Advertisement

Indications for the transition of Kelvin-Helmholtz instabilities into propagating internal waves in a high turbid estuary and their effect on the stratification stability

  • Philipp HeldEmail author
  • Kerstin Bartholomä-Schrottke
  • Alexander Bartholomä
Original

Abstract

Internal waves (IWs) are an ubiquitous phenomenon in natural stratified fluids, including oceanic and coastal waters. Turbulence caused by their breaking can trigger vertical mixing of sediments, nutrients, and other dissolved substances. A major generation mechanism of IWs in coastal waters is the interaction of currents with topographic features. Additionally, current shear can lead to the development of Kelvin-Helmholtz instabilities, independent of the estuarine morphology. These instabilities normally form stationary rolled up vortices, which can also be imaged in echograms. In this study, we present new indications that propagating IWs in the Ems estuary arise from Kelvin-Helmholtz instabilities. The Richardson number drops below 0.25 at lutocline at the beginning of IW generation. However, the subsequently appearing lutocline undulations did not roll up, like the typical Kelvin-Helmholtz billows, but evolve into propagating and growing IWs of Holmboe type. Some of these waves were even subject to wave breaking. IW breaking occurred mainly during the second half of the ebb tides and is accompanied by vertical up-mixing of fluid mud. The turbulence and vertical mixing, caused by IW breaking, strongly decreases the local stratification by up to 60%.

Notes

Acknowledgments

The authors would like to thank the captain and crew of “RV Senckenberg” for their excellent job and inexhaustible patience during the acquisition of the datasets for this study. Jens Boczek from our institute is thanked for his support on board. Our student assistants are thanked for analyzing the water samples. Special thanks go also to Sebastian Krastel and Christian Winter for their helpful comments on the manuscript. We also thank Kilian Etter and Rachel Barrett for their language corrections. The Senckenberg Institute kindly provided the ship time.

Funding

This study was funded by the Deutsche Forschungsgemeinschaft as part of the Cluster of Excellence “The Future Ocean” and by the Federal Ministry of Education and Research in the frame of the Future Ems project (FO 03FO635A).

