Skip to main content
SpringerLink
Log in

The role of eddies on pathways, transports, and entrainment in dense water flows along a slope

  • Published:
Ocean Dynamics Aims and scope Submit manuscript

Abstract

The flow of dense water along slopes has been investigated in several numerical investigations based on the Dynamics of Overflow Mixing and Entrainment (DOME) setup. In the present study, we try to obtain further insight into the pathways, transports, dynamics, and entrainment of such flows by performing numerical model studies with horizontal grid sizes of 10 km and 2.5 km. It is found that the rates of descent of the plumes along the slope are robust to the horizontal resolution. With a high vertical resolution and a bottom boundary condition that facilitates the representation of Ekman drainage, the plumes will follow a deeper path than when using quadratic bottom drag with a constant drag coefficient. In the results from the studies with 2.5 km horizontal grid, ambient lighter water inside anticyclonic eddies is sucked downward. Due to Ekman drainage, this water flows outwards near the bottom and underneath denser plume water. The water column around the core of the anticyclonic eddies becomes unstable, and ambient water is entrained into the plume. Due to the increased mixing and entrainment in the eddy-permitting regime, there is a substantial increase in the along slope plume transports when we reduce the grid size from 10 km (the laminar case) to 2.5 km (the eddy-permitting case).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  • Arneborg L, Fiekas V, Umlauf L, Burchard H (2007) Gravity current dynamics and entrainment - a process study based on observations in the arkona basin. J Phys Oceanogr 37:2094–2113

    Article  Google Scholar 

  • Bates M, Griffies S, England M (2012) A dynamic, embedded Lagrangian model for ocean climate models, Part II: idealised overflow tests. Ocean Model 59-60:60–76

    Article  Google Scholar 

  • Beaird N, Fer I, Rhines P, Eriksen C (2012) Dissipation of turbulent kinetic energy inferred from seagliders: an application to the eastern nordic seas overflows. J Phys Oceanogr 42:2268–2282

    Article  Google Scholar 

  • Beaird N, Rhines P, Eriksen C (2013) Overflow waters at the iceland-Faroe Ridge observed in multiyear seaglider surveys. J Phys Oceanogr 43:2334–2351

    Article  Google Scholar 

  • Bergh J, Berntsen J (2009) Numerical studies of wind forced waves with a nonhydrostatic model. Ocean Dyn 59:1025–1041

    Article  Google Scholar 

  • Bergh J, Berntsen J (2010) The surface boundary condition in nonhydrostatic ocean models. Ocean Dyn 60:317–330

    Article  Google Scholar 

  • Berntsen J (2000) USERS GUIDE for a modesplit σ-coordinate numerical ocean model. Technical Report 135, Dept. of Applied Mathematics, University of Bergen, Johs. Bruns gt.12, N-5008 Bergen, Norway. 48p

  • Berntsen J (2011) A perfectly balanced method for estimating the internal pressure gradients in σ-coordinate ocean models. Ocean Model 38:85–95

    Article  Google Scholar 

  • Berntsen J, Alendal G, Avlesen H, Thiem Ø (2018) Effects of the bottom boundary condition in numerical investigations of dense water cascading on a slope. Ocean Dyn 68:553–573

    Article  Google Scholar 

  • Berntsen J, Darelius E, Avlesen H (2016) Gravity currents down canyons: effects of rotation. Ocean Dyn 66:1353–1378

    Article  Google Scholar 

  • Berntsen J, Oey L-Y (2010) Estimation of the internal pressure gradients in σ-coordinate ocean models: comparison of second, fourth, and sixth order schemes. Ocean Dyn 60:317–330

    Article  Google Scholar 

  • Berntsen J, Thiem Ø, Avlesen H (2015) Internal pressure gradient errors in sigma-coordinate ocean models in high resolution fjord studies. Ocean Model 92:42–55

