Environmental Fluid Mechanics

, Volume 16, Issue 5, pp 923–943 | Cite as

Eddy diffusivity: a single dispersion analysis of high resolution drifters in a tidal shallow estuary

Original Article


In an estuary, mixing and dispersion resulting from turbulence and small scale fluctuation has strong spatio-temporal variability which cannot be resolved in conventional hydrodynamic models while some models employs parameterizations large water bodies. This paper presents small scale diffusivity estimates from high resolution drifters sampled at 10 Hz for periods of about 4 h to resolve turbulence and shear diffusivity within a tidal shallow estuary (depth <3 m). Taylor’s diffusion theorem forms the basis of a first order estimate for the diffusivity scale. Diffusivity varied between 0.001 and 0.02 m2/s during the flood tide experiment. The diffusivity showed strong dependence (R2 > 0.9) on the horizontal mean velocity within the channel. Enhanced diffusivity caused by shear dispersion resulting from the interaction of large scale flow with the boundary geometries was observed. Turbulence within the shallow channel showed some similarities with the boundary layer flow which include consistency with slope of 5/3 predicted by Kolmogorov’s similarity hypothesis within the inertial subrange. The diffusivities scale locally by 4/3 power law following Okubo’s scaling and the length scale scales as 3/2 power law of the time scale. The diffusivity scaling herein suggests that the modelling of small scale mixing within tidal shallow estuaries can be approached from classical turbulence scaling upon identifying pertinent parameters.


Eddy diffusivity Turbulence mixing Lagrangian drifter Shallow water Tidal estuary 



The authors thank all people who participated in the field study, those who assisted with the preparation and data analysis, as well as the Queensland Department of Natural Resources and Mines, Australia for providing access to SunPOZ network for reference station data used for RTK post processing of the high resolution GPS-tracked drifter. The authors acknowledge the support Redland City Council for provision of permit to the study sites. The project is supported through Australia Research Council Linkage Grant LP150101172. The authors acknowledge the contributions of Professor Hubert Chanson and Dr. Charles Wang to the work.


