Ocean Dynamics

, Volume 61, Issue 10, pp 1697–1717 | Cite as

Tidal mixing in sill regions: influence of sill depth and aspect ratio

Article
Part of the following topical collections:
  1. Topical Collection on Joint Numerical Sea Modelling Group Workshop 2010

Abstract

A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth (h s) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing namely Froude number F r as the sill depth (h s) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity U s due to increased depth. Calculations show that the sill Froude number F s based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low F s (namely F s ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high F s, calculations with a narrow sill show that for a given F s value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill with constant U s show that for small values of h s, a near surface mixed layer can occur on the downstream side of the sill. For large values of h s, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate values of h s, “internal mixing” dominates the solution and controls across thermocline mixing.

Keywords

Internal waves Sill Mixing 

Notes

Acknowledgements

The authors are indebted to E. Ashton and L. Parry for typing the text and R. A. Smith for help in figure preparation.

References

  1. Adcroft A, Hill C, Marshall J (1997) Representation of topography by shaved cells in a height coordinate ocean model. Mon Weather Rev 125:2293–2315CrossRefGoogle Scholar
  2. Baines PG (1995) Topographic effects on stratified flows: Cambridge Monographs on Mechanics. Cambridge University Press, CambridgeGoogle Scholar
  3. Berntsen J, Furnes GK (2005) Internal pressure errors in sigma-coordinate ocean models—sensitivity of the growth of the flow to the time stepping method and possible non-hydrostatic effects. Cont Shelf Res 25:829–848CrossRefGoogle Scholar
  4. Berntsen J, Xing J, Alendal G (2006) Assessment of non-hydrostatic ocean models using laboratory scale problems. Cont Shelf Res 26:1433–1447CrossRefGoogle Scholar
  5. Berntsen J, Xing J, Davies AM (2009) Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to grid size. Ocean Dyn 59:1043–1059CrossRefGoogle Scholar
  6. Davies AM, Jones JE (1990) Application of a three-dimensional turbulence energy model to the determination of tidal currents on the northwest European shelf. J Geophys Res 95:18143–18162CrossRefGoogle Scholar
  7. Davies AM, Xing J (2004) Modelling processes influencing wind induced internal wave generation and propagation. Cont Shelf Res 24:2245–2271CrossRefGoogle Scholar
  8. Davies AM, Xing J (2005) The effect of a bottom shelf front upon the generation and propagation of near-inertial internal waves in the coastal ocean. J Phys Oceanogr 35:976–990CrossRefGoogle Scholar
  9. Davies AM, Xing J, Berntsen J (2009) Non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions. Ocean Dyn 59:881–897CrossRefGoogle Scholar
  10. Davies AM, Jones JE, Xing J (2010) Modelling the influence of small scale effects upon the larger scale: an oceanographic challenge (Invited Paper). Ocean Dyn 60:921–932CrossRefGoogle Scholar
  11. Dewey RD, Richmond, Garrett C (2005) Stratified tidal flow over a bump. J Phys Oceanogr 35:1911–1927CrossRefGoogle Scholar
  12. Gerkema T, Zimmerman JTF (1995) Generation of non-linear internal tides and solitary waves. J Phys Oceanogr 25:1081–1094CrossRefGoogle Scholar
  13. Gerkema T (2001) Internal and interfacial tides: beam scattering and local generation of solitary waves. J Mar Res 59:227–251CrossRefGoogle Scholar
  14. Gerkema T (2002) Application of an internal tide generation model to baroclinic spring-neap cycles. J Geophys Res 107(C9):3124. doi: 10.1029/2001JC001177 CrossRefGoogle Scholar
  15. Gillibrand PA, Amundrud TL (2007) A numerical study of the tidal circulation and buoyancy effects in a Scottish fjord: Loch Torridon. J Geophys Res 112:C05030CrossRefGoogle Scholar
  16. Inall ME, Cottier FR, Griffiths C, Rippeth TP (2004) Sill dynamics and energy transformation in a jet fjord. Ocean Dyn 54:307–314CrossRefGoogle Scholar
  17. 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
