Acta Oceanologica Sinica

, Volume 30, Issue 6, pp 1–11 | Cite as

Is the small-scale turbulence an exclusive breaking product of oceanic internal waves

  • Zhisong FanEmail author


On the basis of the theoretical research results by the author and the literature published up to date, the analysis and the justification presented in this paper show that the breaking products of oceanic internal waves are not only turbulence, but also the fine-scale near-inertial internal waves (the oceanic reversible finestructure) for inertial waves and the internal solitary waves for internal tides respectively. It was found that the oceanic reversible finestructure may be induced by the effect of the horizontal component \(\tilde f(\tilde f = 2\Omega cos\varphi )\) of the rotation vector on inertial waves. And a new instability of the theoretical shear and strain spectra due to the effect of \(\tilde f\) occurs at critical vertical wavenumber β c≈0.1 cpm. It happens when the levels of shear and strain of the reversible finestructure are higher than those of inertial waves, which is induced by the effect of \(\tilde f\) along an “iso-potential-pycnal” of internal wave. If all breaking products of internal waves are taken into account, the average kinetic energy dissipation rate is an order of magnitude larger than the values of turbulence observed by microstructure measurements. The author’s theoretical research results are basically in agreement with those observed in IWEX, DRIFTER and PATCHEX experiments. An important impersonal fact is that on the mean temporal scale of thermohaline circulation these breaking products of internal waves exist simultaneously with turbulence. Because inertial waves are generated by winds at the surface, and internal tides are generated by strong tide-topography interactions, the analysis and justification in this paper support in principle the abyssal recipes II: energetics of tidal and wind mixing by Munk & Wunsch in 1998, in despite of the results of microstructure measurements for the turbulent kinetic energy dissipation rate and the diapycnal turbulent eddy diffusivity.

