Skip to main content Accessibility help
×
Home
Hostname: page-component-5959bf8d4d-gl8zf Total loading time: 0.402 Render date: 2022-12-08T03:38:46.416Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Coherent Lagrangian vortices: the black holes of turbulence

Published online by Cambridge University Press:  03 September 2013

G. Haller
Affiliation:
Institute for Mechanical Systems, ETH Zurich, 8092 Zurich, Switzerland
F. J. Beron-Vera*
Affiliation:
Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL 33149, USA
*
Email address for correspondence: georgehaller@ethz.ch

Abstract

We introduce a simple variational principle for coherent material vortices in two-dimensional turbulence. Vortex boundaries are sought as closed stationary curves of the averaged Lagrangian strain. Solutions to this problem turn out to be mathematically equivalent to photon spheres around black holes in cosmology. The fluidic photon spheres satisfy explicit differential equations whose outermost limit cycles are optimal Lagrangian vortex boundaries. As an application, we uncover super-coherent material eddies in the South Atlantic, which yield specific Lagrangian transport estimates for Agulhas rings.

Type
Rapids
Copyright
©2013 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.)

References

Arnold, V. I. 1973 Ordinary Differential Equations. Massachusetts Institute of Technology.Google Scholar
Beal, L. M., De Ruijter, W. P. M., Biastoch, A., Zahn, R. & SCOR/WCRP/IAPSO Working Group, 2011 On the role of the Agulhas system in ocean circulation and climate. Nature 472, 429436.CrossRefGoogle ScholarPubMed
Beem, J. K., Ehrlich, P. L. & Kevin, L. E. 1996 Global Lorentzian Geometry. CRC Press.Google Scholar
Beron-Vera, F. J., Olascoaga, M. J. & Goni, G. J. 2008 Oceanic mesoscale vortices as revealed by Lagrangian coherent structures. Geophys. Res. Lett. 35, L12603.CrossRefGoogle Scholar
Beron-Vera, F. J., Wang, Y., Olascoaga, M. J., Goni, G. J. & Haller, G. 2013 Objective detection of oceanic eddies and the Agulhas leakage. J. Phys. Oceanogr. 43, 14261438.CrossRefGoogle Scholar
Chelton, D. B., Schlax, M. G. & Samelson, R. M. 2011 Global observations of nonlinear mesoscale eddies. Prog. Oceanogr. 91, 167216.CrossRefGoogle Scholar
Denman, K. L. & Gargett, A. E. 1983 Time and space scales of vertical mixing and advection of phytoplankton in the upper ocean. Limnol. Oceanogr. 28, 801815.CrossRefGoogle Scholar
Froyland, G., Horenkamp, C., Rossi, V., Santitissadeekorn, N. & Gupta, A. S. 2012 Three-dimensional characterization and tracking of an Agulhas ring. Ocean Model. 52–53, 6975.CrossRefGoogle Scholar
Goni, G. J., Garzoli, S. L., Roubicek, A. J., Olson, D. B. & Brown, O. B. 1997 Agulhas ring dynamics from TOPEX/Poseidon satellite altimeter data. J. Mar. Res. 55, 861883.CrossRefGoogle Scholar
Haller, G. 2005 An objective definition of a vortex. J. Fluid Mech. 525, 126.CrossRefGoogle Scholar
Haller, G. & Sapsis, T. 2008 Where do inertial particles go in fluid flows? Physica D 237, 573583.CrossRefGoogle Scholar
Hawking, S. & Penrose, R. 1996 The Nature of Space and Time. Princeton University Press.Google Scholar
Jeong, J. & Hussain, F. 1985 On the identification of a vortex. J. Fluid Mech. 285, 6994.CrossRefGoogle Scholar
Provenzale, A. 1999 Transport by coherent barotropic vortices. Annu. Rev. Fluid Mech. 31, 5593.CrossRefGoogle Scholar
Truesdell, C. & Noll, W. 2004 The Nonlinear Field Theories of Mechanics. Springer.CrossRefGoogle Scholar
van Aken, H. M., van Veldhovena, A. K., Vetha, C., de Ruijterb, W. P. M., van Leeuwenb, P. J., Drijfhoutc, S. S., Whittled, C. P. & Rouaultd, M. 2003 Observations of a young Agulhas ring, Astrid, during MARE in March 2000 . Deep-Sea Res. II 50, 167195.CrossRefGoogle Scholar
Supplementary material: PDF

Haller and Beron-Vera supplementary material

Appendix

Download Haller and Beron-Vera supplementary material(PDF)
PDF 375 KB

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org 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 @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ 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.

Coherent Lagrangian vortices: the black holes of turbulence
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.

Coherent Lagrangian vortices: the black holes of turbulence
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.

Coherent Lagrangian vortices: the black holes of turbulence
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? *