  18. Jeans DRG, Sherwin TJ (2001a) The evolution and energetics of large amplitude non-linear internal waves on the Portuguese shelf. J Mar Res 59:327–353CrossRefGoogle Scholar
  19. Jeans DRG, Sherwin TJ (2001b) The variability of strongly non-linear solitary internal waves observed during an upwelling season on the Portuguese shelf. Cont Shelf Res 21:1855–1878CrossRefGoogle Scholar
  20. Klymak JM, Gregg MC (2001) Three-dimensional nature of flow near a sill. J Geophys Res 106:22295–22311CrossRefGoogle Scholar
  21. Legg S, Adcroft A (2003) Internal wave breaking at concave and convex continental slopes. J Phys Oceanogr 33:2224–2246CrossRefGoogle Scholar
  22. Legg S (2004a) Internal tides generated on a corrugated slope. Part I: Cross-slope barotropic forcing. J Phys Oceanogr 34:156–173CrossRefGoogle Scholar
  23. Legg S (2004b) Internal tides generated on a corrugated continental slope. Part II. Along-slope barotropic forcing. J Phys Oceanogr 34:1824–1838CrossRefGoogle Scholar
  24. Marshall J, Hill C, Perelman L, Adcroft A (1997a) Hydrostatic, quasi-hydrostatic and nonhydrostatic ocean modelling. J Geophys Res 102:5733–5752CrossRefGoogle Scholar
  25. Marshall J, Adcroft A, Hill C, Perelman L, Heisey C (1997b) A finite-volume incompressible Navier Stokes model for studies of the ocean on parallel computers. Journal Geophysical Research 102:5753–5766CrossRefGoogle Scholar
  26. New AL, Pingree RD (1990) Evidence for internal tidal mixing near the shelf break in the Bay of Biscay. Deep-Sea Res 37:1783–1803CrossRefGoogle Scholar
  27. Stigebrandt A, Aure J (1989) Vertical mixing in basin waters of fjords. J Phys Oceanogr 19:917–926CrossRefGoogle Scholar
  28. Stigebrandt A (1999) Resistance to barotropic tidal flow in straits by baroclinic wave drag. J Phys Oceanogr 29:191–197CrossRefGoogle Scholar
  29. Thorpe SA (2010) Turbulent hydraulic jumps in a stratified shear flow. J Fluid Mech 654:305–350CrossRefGoogle Scholar
  30. Van Haren H, Howarth J (2004) Enhanced stability during reduction of stratification in the North Sea. Cont Shelf Res 24:805–819CrossRefGoogle Scholar
  31. Van Haren H (2004) Spatial variability of deep-ocean motions above an abyssal plain. J Geophys Res 109:C12014. doi: 10.1029/2004JC002558 CrossRefGoogle Scholar
  32. Vlasenko V, Stashchuk N (2006) Amplification and suppression of internal waves by tides over variable bottom topography. J Phys Oceanogr 36:1959–1973CrossRefGoogle Scholar
  33. Xing J, Davies AM (2001) A three-dimensional baroclinic model of the Irish Sea: formation of the thermal fronts and associated circulation. J Phys Oceanogr 31:94–114CrossRefGoogle Scholar
  34. 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
  35. Xing J, Davies AM (2006a) Internal wave trapping and mixing in a cold water dome. J Geophys Res 111:C07002. doi: 10.1029/2005JC003417 CrossRefGoogle Scholar
  36. Xing J, Davies AM (2006b) Influence of stratification and topography upon internal wave spectra in the region of sills. Geophys Res Lett 33:L23606. doi: 10.1029/2006GL028092 CrossRefGoogle Scholar
  37. Xing J, Davies AM (2007) On the importance of non-hydrostatic processes in determining tidal induced mixing in sill regions. Cont Shelf Res 27:2162–2185CrossRefGoogle Scholar
  38. Xing J, Davies AM (2009a) Influence of bottom frictional effects in sill regions upon lee wave generation and internal mixing. Ocean Dyn 59:837–861CrossRefGoogle Scholar
  39. Xing J, Davies AM (2009b) The effects of large and small scale topography upon tidally induced mixing in sill regions. Ocean Dynamics 60:1–25CrossRefGoogle Scholar
  40. Xing J, Davies AM (2010) Effect of water depth and the bottom boundary layer upon internal wave generation over abrupt topography. Ocean Dyn 60:597–616CrossRefGoogle Scholar
  41. Xing J, Davies AM, Berntsen J (2009) Free surface, current profile and buoyancy effects upon internal wave energy flux profiles in sill regions. Mathematics and Computer in simulations 80:786–793CrossRefGoogle Scholar
  42. Zhai X, Greatbatch RJ, Zhao J (2005) Enhanced vertical propagation of storm-induced near-inertial energy in an eddying ocean channel model. Geophys Res Lett 32:L18602. doi: 10.10291/2005GLO23643 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.National Oceanographic CentreLiverpoolUK

Personalised recommendations