allows us to obtain the potential and kinetic components of the mechanical energy transported by the internal wave beam for different relative values of the maximum topographic slope to the slope of internal wave phase lines, in a quasi-linear regime. Measurements are carefully validated and a combined wavelet and principal component analysis are carried out to extract the most energetic physical processes associated with the internal waves. The duration of the transient regime is evaluated in order to consider only results during the steady regime. We discuss the evolution of the radiated mechanical energy with respect to the forcing frequency, and we show that it reaches a maximum in the near-critical regime, in good agreement with recent numerical and theoretical works. New insights are provided about the role played by the relative values of the maximum topographic slope and the internal wave beam slope in the efficiency of energy transfers from barotropic tide to radiated internal waves. This study is a step toward a better quantification of the energy transported away by internal waves and available for mixing the ocean.

Notes

Acknowledgments

This work has been supported by LEFE-IDAO Program “ondes et marées interne dans l’océan” (LEFE-IDAO-07/29) and ANR “TOPOGI-3D” contract (ANR-05-BLAN-0176). We thank B. Beaudoin, A. Belleudy, J.-C. Boulay, B. Bourdelles, J.-C. Canonici, S. Lassus-Pigat, F. Murguet, M. Morera, and H. Schaffner of the CNRM-GAME (URA1357, METEO-FRANCE and CNRS) fluid mechanics laboratory, as well as J. Gil for their kind support during the experiments. We also wish to thank F. Pétrélis for helpful discussions as well as R. Montroty.