References

  1. Adams CE Jr, Wells JT, Park Y-A (1990) Internal hydraulics of a sediment-stratified channel flow. Mar Geol 95:131–145CrossRefGoogle Scholar
  2. Baines PG (1984) A unified description of two-layer flow over topography. J Fluid Mech 146:127–167CrossRefGoogle Scholar
  3. Becker M, Schrottke K, Bartholomä A, Ernstsen V, Winter C, Hebbeln D (2013) Formation and entrainment of fluid mud layers in troughs of subtidal dunes in an estuarine turbidity zone. J Geophys Res Oceans 118:2175–2187CrossRefGoogle Scholar
  4. Becker M, Maushake C, Winter C (2018) Observations of mud-induced periodic stratification in a hyperturbid estuary. Geophys Res Lett 45:5461–5469CrossRefGoogle Scholar
  5. Birch DA, Sundermeyer MA (2011) Breaking internal wave groups: mixing and momentum fluxes. Phys Fluids 23:1070–6631CrossRefGoogle Scholar
  6. Brandt P, Alpers W, Backhaus JO (1996) Study of the generation and propagation of internal waves in the Strait of Gibraltar using a numerical model and synthetic aperture radar images of the European ERS 1 satellite. J Geophys Res Oceans 101:14237–14252CrossRefGoogle Scholar
  7. Carpenter JR, Balmforth NJ, Lawrence GA (2010) Identifying unstable modes in stratified shear layers. Phys Fluids 22:054104CrossRefGoogle Scholar
  8. Carpenter JR, Tedford EW, Heifetz E, Lawrence GA (2011) Instability in stratified shear flow: review of a physical interpretation based on interacting waves. Appl Mech Rev 64:060801CrossRefGoogle Scholar
  9. Chernetsky AS, Schuttelaars HM, Talke SA (2010) The effect of tidal asymmetry and temporal settling lag on sediment trapping in tidal estuaries. Ocean Dyn 60:1219–1241CrossRefGoogle Scholar
  10. D’Asaro EA, Lien R-C, Henyey F (2007) High-frequency internal waves on the Oregon continental shelf. J Phys Oceanogr 37:1956–1967CrossRefGoogle Scholar
  11. de Jonge VN (1992) Tidal flow and residual flow in the Ems estuary. Estuar Coast Shelf Sci 34:1–22CrossRefGoogle Scholar
  12. de Kreeke JV, Day CM, Mulder HPJ (1997) Tidal variations in suspended sediment concentration in the Ems estuary: origin and resulting sediment flux. J Sea Res 38:1–16CrossRefGoogle Scholar
  13. de Silva IPD, Brandt A, Montenegro LJ, Fernando HJS (1999) Gradient Richardson number measurements in a stratified shear layer. Dyn Atmos Oceans 30:47–63CrossRefGoogle Scholar
  14. Geyer WR, Lavery AC, Scully ME, Trowbridge JH (2010) Mixing by shear instability at high Reynolds number. Geophys Res Lett 37.  https://doi.org/10.1029/2010GL045272
  15. Gratiot N, Mory M, Auchère D (2000) An acoustic Doppler velocimeter (ADV) for the characterisation of turbulence in concentrated fluid mud. Cont Shelf Res 20:1551–1567CrossRefGoogle Scholar
  16. Groeskamp S, Nauw JJ, Maas LRM (2011) Observations of estuarine circulation and solitary internal waves in a highly energetic tidal channel. Ocean Dyn 61:1767–1782CrossRefGoogle Scholar
  17. Guan WB, Kot SC, Wolanski E (2005) 3-D fluid–mud dynamics in the Jiaojiang estuary, China. Estuar Coast Shelf Sci 65:747–762CrossRefGoogle Scholar
  18. Held P, Schrottke K, Bartholomä A (2013) Generation and evolution of high-frequency internal waves in the Ems estuary, Germany. J Sea Res 78:25–35CrossRefGoogle Scholar
  19. Held P, Kegler P, Schrottke K (2014) Influence of suspended particulate matter on salinity measurements. Cont Shelf Res 85:1–8CrossRefGoogle Scholar
  20. Hogg AM, Ivey G (2001) The Kelvin-Helmholtz to Holmboe instability transition in stratified exchange flows. In: Proceedings of the fourteenth Australasian fluid mechanics conference. pp 893896Google Scholar
  21. Huthnance JM (1989) Internal tides and waves near the continental shelf edge. Geophys Astrophys Fluid Dyn 48:81–106CrossRefGoogle Scholar
  22. Jürgens J, Winkel N (2003) Ein Beitrag zur Tidedynamik der Unterems. BAW Mitteilungen 86:29–31Google Scholar
  23. Kantha LH (1979) On generation of internal waves by turbulence in the mixed layer. Dyn Atmos Oceans 3:39–46CrossRefGoogle Scholar
  24. Kirby R (1988) High concentration suspension (fluid mud) layers in estuaries. In: Dronkers J, van Leussen W (eds) Physical processes in estuaries. Springer, BerlinGoogle Scholar
  25. Konyaev KV, Sabinin KD, Serebryany AN (1995) Large-amplitude internal waves at the Mascarene Ridge in the Indian Ocean. Deep-Sea Res I Oceanogr Res Pap 42:2075–2081CrossRefGoogle Scholar
  26. Kurkina O, Rouvinskaya E, Talipova T, Soomere T (2017) Propagation regimes and populations of internal waves in the Mediterranean Sea basin. Estuar Coast Shelf Sci 185:44–54CrossRefGoogle Scholar
  27. Lawrence GA, Browand FK, Redekopp LG (1991) The stability of a sheared density interface. Phys Fluids A 3:2360–2370CrossRefGoogle Scholar
  28. Lefauve A, Partridge J, Zhou Q, Dalziel S, Caulfield C, Linden P (2018) The structure and origin of confined Holmboe waves. J Fluid Mech 848:508–544CrossRefGoogle Scholar
  29. Leichter JJ, Deane GB, Stokes MD (2005) Spatial and temporal variability of internal wave forcing on a coral reef. J Phys Oceanogr 35:1945–1962CrossRefGoogle Scholar
  30. Lott F, Kelder H, Teitelbaum H (1992) A transition from Kelvin–Helmholtz instabilities to propagating wave instabilities. Phys Fluids A 4:1990–1997CrossRefGoogle Scholar
  31. Maa P-Y, Mehta AJ (1987) Mud erosion by waves: a laboratory study. Cont Shelf Res 7:1269–1284CrossRefGoogle Scholar
  32. Manning AJ, Langston WJ, Jonas PJC (2010) A review of sediment dynamics in the Severn Estuary: influence of flocculation. Mar Pollut Bull 61:37–51CrossRefGoogle Scholar
  33. Maxeiner E, Dalrymple RA (2011) Experimental observation of standing interfacial waves induced by surface waves in muddy water. Phys Fluids 23:096603CrossRefGoogle Scholar
  34. McAnally WH, ASCE F, Teeter A, Schoellhamer D, Friedrichs C, Hamilton D, Hayter E, Shrestha P, Rodriguez H, Sheremet A, Kirby R (2007a) Management of fluid mud in estuaries, bays and lakes. II: measurement, modeling, and management. J Hydraul Eng 133:23–38CrossRefGoogle Scholar
  35. McAnally WH, Friedrichs C, Hamilton D, Hayter E, Shrestha P, Rodriguez H, Sheremet A, Teeter A (2007b) Management of fluid mud in estuaries, bays, and lakes. I: present state of understanding on character and behavior. J Hydraul Eng 133:9–22CrossRefGoogle Scholar
  36. Miles JW (1961) On the stability of heterogeneous shear flows. J Fluid Mech 10:496–508CrossRefGoogle Scholar
  37. Nastrom GD, Fritts DC (1992) Sources of mesoscale variability of gravity waves. Part I: topographic excitation. J Atmos Sci 49:101–110CrossRefGoogle Scholar
  38. Papenmeier S, Schrottke K, Bartholomä A, Flemming BW (2012) Sedimentological and rheological properties of the water–solid bed interface in the Weser and Ems estuaries, North Sea, Germany: implications for fluid mud classification. J Coast Res 29:797–808Google Scholar
  39. Pomar L, Morsilli M, Hallock P, Bádenas B (2012) Internal waves, an under-explored source of turbulence events in the sedimentary record. Earth Sci Rev 111:56–81CrossRefGoogle Scholar
  40. Ross MA, Mehta AJ (1989) On the mechanics of lutoclines and fluid mud. J Coast Res 51–62Google Scholar
  41. Schuchardt B, Scholle J, Schulze S, Bildstein T (2007) Vergleichende Bewertung der ökologischen Situation der inneren Ästuare von Eider, Elbe, Weser und Ems: Was hat sich nach 20 Jahren verändert? Coastline Rep 9:15–26Google Scholar
  42. Smyth WD, Moum JN (2012) Ocean mixing by Kelvin-Helmholtz instability. Oceanography 25:140–149CrossRefGoogle Scholar
  43. Smyth WD, Winters KB (2003) Turbulence and mixing in Holmboe waves. J Phys Oceanogr 33:694–711CrossRefGoogle Scholar
  44. Smyth WD, Carpenter JR, Lawrence GA (2007) Mixing in symmetric Holmboe waves. J Phys Oceanogr 37:1566–1583CrossRefGoogle Scholar
  45. Sottolichio A, Hurther D, Gratiot N, Bretel P (2011) Acoustic turbulence measurements of near-bed suspended sediment dynamics in highly turbid waters of a macrotidal estuary. Cont Shelf Res 31:36–49CrossRefGoogle Scholar
  46. Spingat F, Oumeraci H (2000) Schwebstoffdynamik in der Trübungszone des Ems-Ästuars. Die Küste 62 https://hdl.handle.net/20.500.11970/101434
  47. Sutherland B (2001) Internal gravity waves. Cambridge University Press, Cambridge.  https://doi.org/10.1017/CBO9780511780318 Google Scholar
  48. Sutherland BR, Hughes GO, Dalziel SB, Linden PF (2000) Internal waves revisited. Dyn Atmos Oceans 31:209–232CrossRefGoogle Scholar
  49. Talke SA, de Swart HE, Schuttelaars HM (2009) Feedback between residual circulations and sediment distribution in highly turbid estuaries: an analytical model. Cont Shelf Res 29:119–135CrossRefGoogle Scholar
  50. Tedford EW, Carpenter JR, Pawlowicz R, Pieters R, Lawrence GA (2009) Observation and analysis of shear instability in the Fraser River estuary. J Geophys Res 114:C11006CrossRefGoogle Scholar
  51. Traykovski P, Geyer WR, Irish JD, Lynch JF (2000) The role of wave-induced density-driven fluid mud flows for cross-shelf transport on the Eel River continental shelf. Cont Shelf Res 20:2113–2140CrossRefGoogle Scholar
  52. UNESCO (1981) The Practical Salinity Scale 1978 and the International Equation of state of Seawater 1980. Technical Papers in Marine Science, p 36Google Scholar
  53. van Haren H (2015) Instability observations associated with wave breaking in the stable-stratified deep-ocean. Phys D 292-293:62–69CrossRefGoogle Scholar
  54. van Leussen W (1999) The variability of settling velocities of suspended fine-grained sediment in the Ems estuary. J Sea Res 41:109–118CrossRefGoogle Scholar
  55. Vilibić I, Dadić V, Mihanović H (2004) Large-amplitude internal Kelvin waves trapped off Split (Middle Adriatic Sea). Estuar Coast Shelf Sci 61:623–630CrossRefGoogle Scholar
  56. Wolanski E, Asaeda T, Imberger J (1989) Mixing across a lutocline. Limnol Oceanogr 34:931–938CrossRefGoogle Scholar
  57. World Meteorological Organization (1998) Guide to wave analysis and forecasting. WMO-No. 702Google Scholar
  58. Wunderlich J, Müller S (2003) High-resolution sub-bottom profiling using parametric acoustics. Int Ocean Syst 7:6–11Google Scholar
  59. Wunsch S, Keller K (2013) Unstable modes of sheared pycnocline above a stratified layer. Dyn Atmos Oceans 60:1–27CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Marine Geophysics and HydroacousticsInstitute of Geosciences at Kiel UniversityKielGermany
  2. 2.SedimentologyInstitute of Geosciences at Kiel UniversityKielGermany
  3. 3.Department of Marine ResearchSenckenberg InstituteWilhelmshavenGermany

Personalised recommendations