  1. 1.
    Elder J (1959) The dispersion of marked fluid in turbulent shear flow. J Fluid Mech 5(04):544–560. doi: 10.1017/S0022112059000374 CrossRefGoogle Scholar
  2. 2.
    Okubo A (1971) Oceanic diffusion diagrams. Deep Sea Res Oceanogr Abstr 18(8):789–802. doi: 10.1016/0011-7471(71)90046-5 CrossRefGoogle Scholar
  3. 3.
    MacCready P, Geyer WR (2010) Advances in estuarine physics. Ann Rev Mar Sci 2:35–58. doi: 10.1146/annurev-marine-120308-08101 CrossRefGoogle Scholar
  4. 4.
    Fischer HB, List EJ, Koh RC, Imberger J, Brooks NH (1979) Mixing in inland and coastal waters. Academic Press, LondonGoogle Scholar
  5. 5.
    Riddle A, Lewis R (2000) Dispersion experiments in UK coastal waters. Estuar Coast Shelf Sci 51(2):243–254. doi: 10.1006/ecss.2000.0661 CrossRefGoogle Scholar
  6. 6.
    Poje AC, Özgökmen TM, Lipphardt BL, Haus BK, Ryan EH, Haza AC, Jacobs GA, Reniers A, Olascoaga MJ, Novelli G (2014) Submesoscale dispersion in the vicinity of the Deepwater Horizon spill. Proc Natl Acad Sci 111(35):12693–12698. doi: 10.1073/pnas.1402452111 CrossRefGoogle Scholar
  7. 7.
    Schroeder K, Chiggiato J, Haza AC, Griffa A, Özgökmen TM, Zanasca P, Molcard A, Borghini M, Poulain PM, Gerin R, Zambianchi E, Falco P, Trees C (2012) Targeted Lagrangian sampling of submesoscale dispersion at a coastal frontal zone. Geophys Res Lett 39(11):L11608. doi: 10.1029/2012GL051879 CrossRefGoogle Scholar
  8. 8.
    Torsvik T, Kalda J (2014) Analysis of surface current properties in the Gulf of Finland using data from surface drifters. In: Baltic international symposium (BALTIC), 2014 IEEE/OES, 2014, pp 1–9Google Scholar
  9. 9.
    Stocker R, Imberger J (2003) Horizontal transport and dispersion in the surface layer of a medium-sized lake. Limnol Oceanogr 48(3):971–982. doi: 10.4319/lo.2003.48.3.0971 CrossRefGoogle Scholar
  10. 10.
    Tseng RS (2002) On the dispersion and diffusion near estuaries and around islands. Estuar Coast Shelf Sci 54(1):89–100. doi: 10.1006/ecss.2001.0830 CrossRefGoogle Scholar
  11. 11.
    Spydell MS, Feddersen F, Olabarrieta M, Chen J, Guza RT, Raubenheimer B, Elgar S (2015) Observed and modeled drifters at a tidal inlet. J Geophys Res Oceans 120(7):4825–4844. doi: 10.1002/2014JC010541 CrossRefGoogle Scholar
  12. 12.
    Suara K, Wang C, Feng Y, Brown RJ, Chanson H, Borgas M (2015) High resolution GNSS-tracked drifter for studying surface dispersion in shallow water. J Atmos Ocean Technol 32(3):579–590. doi: 10.1175/JTECH-D-14-00127.1 CrossRefGoogle Scholar
  13. 13.
    Pinton J-F, Sawford BL (2012) A Lagrangian view of turbulent dispersion and mixing. In: Davidson P et al (eds) Ten chapters in turbulence. Cambridge University Press, Cambridge, pp 133–175Google Scholar
  14. 14.
    Volk R, Calzavarini E, Leveque E, Pinton J-F (2011) Dynamics of inertial particles in a turbulent von Kármán flow. J Fluid Mech 668:223–235. doi: 10.1017/S0022112010005690 CrossRefGoogle Scholar
  15. 15.
    LaCasce J (2008) Lagrangian statistics from oceanic and atmospheric observations. In: Transport and mixing in geophysical flows. Springer, Berlin, pp 165–218. doi: 10.1007/978-3-540-75215-8_8
  16. 16.
    LaCasce J, Bower A (2000) Relative dispersion in the subsurface North Atlantic. J Mar Res 58(6):863–894. doi: 10.1357/002224000763485737 CrossRefGoogle Scholar
  17. 17.
    Taylor GI (1921) Diffusion by continuous movements. Proc Lond Math Soc 20:196–211Google Scholar
  18. 18.
    Suara K, Brown R, Wang C, Borgas M, Feng Y (2015) Estimate of Lagrangian integral scales in shallow tidal water using high resolution GPS-tracked drifters. In: E-proceeding of the 36th IAHR World Congress, The World Forum, Delft-The HagueGoogle Scholar
  19. 19.
    Chanson H (2008) Field observations in a small subtropical estuary during and after a rainstorm event. Estuar Coast Shelf Sci 80(1):114–120. doi: 10.1016/j.ecss.2008.07.013 CrossRefGoogle Scholar
  20. 20.
    Trevethan M, Chanson H, Brown R (2008) Turbulent measurements in a small subtropical estuary with semidiurnal tides. J Hydraul Eng 134(11):1665–1670. doi: 10.1061/(ASCE)0733-9429(2008)134%3A11(1665) CrossRefGoogle Scholar
