Journal of Oceanography

, Volume 57, Issue 6, pp 709–721 | Cite as

Observations of a Kelvin-Helmholtz Billow in the Ocean

  • Hua Li
  • Hidekatsu Yamazaki


We identified a Kelvin-Helmholtz billow from vertical turbulence velocity and instantaneous heat flux signals obtained from airfoil shear probes and thermistors mounted on a research submarine. The vertical turbulence velocity indicates that the horizontal scale of the billow was about 3.5 m. The spectral slope of the vertical turbulence velocity component is close to −2, revealing the flow is two-dimensional. We show a remarkable agreement between the length scales of the observed billow and those computed from direct numerical simulations based on similar conditions.

Kelvin-Helmholtz billow shear instability length scale 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Batchelor, G. K. (1953): The Theory of Homogeneous Turbulence. Cambridge University Press, 197 pp.Google Scholar
  2. De Silva, I. P. D., H. J. S. Fernando, F. Eaton and D. Herbert (1996): Evolution of Kelvin-Helmholtz billows in nature and laboratory. Earth and Planetary Letters, 143, 217-231.CrossRefGoogle Scholar
  3. Ellison, T. H. (1957): Turbulent transport of heat and momentum from an infinite rough plane. J. Fluid Mech., 2, 456-466.CrossRefGoogle Scholar
  4. Fernando, H. J. S. and J. C. R. Hunt (1996): Some aspects of turbulence and mixing in stably stratified layers. Dyn. Atmos. Oceans, 23, 35-62.CrossRefGoogle Scholar
  5. Gargett, A. E., T. R. Osborn and P. W. Naysmyth (1984): Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech., 144, 231-280.CrossRefGoogle Scholar
  6. Gerz, T. and H. Yamazaki (1993): Direct numerical simulation of buoyancy-driven turbulence in a stably stratified fluid. J. Fluid Mech., 249, 415-440.CrossRefGoogle Scholar
  7. Gibson, C. H. and W. H. Schwarz (1963): The universal equilibrium spectra of turbulent velocity and scalar fields. J. Fluid Mech., 16, 365-384.CrossRefGoogle Scholar
  8. Grant, H. L., B. A. Hughes, W. M. Vogel and A. Moilliet (1968): The spectrum of temperature fluctuations in turbulent flow. J. Fluid Mech., 34, 423-442.CrossRefGoogle Scholar
  9. Gregg, M. C. (1999): Uncertainties and limitations in measuring ɛ and x. J. Atmos. Oceanic Technol., 16, 1483-1490.CrossRefGoogle Scholar
  10. Gregg, M. C., T. Meagher, A. Pederson and E. Aagaard (1978): Low noise temperature microstructure measurements with thermistors. Deep-Sea Res., 25, 843-856.CrossRefGoogle Scholar
  11. Hebert, D., J. N. Moum, C. A. Paulson and D. R. Caldwell (1992): Turbulence and internal waves at the equator. Part II: Details of a single event. J. Phys. Oceanogr., 22, 1346-1356.CrossRefGoogle Scholar
  12. Itsweire, E. C. and T. R. Osborn (1988): Microstructure and vertical velocity shear distribution in Monterey bay. p. 213-228. In Small Scale Turbulence and Mixing in the Ocean, ed. by J. C. J. Nihoul and B. J. Jamart, Elsevier.Google Scholar
  13. Itsweire, E. C., K. N. Helland and C. W. Van Atta (1986): The evolution of grid-generated turbulence in a stably stratified fluid. J. Fluid Mech., 162, 299-338.CrossRefGoogle Scholar
  14. Klaassen, G. P. and W. R. Peltier (1985): The onset of turbulence in finite-amplitude Kelvin-Helmholtz billows. J. Fluid Mech., 155, 1-35.CrossRefGoogle Scholar
  15. Lawrence, G. A., F. K. Browand and L. G. Redekop (1991): The stability of sheared density interface. Phys. Fluids, A3(10), 2360-2370.Google Scholar
  16. Moum, J. N., M. C. Gregg, R.-C. Lien and M. E. Carr (1995): Comparison of turbulence kinetic energy dissipation rate estimates from two ocean microstructure profilers. J. Atmos. Oceanic Tech., 12, 346-366.CrossRefGoogle Scholar
  17. Mudge, T. D. and R. G. Lueck (1994): Digital signal processing to enhance oceanographic observations. J. Atmos. Oceanic Tech., 11, 825-836.CrossRefGoogle Scholar