Key words

internal waves inertial waves internal tides turbulence oceanic interior mixing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Apel J R, Holbrook J R, Liu A K, et al. 1985. The Sulu Sea internal soliton experiment. J Phys Oceanogr, 15: 1625–1651CrossRefGoogle Scholar
  2. Bogucki D, Garrett C. 1993. A simple model for the shear-induced decay of an internal solitary wave. J Phys Oceanogr, 23: 1767–1776CrossRefGoogle Scholar
  3. Chapman D C, Giese G S. 1990. A model for the generation of coastal seiches by deep-sea internal waves. J Phys Oceanogr, 20: 1459–1467CrossRefGoogle Scholar
  4. Chapman D C, Giese G S, Collins M G, et al. 1991. Evidence of internal swash associated with Sulu Sea solitary waves? Cont Shelf Res, 11: 591–599CrossRefGoogle Scholar
  5. D’Asaro E A, Perkins H. 1984. A near-inertial internal wave spectrum for the Sargasso Sea in late summer. J Phys Oceanogr, 14: 489–505CrossRefGoogle Scholar
  6. Dillon T M. 1982. Vertical overturns: a comparison of Thorpe and Ozmidov length scales. J Geophys Res, 87: 9601–9613CrossRefGoogle Scholar
  7. Djordjevic V D, Redekopp L G. 1978. The fission and disintegration of internal solitary waves moving over two-dimensional topography. J Phys Oceanogr, 8: 1016–1024CrossRefGoogle Scholar
  8. Duda T F, Lynch J F, Irish J D, et al. 2004. Internal tide and nonlinear internal wave behavior at the continental slope in the northern South China Sea. IEEE J Oceanic Eng, 29(4): 1105–1130CrossRefGoogle Scholar
  9. Eckart C. 1960. Hydrodynamics of Oceans and Atmospheres. Oxford, ergamon: 96Google Scholar
  10. Fan Zhisong. 2002. Research Fundamentals of Ocean Interior Mixing (in Chinese). Beijing, China Ocean Press: 130Google Scholar
  11. Fan Zhisong, Fang Xinhua. 1998a. Effect of horizontal component of rotation vector on equations for oceanic internal waves. Acta Oceanologica Sinica (in Chinese), 20(3): 129–133Google Scholar
  12. Fan Zhisong, Fang Xinhua. 1998b. An asymptotic solution of equations for oceanic internal waves under considering horizontal component of rotation vector. Acta Oceanologica Sinica (in Chinese), 20(4): 1–8Google Scholar
  13. Fan Zhisong, Fang Xinhua. 1999. A possible mechanism of ocean finestructure. Part I: Energy and coherence. Journal of Ocean University of Qingdao, 29(2): 207–214Google Scholar
  14. Fan Zhisong, Fang Xinhua. 2000. A possible mechanism of ocean finestructure. Part III: Estimation of the kinetic energy dissipation in mixing. Journal of Ocean University of Qingdao, 30(1): 7–14Google Scholar
  15. Fan Zhisong, Fang Xinhua, Xu Qichun. 1999. A possible mechanism of ocean finestructure. Part II: Shear and strain. Journal of Ocean University of Qingdao, 29(3): 405–414Google Scholar
  16. Fan Zhisong, Zhang Yuanling, Song Mei. 2008. A study of SAR remote sensing of internal solitary waves in the north of the South China Sea: I. Simulation of internal tide transformation. Acta Oceanologica Sinica, 27(4): 39–56Google Scholar
  17. Fu Leelueng. 1981. Observations and model of inertial waves in the deep ocean. Rev Geophys Space Phys, 19: 141–170CrossRefGoogle Scholar
  18. Gargett A E. 1990. Do we really know how to scale the turbulent kinetic energy dissipation rate due to breaking of oceanic internal waves? J Geophys Res, 95: 15971–15974CrossRefGoogle Scholar
  19. Garrett C J R. 2001. What is the “near-inertial” band and why is it different from the rest of the internal wave spectrum? J Phys Oceanogr, 31: 962–971CrossRefGoogle Scholar
  20. Garrett C J R, Munk W H. 1972. Space-time scales of internal waves. Geophys Fluid Dyn, 2: 225–264Google Scholar
  21. Giese G S, Hollander R B. 1987. The relationship between coastal seiches at Parawan Island and tide-generated internal solitary waves in the Sulu Sea. J Geophys Res, 92: 5151–5156CrossRefGoogle Scholar
  22. Gregg M C. 1989. Scaling turbulent dissipation in the thermocline. J Geophys Res, 94: 9686–9698CrossRefGoogle Scholar
  23. Gregg M C, D’Asaro E A, Shay T J, et al. 1986. Observations of persistent mixing and near-inertial internal waves. J Phys Oceanogr, 16: 856–885CrossRefGoogle Scholar
  24. Holloway G. 1983. A conjecture relating oceanic internal waves and small-scale processes. Atmos Oceans, 21: 107–122CrossRefGoogle Scholar
  25. Kamenkovich V M. 1977. Fundamentals of Ocean Dynamics (in English). Amsterdam, ElsevierGoogle Scholar
  26. Klymak J M, Pinkel R, Liu C-T, et al. 2006. Prototypical solitions in the South China Sea. Geophys Res Lett, 33: L11607, doi: 10.1029/2006GL025932CrossRefGoogle Scholar
  27. Kunze E, Sanford T B. 1996. Abyssal mixing: Where it is not. J Phys Oceanogr, 26: 2286–2296CrossRefGoogle Scholar
  28. Kunze E, Briscoe M G, Williams III A J. 1990. Interpreting shear and strain finestructure from a neutrally buoyant float. J Geophys Res, 95: 18111–18125CrossRefGoogle Scholar