References

  1. Auclair F, Estournel C, Floor J, Hermann M, N’Guyen C, Marsaleix P (2011) A non-hydrostatic, energy conserving algorothm for regional ocean modelling. In press, Ocean modellingGoogle Scholar
  2. Balmforth NJ, Peacock T (2009) Tidal conversion by supercritical topography. J Phy Oceanogr 39(8):1965CrossRefGoogle Scholar
  3. Balmforth NJ, Ierley GR, Young WR (2002) Tidal conversion by subcritical topography. J Phys Oceanogr 32:2900–2914CrossRefGoogle Scholar
  4. Bell T (1975a) Lee waves in stratified flows with simple harmonic time-dependence. J Fluid Mech 67(feb25):705–722MATHCrossRefGoogle Scholar
  5. Bell T (1975b) Topographically generated internal waves in open ocean. J Geophys Res 80(3):320–327CrossRefGoogle Scholar
  6. Björnsson H, Venegas SA (1997) A manual for EOF and SVD analyses of climatic data. C²GCR report, no. 97.1Google Scholar
  7. Dalziel SB, Hughes GO, Sutherland BR (2000) Whole-field density measurements by ‘synthetic schlieren’. Exp Fluids 28(4):322–335CrossRefGoogle Scholar
  8. Dalziel SB, Carr M, Sveen JK, Davies PA (2007) Simultaneous synthetic schlieren and PIV measurements for internal solitary waves. Meas Sci Technol 18:533CrossRefGoogle Scholar
  9. Dohan K, Sutherland BR (2005) Numerical and laboratory generation of internal waves from turbulence. Dyn Atmospheres Oceans 40(1–2):43–56CrossRefGoogle Scholar
  10. Floor JW (2009) Energetics of internal tide generation, propagation and dissipation. Ph.D. thesis. University of Toulouse Paul SabatierGoogle Scholar
  11. Floor JW, Auclair F, Marsaleix P (2011) Energy transfers in internal tide generation, propagation and dissipation in the deep ocean. In press, Ocean modellingGoogle Scholar
  12. Gerkema T, Zimmerman J (1995) Generation of nonlinear internal tides and solitary waves. J Phys Oceanogr 25(6):1081–1094CrossRefGoogle Scholar
  13. Gill AE (1981) Atmosphere-ocean dynamics. In: International geophysics series, vol 30. Academic PressGoogle Scholar
  14. Gostiaux L, Dauxois T (2007) Laboratory experiments on the generation of internal tidal beams over steep slopes. Phys Fluids 19(2):028102CrossRefGoogle Scholar
  15. Gostiaux L, Didelle H, Mercier S, Dauxois T (2007) A novel internal waves generator. Exp Fluids 42(1):123–130CrossRefGoogle Scholar
  16. Holloway PE, Merrifield MA (1999) Internal tide generation by seamounts, ridges, and islands. J Geophys Res 104(C11): 25,937–25,951Google Scholar
  17. Hurley DG, Keady G (1997) The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solution. J Fluid Mech 351(-1):119–138MathSciNetMATHCrossRefGoogle Scholar
  18. Ihle CF, Dalziel SB, Nino Y (2009) Simultaneous particle image velocimetry and synthetic schlieren measurements of an erupting thermal plume. Meas Sci Technol 20:125402Google Scholar
  19. King B, Zhang HP, Swinney HL (2009) Tidal flow over three-dimensional topography in a stratified fluid. Phys Fluids 21(11):116601CrossRefGoogle Scholar
  20. Knigge C, Etling D, Paci A, Eiff O (2010) Laboratory experiments on mountain-induced rotors. QJR Meteorol Soc 136:442–450CrossRefGoogle Scholar
  21. Laurent L, Stringer S, Garett C, Perrault-Joncas D (2003) The generation of internal tides at abrupt topography. Deep-Sea Res Part 1 50:987–1003CrossRefGoogle Scholar
  22. Mathur M, Peacock T (2009) Internal wave beam propagation in non-uniform stratifications. J Fluid Mech 639:133–152MATHCrossRefGoogle Scholar
  23. Meunier P, Leweke T (2003) Analysis and minimization of errors due to high gradients in particle image velocimetry. Exp Fluids 35(5):408–421CrossRefGoogle Scholar
  24. Munk W, Wunsch C (1998) Abyssal recipes II: energetics of tidal and wind mixing. Deep Sea Res Part I Oceanogr Res Pap 45(12):1977–2010CrossRefGoogle Scholar
  25. Munroe J, Lamb K (2005) Topographic amplitude dependence of internal wave generation by tidal forcing over idealized three-dimensional topography. J Geophys Res-Oceans 110(C2):C02001Google Scholar
  26. Nycander J (2005) Generation of internal waves in the deep ocean by tides. J Geophys Res 110:C10028CrossRefGoogle Scholar
  27. Nycander J (2006) Tidal generation of internal waves from a periodic array of steep ridges. J Fluid Mech 567:415MathSciNetMATHCrossRefGoogle Scholar
  28. Pairaud I, Auclair F (2005) Combined wavelet and principal component analysis (WEof) of a scale-oriented model of coastal ocean gravity waves. Dyn Atmospheres Oceans 40(4):254–282CrossRefGoogle Scholar
  29. Peacock T, Echeverri P, Balmforth NJ (2007) An experimental investigation of internal tide generation by two-dimensional topography. J Phys Oceanogr 38(1):235CrossRefGoogle Scholar
  30. Pétrélis F, Smith SL, Young WR (2006) Tidal conversion at a submarine ridge. J Phys Oceanogr 36:1053–1071CrossRefGoogle Scholar
  31. Ray RD, Mitchum GT (1996) Surface manifestation of internal tides generated near Hawaii. Geophys Res Lett 23:2101–2104CrossRefGoogle Scholar
  32. Smith SGL, Young WR (2002) Conversion of the barotropic tide. J Phys Oceanogr 32:1554–1566MathSciNetCrossRefGoogle Scholar
  33. Smith SGL, Young WR (2003) Tidal conversion at a very steep ridge. J Fluid Mech 495:175–191MathSciNetMATHCrossRefGoogle Scholar
  34. Sveen JK, Dalziel SB (2005) A dynamic masking technique for combined measurements of PIV and synthetic schlieren applied to internal gravity waves. Meas Sci Technol 16:1954CrossRefGoogle Scholar
  35. Tailleux R (2009) On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy. J Fluid Mech 638(-1):339–382MATHCrossRefGoogle Scholar
  36. Vallis GK (2006) Atmospheric and oceanic fluid dynamics. Cambridge University Press, New YorkCrossRefGoogle Scholar
  37. Voisin B, Ermanyuk EV, Flor JB (2010) Internal wave generation by oscillation of a sphere, with application to internal tide. In press, J Fluid MechGoogle Scholar
  38. Weast RC (1981) Handbook of chemistry and physics, 62nd edn. CRC Press, Boca RatonGoogle Scholar
  39. Winters KB, Young WR (2009) Available potential energy and buoyancy variance in horizontal convection. J Fluid Mech 629:221MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Yuan Dossmann
    • 1
    • 2
  • Alexandre Paci
    • 1
  • Francis Auclair
    • 2
  • Jochem W. Floor
    • 3
  1. 1.CNRM-GAME/GMEI/SPEAToulouse cedex 01France
  2. 2.Laboratoire d’AérologieToulouseFrance
  3. 3.VessemThe Netherlands

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