  18. Ninnis, R. (1984): The effects of spatial averaging on air-foil probe measurements of oceanic velocity microstructure. Ph.D. Thesis, University of British Columbia.Google Scholar
  19. Oakey, N. S. (1982): Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr., 12, 254-271.Google Scholar
  20. Osborn, T. R. and R. G. Lueck (1984): Oceanic shear spectra from a submarine. p. 25-50. In Internal Gravity Waves and Small-Scale Turbulence, Proceedings, Hawaiian Winter Workshop, ed. by P. Muller and R. Pujalet, Hawaii Institute of Geophysics, Honolulu.Google Scholar
  21. Seim, H. E. and M. C. Gregg (1994): Detailed observation of a naturally occurring shear instability. J. Geophys. Res., 99, 10049-10073.CrossRefGoogle Scholar
  22. Shih, L. H., J. R. Koseff, J. H. Ferziger and C. R. Rehmann (2000): Scaling and parameterization of stratified homogeneous turbulent shear flow. J. Fluid Mech. (submitted).Google Scholar
  23. Smyth, W. D. (1999): Dissipation range geometry and scalar mixing in sheared, stratified turbulence. J. Fluid Mech., 401, 209-242.CrossRefGoogle Scholar
  24. Smyth, W. D. and J. N. Moum (2000a): Length scales of turbulence in a stably stratified mixing layer. Phys. Fluids, 12, 1327-1342.CrossRefGoogle Scholar
  25. Smyth, W. D. and J. N. Moum (2000b): Anisotropy of turbulence in stably stratified mixing layers. Phys. Fluids, 12, 1343-1362.CrossRefGoogle Scholar
  26. Staquet, C. (2000): Mixing in a stably stratified shear layer: two and three dimensional numerical experiment. Fluid Dynamics Res., 27, 367-404.CrossRefGoogle Scholar
  27. Stillinger, D. C., K. N. Helland and C. W. Van Atta (1983): Experiments on the transition of homogenous turbulence to internal waves in a stratified fluid. J. Fluid Mech., 131, 91-122.CrossRefGoogle Scholar
  28. Strang, E. and H. J. Fernando (2001): Entrainment and mixing in stratified shear flows. J. Fluid Mech., 428, 349-386.CrossRefGoogle Scholar
  29. Thorpe, S. A. (1973): Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech., 61, 731-751.CrossRefGoogle Scholar
  30. Thorpe, S. A. (1985): Laboratory observations of secondary structures in Kelvin-Helmholtz billows and consequences for ocean mixing. Geophys. Astrophy. Fluid Dyn., 34, 175-199.Google Scholar
  31. Thorpe, S. A. (1987): Transitional phenomena and the development of turbulence in stratifies fluids. J. Geophys. Res., 92, 5231-5248.CrossRefGoogle Scholar
  32. Thorpe, S. A. and A. J. Hall (1974): Evidence of Kelvin-Helmholtz billows in Loch Ness. Limnol. Oceanogr., 19, 973-976.CrossRefGoogle Scholar
  33. Thorpe, S. A., A. J. Hall, C. Taylor and J. Allen (1977): Billows in Loch Ness. Deep-Sea Res., 24, 371-379.Google Scholar
  34. Wolk, F. and R. Lueck (2001): Heat flux and mixing efficiency in the surface mixing layer. J. Geophys. Res. (submitted).Google Scholar
  35. Woods, J. D. (1968): Wave-induced shear instability in the summer thermocline. J. Fluid Mech., 32, 791-800.CrossRefGoogle Scholar
  36. Yamazaki, H. (1990): Stratified turbulence near a Critical Dissipation Rate. J. Phys. Oceanogr., 20, 1583-1598.CrossRefGoogle Scholar
  37. Yamazaki, H. (1996): An observation of gravitational collapse caused by turbulence mixing. J. Phys. Oceanogr., 26, 826-831.CrossRefGoogle Scholar
  38. Yamazaki, H. and T. R. Osborn (1990): Dissipation estimates for stratified turbulence. J. Geophys. Res., 95, 9739-9744.Google Scholar
  39. Yamazaki, H. and T. R. Osborn (1993): Direct estimation of heat flux in a seasonal thermocline. J. Phys. Oceanogr., 23, 503-516.CrossRefGoogle Scholar

Copyright information

© The Oceanographic Society of Japan 2001

Authors and Affiliations

  • Hua Li
    • 1
  • Hidekatsu Yamazaki
    • 1
  1. 1.Department of Ocean SciencesTokyo University of FisheriesTokyoJapan

Personalised recommendations