  21. 21.
    Chanson H, Trevethan M (2010) Turbulence, turbulent mixing and diffusion in shallow-water estuaries. Atmospheric turbulence, meteorological modeling and aerodynamics. Nova Science Publishers, New York, pp 167–204Google Scholar
  22. 22.
    Situ R, Brown RJ (2013) Mixing and dispersion of pollutants emitted from an outboard motor. Mar Pollut Bull 69(1–2):19. doi: 10.1016/j.marpolbul.2012.12.015 CrossRefGoogle Scholar
  23. 23.
    Takasu T, Yasuda A (2009) Development of the low-cost RTK-GPS receiver with an open source program package RTKLIB. In: International symposium on GPS/GNSS, International Convention Center Jeju, KoreaGoogle Scholar
  24. 24.
    Suara K, Brown RJ, Chanson H (2015) Turbulence and mixing in the environment: multi-device study in a sub-tropical estuary. Hydraulic model report CH series CH99/15, School of Civil Engineering, The University of QueenslandGoogle Scholar
  25. 25.
    Goring DG, Nikora VI (2002) Despiking acoustic Doppler velocimeter data. J Hydraul Eng 128(1):117–126. doi: 10.1061/(ASCE)0733-9429(2002)128:1(117) CrossRefGoogle Scholar
  26. 26.
    Spydell M, Feddersen F, Guza R, Schmidt W (2007) Observing surf-zone dispersion with drifters. J Phys Oceanogr 37(12):2920–2939. doi: 10.1175/2007JPO3580.1 CrossRefGoogle Scholar
  27. 27.
    Schafer RW (2011) What is a Savitzky–Golay filter? Sig Process Mag IEEE 28(4):111–117CrossRefGoogle Scholar
  28. 28.
    Legleiter CJ, Kyriakidis PC (2006) Forward and inverse transformations between Cartesian and channel-fitted coordinate systems for meandering rivers. Math Geol 38(8):927–958. doi: 10.1007/s11004-006-9056-6 CrossRefGoogle Scholar
  29. 29.
    Suara K, Brown R, Chanson H Turbulence measurements in a shallow tidal estuary: analysis based on triple decomposition. In: 19AFMC: 19th Australasian Fluid Mechanics Conference, 2014. Vol Paper 359. Australasian Fluid Mechanics Society, pp 1–4Google Scholar
  30. 30.
    Haza AC, Özgökmen TM, Griffa A, Poje AC, Lelong M-P (2014) How does drifter position uncertainty affect ocean dispersion estimates? J Atmos Ocean Technol 31(12):2809–2828. doi: 10.1175/JTECH-D-14-00107.1 CrossRefGoogle Scholar
  31. 31.
    Xia H, Francois N, Punzmann H, Shats M (2013) Lagrangian scale of particle dispersion in turbulence. Nat Commun. doi: 10.1038/ncomms3013 Google Scholar
  32. 32.
    Ohlmann JC, LaCasce JH, Washburn L, Mariano AJ, Emery B (2012) Relative dispersion observations and trajectory modeling in the Santa Barbara Channel. J Geophys Res Oceans (1978–2012). doi: 10.1029/2011JC007810
  33. 33.
    Qian Y-K, Peng S, Liang C-X, Lumpkin R (2014) On the estimation of Lagrangian diffusivity: influence of nonstationary mean flow. J Phys Oceanogr 44(10):2796–2811CrossRefGoogle Scholar
  34. 34.
    Colin de Verdiere A (1983) Lagrangian eddy statistics from surface drifters in the eastern North Atlantic. J Mar Res 41(3):375–398. doi: 10.1357/002224083788519713 CrossRefGoogle Scholar
  35. 35.
    Davidson PA (2004) Turbulence: an introduction for scientists and engineers. Oxford University Press, OxfordGoogle Scholar
  36. 36.
    Chanson H, Gibbes B, Brown RJ (2014) Turbulent mixing and sediment processes in peri-urban Estuariesin South-East Queensland (Australia). In: Wolanski E (ed) Estuaries of Australia in 2050 and Beyond. Springer, BerlinGoogle Scholar
  37. 37.
    Trevethan M, Chanson H (2009) Turbulent mixing in a small estuary: detailed measurements. Estuar Coast Shelf Sci 81(2):191–200. doi: 10.1016/j.ecss.2008.10.020 CrossRefGoogle Scholar
  38. 38.
    Richardson LF (1926) Atmospheric diffusion shown on a distance-neighbour graph. In: Proceedings of the Royal Society of London Series A, containing papers of a mathematical and physical character, vol 110(756), pp 709–737Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Science and Engineering FacultyQueensland University of TechnologyBrisbaneAustralia
  2. 2.Marine and Atmospheric ResearchCommonwealth Scientific and Industrial Research Organisation (CSIRO)AspendaleAustralia

Personalised recommendations