    Article  Google Scholar 

  • Berntsen J, Xing J, Alendal G (2006) Assessment of non-hydrostatic ocean models using laboratory scale problems. Cont Shelf Res 26:1433–1447

    Article  Google Scholar 

  • Berntsen J, Xing J, Davies A (2008) Numerical studies of internal waves at a sill: sensitivity to horizontal size and subgrid scale closure. Cont Shelf Res 28:1376–1393

    Article  Google Scholar 

  • Berntsen J, Xing J, Davies A (2009) Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size. Ocean Dyn 59:1043–1059

    Article  Google Scholar 

  • Blumberg A, Mellor G (1987) A description of a three-dimensional coastal ocean circulation model. In: Heaps N (ed) Three-dimensional coastal ocean models, volume 4 of coastal and estuarine series. American Geophysical Union, pp 1–16

  • Cenedese C, Linden P (1999) Cyclone and anticyclone formation in a rotating stratified fluid over a sloping bottom. J Fluid Mech 381:199–223

    Article  Google Scholar 

  • Cenedese C, Whitehead J, Ascarelli T, Ohiwa M (2004) A dense current flowing down a sloping bottom in a rotating fluid. J Phys Oceanogr 34:188–203

    Article  Google Scholar 

  • Condie S (1995) Descent of dense water masses along continental slopes. J Mar Res 53:897–928

    Article  Google Scholar 

  • Cortės A, Wells M, Fringer O, Arthur R, Rueda F (2015) Numerical investigation of split flows by gravity currents into two-ayered stratified water bodies. J Geophys Res Oceans 120:5254–5271

    Article  Google Scholar 

  • Cushman-Roisin B (1994) Introduction to geophysical fluid dynamics. Prentice Hall. ISBN-0-13-353301-8

  • Darelius E, Fer I, Quadfasel D (2011) Faroe bank channel overflow: mesoscale variability. J Phys Oceanogr 41:2137–2154

    Article  Google Scholar 

  • Darelius E, Smedsrud L, Østerhus S, Foldvik A, Gammelsrød T (2009) Structure and variability of the Filchner overflow plume. Tellus 61A:446–464

    Article  Google Scholar 

  • Darelius E, Ullgren J, Fer I (2013) Observations of barotropic oscillations and their influence on mixing in the faroe bank channel overflow region. J Phys Oceanogr 43:1525–1532

    Article  Google Scholar 

  • Ezer T (2005) Entrainment, diapycnal mixing and transport in three-dimensional bottom gravity current simulations using the Mellor-Yamada turbulence scheme. Ocean Model 9:151–168

    Article  Google Scholar 

  • Ezer T (2006) Topographic influence on overflow dynamics: idealized numerical simulations and the Faroe Bank Channel overflow. J Geophys Res 111:C02002. https://doi.org/10.1029/2005JC3195

    Article  Google Scholar 

  • Ezer T, Mellor G (2004) A generalized coordinate ocean model and a comparison of the bottom boundary layer dynamics in terrain-following and in z-level grids. Ocean Model 6:379–403

    Article  Google Scholar 

  • Garrett C, MacCready P, Rhines P (1993) Boundary mixing and arrested Ekman layers: rotating stratified flow near a sloping boundary. Annu Rev Fluid Mech 25:291–323

    Article  Google Scholar 

  • Gawarkiewicz G (2000) Effects of ambient stratification on offshore transport of dense water on continental shelves. J Geophys Res 105(C2):3307–3324

    Article  Google Scholar 

  • Gawarkiewicz G, Chapman D (1995) A numerical study of dense water formation and transport on a shallow, sloping continental shelf. J Geophys Res 100(C3):4489–4507

    Article  Google Scholar 

  • Geyer F, Østerhus S, Hansen B, Quadfasel D (2006) Observations of highly regular oscillations in the overflow plume downstream of the Faroe Bank Channel. J Geophys Res 111:C12020

    Article  Google Scholar 

  • Hansen B, Hátún LK (2016) A stable Faroe bank channel overflow 1995-2015. Ocean Sci 12:1205–1220