  29. Kunze E, Williams III A J, Briscoe M G. 1990. Observations of shear and vertical stability from a neutrally buoyant float. J Geophys Res, 95: 18127–18142CrossRefGoogle Scholar
  30. Ledwell J R, Montgomery E T, Polzin K L, et al. 2000. Evidence for enhanced mixing over rough topography in the abyssal ocean. Nature, 403: 179–182CrossRefGoogle Scholar
  31. Levine M D. 1990. Internal waves under the Arctic pack ice during AIWEX: The coherence structure. J Geophys Res, 95: 7347–7357CrossRefGoogle Scholar
  32. Lien R-C, Gregg M C. 2001. Observation of turbulence in a tidal beam and across a coastal ridge. J Geophys Res, 106: 4575–4591CrossRefGoogle Scholar
  33. Lien R-C, Tang T-Y, Chang M-H, et al. 2005. Energy of nonlinear internal waves in the South China Sea. Geophys Res Lett, 32, L05615, doi: 10.1029/2004GL022012CrossRefGoogle Scholar
  34. Liu A K, Holbrook J R, Apel J R. 1985. Nonlinear internal wave evolution in the Sulu Sea. J Phys Oceanogr, 15: 1613–1624CrossRefGoogle Scholar
  35. McComas C H, Müller P. 1981. The dynamic balance of internal waves. J Phys Oceanogr, 11: 970–986CrossRefGoogle Scholar
  36. Munk W H. 1997. Once again: Once again-tidal friction. Prog Oceanogr, 40: 7–35CrossRefGoogle Scholar
  37. Munk W H, Phillips N. 1968. Coherence and band structure of inertial motion in the sea. Rev Geophys Space Phys, 6: 447–472CrossRefGoogle Scholar
  38. Munk W H, Wunsch C. 1998. Abyssal recipes II: Energetics of tidal and wind mixing. Deep-Sea Res, Part I, 45: 1977–2010CrossRefGoogle Scholar
  39. Müller P. 1984. Smallscale vortical motions. In: Müller P, Pujalet R, eds. Internal GravityWaves and Small-Scale Turbulence. Proceedings of the Aha Hulikoá Hawaiian Winter Workshop, Hawaiian Institute of Geophysics, Honolulu, 249–262Google Scholar
  40. Müller P, Olbers D, Willebrand J. 1978. The IWEX spectrum. J Geophys Res, 83: 479–500CrossRefGoogle Scholar
  41. Müller P, Lien R-C, Williams R. 1988. Estimates of potential vorticity at small scales in the ocean. J Phys Oceanogr, 18: 401–416CrossRefGoogle Scholar
  42. Nasmyth P. 1970. Oceanic turbulence. [dissertation], Institute of Oceanography, University of British Columbia, 69Google Scholar
  43. 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: 256–271CrossRefGoogle Scholar
  44. Olbers D J. 1976. Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean. J Fluid Mech, 74: 375–399CrossRefGoogle Scholar
  45. Olbers D J. 1983. Models of the oceanic internal wave field. Rev Geophys Space Phys, 21: 1567–1606CrossRefGoogle Scholar
  46. Phillips O M. 1977. The Dynamics of the Upper Ocean, 2nd ed. London and New York, Cambridge University Press: 336Google Scholar
  47. Pinkel R, Sherman J, Smith J, et al. 1991. Strain: observations of the vertical gradient of insopycnal vertical displacement. J Phys Oceanogr, 21: 527–540CrossRefGoogle Scholar
  48. Polzin K L, Toole J M, Ledwell J R, et al. 1997. Spatial variability of turbulent mixing in the abyssal ocean. Science, 276: 93–96CrossRefGoogle Scholar
  49. Ramp S R, Tang D, Duda T F, et al. 2004. Internal solitons in the northeast South China Sea: Part I. Sources and deep water propagation. IEEE J Oceanic Eng, 29(4): 1157–1181CrossRefGoogle Scholar
  50. Serebryany A N, Shapiro G I. 2000. Overturning of soliton-like internal waves: observations on the Pechora Sea shelf. Fifth Int Symp on Stratified Flows, Vancouver, BC, Canada, University of British Columbia, 1029–1034Google Scholar
  51. Sherman J T, Pinkel R. 1991. Estimates of the vertical wavenumber-frequency spectra of vertical shear and strain. J Phys Oceanogr, 21: 292–303CrossRefGoogle Scholar
  52. Thorpe S A. 1973. Experiments on instability and turbulence in a stably stratified shear flow. J Fluid Mech, 61: 731–751CrossRefGoogle Scholar
  53. Toole J M, Hayes S P. 1984. Finescale velocity-density characteristics and Richardson number statistics of the eastern equatorial Pacific. J Phys Oceanogr, 14: 712–726CrossRefGoogle Scholar
  54. Vlasenko V, Hutter K. 2002. Numerical experiments on the breaking of solitary internal waves over a slopeshelf topography. J Phys Oceanogr, 32: 1779–1793CrossRefGoogle Scholar
  55. Willebrand J. 1978. Temporal and spatial scales of the wind field over the North Pacific and North Atlantic. J Phys Oceanogr, 8: 1080–1094CrossRefGoogle Scholar
  56. Xu Zhenhua, Yin Baoshu, Hou Yijun, et al. 2010. A study of internal solitary waves observed on the continental shelf in the northwestern South China Sea. Acta Oceanologica Sinica, 29(3): 18–25CrossRefGoogle Scholar
  57. Yang Y-J, Tang T-Y, Chang M-H, et al. 2004. Solitons northeast of Tungsha Island during the ASIAEX pilot studies. IEEE J Oceanic Eng, 29(4): 1182–1199CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Oceanography and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.College of Physical and Environmental OceanographyOcean University of ChinaQingdaoChina

Personalised recommendations