Skip to main content Accessibility help
Hostname: page-component-55597f9d44-xbgml Total loading time: 0.37 Render date: 2022-08-13T06:49:47.365Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Steady turbulent density currents on a slope in a rotating fluid

Published online by Cambridge University Press:  02 April 2014

G. E. Manucharyan*
Yale University, New Haven, CT 06520, USA
W. Moon
Yale University, New Haven, CT 06520, USA
F. Sévellec
Yale University, New Haven, CT 06520, USA University of Southampton, Southampton SO14 3ZH, UK
A. J. Wells
Yale University, New Haven, CT 06520, USA University of Oxford, Oxford OX1 3PU, UK
J.-Q. Zhong
Yale University, New Haven, CT 06520, USA Tongji University, Shanghai 200092, PR China
J. S. Wettlaufer
Yale University, New Haven, CT 06520, USA University of Oxford, Oxford OX1 3PU, UK
Email address for correspondence:


We consider the dynamics of actively entraining turbulent density currents on a conical sloping surface in a rotating fluid. A theoretical plume model is developed to describe both axisymmetric flow and single-stream currents of finite angular extent. An analytical solution is derived for flow dominated by the initial buoyancy flux and with a constant entrainment ratio, which serves as an attractor for solutions with alternative initial conditions where the initial fluxes of mass and momentum are non-negligible. The solutions indicate that the downslope propagation of the current halts at a critical level where there is purely azimuthal flow, and the boundary layer approximation breaks down. Observations from a set of laboratory experiments are consistent with the dynamics predicted by the model, with the flow approaching a critical level. Interpretation in terms of the theory yields an entrainment coefficient $E\propto 1/\Omega $ where the rotation rate is $\Omega $. We also derive a corresponding theory for density currents from a line source of buoyancy on a planar slope. Our theoretical models provide a framework for designing and interpreting laboratory studies of turbulent entrainment in rotating dense flows on slopes and understanding their implications in geophysical flows.

© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Baines, W. D. & Turner, J. S. 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37, 5180.CrossRefGoogle Scholar
Borenäs, K. & Wåhlin, A. K. 2000 Limitations of the streamtube model. Deep-Sea Res. I 47, 13331350.CrossRefGoogle Scholar
Carmack, E. C. 2000 The Arctic Ocean’s freshwater budget: sources, storage and export. In Proceedings of the NATO Advanced Research Workshop on The Freshwater Budget of the Arctic Ocean (ed. Lewis, E. L.), pp. 91126. Kluwer.CrossRefGoogle Scholar
Cenedese, C. & Adduce, C. 2008 Mixing in a density-driven current flowing down a slope in a rotating fluid. J. Fluid Mech. 604, 369388.CrossRefGoogle Scholar
Cenedese, C. & Adduce, C. 2010 A new parameterisation for entrainment in overflows. J. Phys. Oceanogr. 40 (8), 18351850.CrossRefGoogle Scholar
Cenedese, C., Whitehead, J. A., Ascarelli, T. A. & Ohiwa, M. 2004 A dense current flowing down a sloping bottom in a rotating fluid. J. Phys. Oceanogr. 34 (1), 188203.2.0.CO;2>CrossRefGoogle Scholar
Cleveland, W. S. 1981 LOWESS: a programme for smoothing scatterplots by robust locally weighted regression. Am. Statist. 35 (1), 54.CrossRefGoogle Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6 (3), 423448.CrossRefGoogle Scholar
Garratt, J. R., Howells, P. A. C. & Kowalczyk, E. 1989 The behaviour of dry cold fronts travelling along a coastline. Mon. Weath. Rev. 117 (6), 12081220.2.0.CO;2>CrossRefGoogle Scholar
Griffiths, R. W. 1986 Gravity currents in rotating systems. Annu. Rev. Fluid Mech. 18, 5989.CrossRefGoogle Scholar
Hughes, G. O. & Griffiths, R. W. 2006 A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions. Ocean Model. 12 (1–2), 4679.CrossRefGoogle Scholar
Hunt, G. R. & Kaye, N. G. 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377396.CrossRefGoogle Scholar
Huppert, H. E. 2006 Gravity currents: a personal perspective. J. Fluid Mech. 554, 299322.CrossRefGoogle Scholar
Ivanov, V. V., Shapiro, G. I., Huthnance, J. M., Aleynik, D. L. & Golovin, P. N. 2004 Cascades of dense water around the world ocean. Prog. Oceanogr. 60 (1), 4798.CrossRefGoogle Scholar
Lane-Serff, G. F. & Baines, P. G. 1998 Eddy formation by dense flows on slopes in a rotating fluid. J. Fluid Mech. 363, 229252.CrossRefGoogle Scholar
Lignieres, F., Catala, C. & Mangeney, A. 1996 Angular momentum transfer in pre-main-sequence stars of intermediate mass. Astron. Astrophys. 314 (2), 465476.Google Scholar
Linden, P. F.2000 Convection in the environment. In Perspectives in Fluid Mechanics, chap. 6, pp. 303–321. Cambridge University Press.Google Scholar
McKee, C. F. & Ostriker, E. C. 2007 Theory of star formation. Annu. Rev. Astron. Astrophys. 45, 565687.CrossRefGoogle Scholar
Monaghan, J. J. 2007 Gravity current interaction with interfaces. Annu. Rev. Fluid Mech. 39, 245261.CrossRefGoogle Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234 (1196), 132.CrossRefGoogle Scholar
Nof, D. 1983 The translation of isolated cold eddies on a sloping bottom. Deep-Sea Res. A 30 (2), 171182.CrossRefGoogle Scholar
Pratt, L. J., Riemenschneider, U. & Helfrich, K. R. 2007 A transverse hydraulic jump in a model of the Faroe Bank Channel outflow. Ocean Model. 19, 19.CrossRefGoogle Scholar
Price, J. F. & Baringer, M. O. 1994 Outflows and deep-water production by marginal seas. Prog. Oceanogr. 33 (3), 161200.CrossRefGoogle Scholar
Princevac, M., Fernando, H. J. S. & Whiteman, C. D. 2005 Turbulent entrainment into natural gravity-driven flows. J. Fluid Mech. 533, 259268.CrossRefGoogle Scholar
Rieutord, M. & Zahn, J. P. 1995 Turbulent plumes in stellar convective envelopes. Astron. Astrophys. 296 (1), 127138.Google Scholar
Schlichting, H. 1968 Boundary Layer Theory. 6th edn. McGraw Hill.Google Scholar
Shapiro, G. I. & Hill, A. E. 1997 Dynamics of dense water cascades at the shelf edge. J. Phys. Oceanogr. 27 (11), 23812394.2.0.CO;2>CrossRefGoogle Scholar
Shapiro, G. I. & Zatsepin, A. G. 1997 Gravity current down a steeply inclined slope in a rotating fluid. Ann. Geophys. 15, 366374.CrossRefGoogle Scholar
Simpson, J. E. 1997 Gravity Currents in the Environment and the Laboratory. Cambridge University Press.Google Scholar
Smith, P. C. 1975 A streamtube model for bottom boundary currents in the ocean. Deep-Sea Res. Oceanogr. Abstr. 22 (12), 853873.CrossRefGoogle Scholar
Sutherland, B. R., Nault, J., Yewchuk, K. & Swaters, G. E. 2004 Rotating dense currents on a slope. Part 1. Stability. J. Fluid Mech. 508, 241264.CrossRefGoogle Scholar
Taylor, G. I. 1920 Tidal friction in the Irish Sea. Phil. Trans. R. Soc. Lond. A 220, 133.CrossRefGoogle Scholar
Timmermans, M. -L., Francis, J., Proshutinsky, A. & Hamilton, L. 2009 Taking stock of Arctic sea ice and climate. Bull. Am. Meteorol. Soc. 90 (9), 13511353.CrossRefGoogle Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431471.CrossRefGoogle Scholar
Wåhlin, A. K. & Cenedese, C. 2006 How entraining density currents influence the stratification in a one-dimensional ocean basin. Deep-Sea Res. II 53 (1–2), 172193.CrossRefGoogle Scholar
Wåhlin, A. K., Darelius, E., Cenedese, C. & Lane-Serff, G. F. 2008 Laboratory observations of enhanced entrainment in dense overflows in the presence of submarine canyons and ridges. Deep-Sea Res. I 55, 737750.CrossRefGoogle Scholar
Wåhlin, A. K. & Walin, G. 2001 Downward migration of dense bottom currents. Environ. Fluid Mech. 1, 257279.CrossRefGoogle Scholar
Wells, M. G. 2007 Influence of Coriolis forces on turbidity currents and sediment deposition. In Particle-Laden Flow: From Geophysical to Kolmogorov Scales (ed. Geurts, B. J., Clercx, H. & Uijttewaal, W.), vol. 11, pp. 331343. Springer.CrossRefGoogle Scholar
Wells, M. G., Cenedese, C. & Caulfield, C. P. 2010 The relationship between flux coefficient and entrainment ratio in density currents. J. Phys. Oceanogr. 40 (12), 27132727.CrossRefGoogle Scholar
Wells, M. G. & Wettlaufer, J. S. 2005 Two-dimensional density currents in a confined basin. Geophys. Astrophys. Fluid Dyn. 99 (3), 199218.CrossRefGoogle Scholar
Wells, M. G. & Wettlaufer, J. S. 2007 The long-term circulation driven by density currents in a two-layer stratified basin. J. Fluid Mech. 572, 3758.CrossRefGoogle Scholar
Wilchinsky, A. V., Feltham, D. L. & Holland, P. R. 2007 The effect of a new drag-law parameterisation on ice shelf water plume dynamics. J. Phys. Oceanogr. 37 (7), 17781792.CrossRefGoogle Scholar
Wirth, A. 2009 On the basic structure of oceanic gravity currents. Ocean Dyn. 59 (4), 551563.CrossRefGoogle Scholar
Wirth, A. 2011 Estimation of friction parameters in gravity currents by data assimilation in a model hierarchy. Ocean Sci. Discus. 8 (1), 159187.CrossRefGoogle Scholar
Wobus, F., Shapiro, G. I., Maqueda, M. A. M. & Huthnance, J. M. 2011 Numerical simulations of dense water cascading on a steep slope. J. Mar. Res. 69, 391415.CrossRefGoogle Scholar
Youdin, A. N. & Shu, F. H. 2002 Planetesimal formation by gravitational instability. Astrophys. J. 580 (1), 494505.CrossRefGoogle Scholar
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Steady turbulent density currents on a slope in a rotating fluid
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Steady turbulent density currents on a slope in a rotating fluid
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Steady turbulent density currents on a slope in a rotating fluid
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *