Ocean Dynamics

, Volume 59, Issue 6, pp 837–861 | Cite as

Influence of bottom frictional effects in sill regions upon lee wave generation and implications for internal mixing

  • Jiuxing XingEmail author
  • Alan M. Davies


A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition, associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient is increased.


Bottom frictional effects Sill regions Lee wave generation Internal mixing 



The authors are indebted to Mrs. L. Parry and E. Ashton for preparing the text.


  1. Afanasyev YD, Peltier WR (2001) On breaking internal waves over the sill in Knight Inlet. Proc R Soc Lond A457:2799–2825Google Scholar
  2. Baines PG (1995) Topographic effects on stratified flows. Cambridge monographs on mechanics. Cambridge University Press, CambridgeGoogle Scholar
  3. Cummins PF (2000) Stratified flow over topography: time-dependent comparisons between model solutions and observations. Dyn Atmos Oceans 33:43–72CrossRefGoogle Scholar
  4. Cummins PF, Vagle S, Armi L, Farmer DM (2003) Stratified flow over topography: upstream influence and generation of non-linear internal waves. Proc R Soc Lond A459:1467–1487Google Scholar
  5. Davies AM, Xing J (2006) Effect of topography and mixing parameterization upon the circulation in cold water domes. J Geophys Res 111:C03018. doi: 10.1029/2005JC003066 CrossRefGoogle Scholar
  6. Davies AM, Xing J (2007) On the influence of stratification and tidal forcing upon mixing in sill regions. Ocean Dynam 57:431–451CrossRefGoogle Scholar
  7. Farmer DM, Freeland HJ (1983) The physical oceanography of fjords. Prog Oceanogr 12:147–220CrossRefGoogle Scholar
  8. Gerkema T, Zimmerman JTF (1995) Generation of non-linear internal tides and solitary waves. J Phys Oceanogr 25:1081–1094CrossRefGoogle Scholar
  9. Gerkema T, Staquet C, Bouruet-Aubertot P (2006) Non-linear effects in internal-tide beams and mixing. Ocean Model 12:302–318CrossRefGoogle Scholar
  10. Hill AE (1996) Spin-down and the dynamics of dense pool gyres in shallow seas. J Mar Res 54:471–486CrossRefGoogle Scholar
  11. Hill AE, Durazo R, Smeed DA (1994) Observations of a cyclonic gyre in the western Irish Sea. Cont Shelf Res 14:479–490CrossRefGoogle Scholar
  12. Inall ME, Cottier FR, Griffiths C, Rippeth TP (2004) Sill dynamics and energy transformation in a jet fjord. Ocean Dynam 54:307–314CrossRefGoogle Scholar
  13. Inall ME, Rippeth TP, Griffiths C, Wiles P (2005) Evolution and distribution of TKE production and dissipation within stratified flow over topography. Geophys Res Lett 32:L08607. doi: 10.1029/2004GL022289 CrossRefGoogle Scholar
  14. Khatiwala S (2003) Generation of internal tides in an ocean of finite depth: analytical and numerical calculations. Deep-Sea Res 50:3–21CrossRefGoogle Scholar
  15. Klymak JM, Gregg MC (2001) Three-dimensional nature of flow near a sill. J Geophys Res 106:22295–22311CrossRefGoogle Scholar
  16. Klymak JM, Gregg MC (2003) The role of upstream waves and a downstream density pool in the growth of lee waves: stratified flow over the Knight Inlet sill. J Phys Oceanogr 33:1446–1461CrossRefGoogle Scholar
  17. Klymak JM, Gregg MC (2004) Tidally generated turbulence over the Knight Inlet sill. J Phys Oceanogr 34:1135–1151CrossRefGoogle Scholar
  18. Lamb KG (2004a) Non-linear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys Res Lett 31:L09313. doi: 10.1029/2003GL019393 CrossRefGoogle Scholar
  19. Lamb KG (2004b) On boundary-layer separation and internal wave generation at the Knight Inlet sill. Proc R Soc Lond A460:2305–2337Google Scholar
  20. Legg S, Adcroft A (2003) Internal wave breaking at concave and convex continental slopes. J Phys Oceanogr 33:2224–2246CrossRefGoogle Scholar
  21. Legg S, Huijts KMH (2006) Preliminary simulations of internal waves and mixing generated by finite amplitude tidal flow over isolated topography. Deep-Sea Res 53:140–156CrossRefGoogle Scholar
  22. Marshall J, Hill C, Perelman L, Adcroft A (1997) Hydrostatic, quasi-hydrostatic and non-hydrostatic ocean modelling. J Geophys Res 102:5733–5752CrossRefGoogle Scholar
  23. Nakamura T, Awaji T (2001) A growth mechanism for topographic internal waves generated by an oscillatory flow. J Phys Oceanogr 31:2511–2524CrossRefGoogle Scholar
  24. Nakamura T, Awaji T, Hatayama T, Akitomo K (2000) The generation of large-amplitude unsteady lee waves by sub-inertial K1 tidal flow: a possible vertical mixing mechanism in the Kuril Straits. J Phys Oceanogr 30:1601–1621CrossRefGoogle Scholar
  25. Nash JD, Moum JN (2001) Internal hydraulic flows on the continental shelf: high drag states over a small bank. J Geophys Res 106(C3):4593–4612. doi: 10.1029/1999JC000183 CrossRefGoogle Scholar
  26. Peltier WR, Caulfield CP (2003) Mixing efficiency in stratified shear flows. Annu Rev Fluid Mech 35:135–167CrossRefGoogle Scholar
  27. Saenko OA (2006) The effect of localized mixing on the ocean circulation and time-dependent climate change. J Phys Oceanogr 36:140–160CrossRefGoogle Scholar
  28. Samelson RM (1998) Large scale circulation with locally enhanced vertical mixing. J Phys Oceanogr 28:712–726CrossRefGoogle Scholar
  29. Soulsby RL (1983) The bottom boundary layer of shelf seas. In: Johns B (ed) Physical oceanography of coastal and shelf sea. Elsevier, Amsterdam, pp 189–262CrossRefGoogle Scholar
  30. Spall MA (2001) Large scale circulations forced by localized mixing over a sloping bottom. J Phys Oceanogr 31:2369–2384CrossRefGoogle Scholar
  31. Stashchuk N, Inall M, Vlasenko V (2007) Analysis of supercritical stratified tidal flow in a Scottish Fjord. J Phys Oceanogr 37:1793–1810CrossRefGoogle Scholar
  32. Stigebrandt A (1999) Resistance to barotropic tidal flow in straits by baroclinic wave drag. J Phys Oceanogr 29:191–197CrossRefGoogle Scholar
  33. Stigebrandt A, Aure J (1989) Vertical mixing in basin waters of fjords. J Phys Oceanogr 19:917–926CrossRefGoogle Scholar
  34. Van Haren H, Howarth J (2004) Enhanced stability during reduction of stratification in the North Sea. Cont Shelf Res 24:805–819CrossRefGoogle Scholar
  35. Vlasenko V, Stashchuk N, Hutter K (2002) Water exchange in fjords induced by tidally generated internal lee waves. Dyn Atmos Ocean 35(1):63–83CrossRefGoogle Scholar
  36. Vlasenko V, Stashchuk N, Hutter K (2005) Baroclinic tides. Theoretical modelling and observational evidence. Cambridge University Press, CambridgeGoogle Scholar
  37. Willmott A, Edwards PA (1987) A numerical model for the generation of tidally forced non-linear waves over topography. Cont Shelf Res 7:457–484CrossRefGoogle Scholar
  38. Xing J, Davies AM (2005) Influence of a cold water bottom dome on internal wave trapping. Geophys Res Lett 32:L03601. doi: 10.1029/2004GL021833 CrossRefGoogle Scholar
  39. Xing J, Davies AM (2006) Processes influencing tidal mixing in the region of sills. Geophys Res Lett 33:L04603. doi: 10.1029/2005GL025226 CrossRefGoogle Scholar
  40. Xing J, Davies AM (2007) On the importance of non-hydrostatic processes in determining tidally induced mixing in sill regions. Cont Shelf Res 27:2162–2185CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Proudman Oceanographic LaboratoryLiverpoolUK

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