    Article  Google Scholar 

  • Hansen B, Larsen K, Olsen S, Quadfasel D, Jochumsen K, Østerhus S (2018) Overflow of cold water across the iceland-Faroe ridge through the western valley. In: press

  • Hansen B, Østerhus S (2007) Faroe bank channel overflow 1995-2005. Prog Oceanogr 75:817–856

    Article  Google Scholar 

  • Høyer J, Quadfasel D (2001) Detection of deep overflows with satellite altimetry. Geophys Res Lett 28:1611–1614

    Article  Google Scholar 

  • Ilicak M, Legg S, Adcroft A, Hallberg R (2011) Dynamics of a dense gravity current flowing over a corrugation. Ocean Model 38:71–84

    Article  Google Scholar 

  • Ilicak M, Özgökmen T, Peters H, Baumert H, Iskandarani M (2008) Very large eddy simulation of the Red Sea overflow. Ocean Model 20:183–206

    Article  Google Scholar 

  • Ivanov V, Shapiro G, Huthnance J, Aleynik D, Golovin P (2004) Cascades of dense water around the world ocean. Prog Oceanogr 60:47–98

    Article  Google Scholar 

  • Jiang L, Garwood R Jr (1998) Effects of topographic steering and ambient stratification on overflows on continental slopes: a model study. J Geophys Res 103(C3):5459–5476

    Article  Google Scholar 

  • Keilegavlen E, Berntsen J (2009) Non-hydrostatic pressure in σ-coordinate ocean models. Ocean Model 28:240–249

    Article  Google Scholar 

  • Laanaia N, Wirth A, Barnier B, Verron J (2010) On the numerical resolution of the bottom layer in simulations of oceanic gravity currents. Ocean Sci 6:563–572

    Article  Google Scholar 

  • Legg S, Hallberg R, Girton J (2006) Comparison of entrainment in overflows simulated by z-coordinate, isopycnal and non-hydrostatic models. Ocean Model 11:69–97

    Article  Google Scholar 

  • Legg S, Jackson L, Hallberg R (2008) Eddy-resolving modeling of overflows. In: Hecht M, Hasumi H (eds) Ocean modeling in an eddying regime, vol 177. AGU-Geophysical Monograph, pp 63–81

  • Lynch D, Ip J, Naimie C, Werner F (1995) Convergence studies of tidally-rectified circulation on Georges Bank. In: Lynch DR, Davies AM (eds) Quantitative skill assessment for coastal ocean models. American Geophysical Union

  • MacCready P, Rhines P (1991) Buoyant inhibition of Ekman transport on a slope and its effect on stratified spin-up. J Fluid Mech 223:631–661

    Article  Google Scholar 

  • Manucharyan G, Moon W, Sevellec F, Wells A, Zhong J-Q, Wettlaufer J (2014) Steady turbulent density currents on a slope in a rotating fluid. J Fluid Mech 746:405–436

    Article  Google Scholar 

  • Marques G, Wells G, Padman L, Özgökmen T (2017) Flow splitting in numerical simulations of oceanic dense-water outflows. Ocean Model 113:66–84

    Article  Google Scholar 

  • Mauritzen C, Price J, Sanford T, Torres D (2005) Circulation and mixing in the Faroese Channels. Deep-Sea Res I(52):883–913

    Article  Google Scholar 

  • Mellor G (2002) Oscillatory Bottom Boundary Layers. J Phys Oceanogr 32:3075–3088

    Article  Google Scholar 

  • Mellor G, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problems. Rev Geophys Space Phys 20:851–875

    Article  Google Scholar 

  • Nof D (1983) The translation of isolated cold eddies on a sloping bottom. Dee-Sea Res 30(2A):171–182

    Article  Google Scholar 

  • Olsen S, Hansen B, Quadfasel D, Østerhus S, Valdimarsson H (2016) Biased thermohaline exchanges with the Arctic across the Iceland-Faroe Ridge in ocean climate models. Ocean Sci 12:545–560

    Article  Google Scholar 

  • Østerhus S, Sherwin T, Quadfasel D, Hansen B (2008) The overflow transport east of iceland. In: Dickson R, Meincke R, Rhines P (eds) Arctic-subarctic ocean fluxes. Springer, pp 427–441

  • Özgökmen T, Fischer P, Duan J, Iliescu T (2004) Three-dimensional turbulent bottom density currents from a High-Order Nonhydrostatic spectral element model. J Phys Oceanogr 34:2006–2026

    Article  Google Scholar 

  • Reckinger S, Petersen M, Reckinger S (2015) A study of overflow simulations using MPAS-Ocean: vertical grids, resolution, and viscosity. Ocean Model 96:291–313

    Article  Google Scholar 

  • Seim K, Fer I (2011) Mixing in the stratified interface of the Faroe bank channel overflow: The role of transverse circulation and internal waves. J Geophys Res 116:C07022. https://doi.org/10.1029/2010JC006805

    Article  Google Scholar 

  • Seim K, Fer I, Berntsen J (2010) Regional simulations of the Faroe Bank Channel overflow using a σ-coordinate ocean model. Ocean Model 35:31–44

    Article  Google Scholar 

  • Shapiro G, Hill A (1997) Dynamics of dense water cascades at the shelf edge. J Phys Oceanogr 27:2381–2394

    Article  Google Scholar 

  • Smagorinsky J (1963) General circulation experiments with the primitive equations, I. The basic experiment. Mon Weather Rev 91:99–164

    Article  Google Scholar 

  • Tseng Y-H, Dietrich D (2006) Entrainment and transport in idealized three-dimensional gravity current simulation. J Atmos Oceanic Tech 23:1249–1269

    Article  Google Scholar 

  • Ullgren J, Darelius E, Fer I (2016) Volume transport and mixing of the Faroe bank Channel overflow from one year of moored measurements. Ocean Sci 12:451–470

    Article  Google Scholar 

  • Wåhlin A, Walin G (2001) Downward migration of dense bottom currents. Environ Fluid Mech 1:257–279

    Article  Google Scholar 

  • Wang Q, Danilov S, Schröter J (2008) Comparison of overflow simulations on different vertical grids using the Finite Element Ocean circulation Model. Ocean Model 30:313–335

    Article  Google Scholar 

  • Weatherly G, Martin P (1978) On the structure and dynamics of the ocean bottom boundary. J Phys Oceanogr 8:557–570

    Article  Google Scholar 

  • Wobus F, Shapiro G, Maquead M, Huthnance J (2011) Numerical simulations of dense water cascading on a steep slope. J Mar Res 69:391–415

    Article  Google Scholar 

  • Yang H, Przekwas A (1992) A comparative study of advanced shock-capturing schemes applied to Burgers equation. J Comput Phys 102:139–159

    Article  Google Scholar 

Download references

Funding

The authors have received financial support from EC/H2020 project number 654462 and from the Research Council of Norway project numbers 254711, 193825, and 239033.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Bergen, Bergen, Norway

    Jarle Berntsen & Guttorm Alendal

  2. NORCE Norwegian Research Centre, Bjerknes Centre for Climate Research, Bergen, Norway

    Helge Avlesen

Authors
  1. Jarle Berntsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guttorm Alendal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Helge Avlesen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jarle Berntsen.

Additional information

Responsible Editor: Tal Ezer

This article is part of the Topical Collection on the 10th International Workshop on Modeling the Ocean (IWMO), Santos, Brazil, 25–28 June 2018

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Berntsen, J., Alendal, G. & Avlesen, H. The role of eddies on pathways, transports, and entrainment in dense water flows along a slope. Ocean Dynamics 69, 841–860 (2019). https://doi.org/10.1007/s10236-019-01276-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10236-019-01276-0

Keywords

Search

Navigation