Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-17T21:38:24.515Z Has data issue: false hasContentIssue false
  • English
  • Français

Forecasting long-lived Lagrangian vortices from their objective Eulerian footprints

Published online by Cambridge University Press:  19 January 2017

Mattia Serra  and
George Haller
Mattia Serra
Affiliation:
Department of Mechanical and Process Engineering, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland
George Haller*
Affiliation:
Department of Mechanical and Process Engineering, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland
*
†Email address for correspondence: georgehaller@ethz.ch
Get access Rights & Permissions [Opens in a new window]

Abstract

We derive a non-dimensional metric to quantify the expected Lagrangian persistence of objectively defined Eulerian vortices in two-dimensional unsteady flows. This persistence metric is the averaged deviation of the vorticity from its spatial mean over the Eulerian vortex, normalized by the instantaneous material leakage from the Eulerian vortex. The metric offers a model- and frame-independent tool for uncovering the instantaneous Eulerian signature of long-lived Lagrangian vortices. Using satellite-derived ocean velocity data, we show that Lagrangian vortex-persistence predictions by our metric significantly outperform those inferred from other customary Eulerian diagnostics, such as the potential vorticity gradient and the Okubo–Weiss criterion.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , pp. 436 - 457
Check for updates
Copyright
© 2017 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. 1973 Ordinary Differential Equations. MIT Press.Google Scholar
Batchelor, G. K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Beal, L. M., De Ruijter, W. P. M., Biastoch, A., Zahn, R. & Group, SCOR/WCRP/IAPSO WORKING 2011 On the role of the Agulhas system in ocean circulation and climate. Nature 472 (7344), 429–436.Google 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, 1426–1438.CrossRefGoogle Scholar
Chaigneau, A., Gizolme, A. & Grados, C. 2008 Mesoscale eddies off Peru in altimeter records: identification algorithms and eddy spatio-temporal patterns. Prog. Oceanogr. 79 (2–4), 106–119.Google Scholar
Chelton, D. B., deSzoeke, R. A., Schlax, M. G., Naggar, K. E. & Siwertz, N. 1998 Geographical variability of the first baroclinic Rossby radius of deformation. J. Phys. Oceanogr. 28 (3), 433–460.Google Scholar
Chelton, D. B., Schlax, M. G. & Samelson, R. M. 2011 Global observations of nonlinear mesoscale eddies. Prog. Oceanogr. 91 (2), 167–216.Google Scholar
Chelton, D. B., Schlax, M. G., Samelson, R. M. & De Szoeke, R. A. 2007 Global observations of large oceanic eddies. Geophys. Res. Lett. 34.CrossRefGoogle Scholar
Early, J. J., Samelson, R. M. & Chelton, D. B. 2011 The evolution and propagation of quasigeostrophic ocean eddies*. J. Phys. Oceanogr. 41, 1535–1555.CrossRefGoogle Scholar
Farazmand, M., Blazevski, D. & Haller, G. 2014 Shearless transport barriers in unsteady two-dimensional flows and maps. Physica D 278, 44–57.Google Scholar
Farazmand, M. & Haller, G. 2016 Polar rotation angle identifies elliptic islands in unsteady dynamical systems. Physica D 315, 1–12.Google Scholar
Griffa, A., Kirwan, A. D., Mariano, A. J., Özgökmen, T. & Rossby, H. T. 2007 Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Guckenheimer, J. & Holmes, P. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, vol. 42. Springer Science & Business Media.Google Scholar
Haller, G. 2015 Lagrangian coherent structures. Annu. Rev. Fluid Mech. 47, 137–162.CrossRefGoogle Scholar
Haller, G. & Beron-Vera, F. J. 2013 Coherent Lagrangian vortices: the black holes of turbulence. J. Fluid Mech. 731, R4.Google Scholar
Haller, G., Hadjighasem, A., Farazmand, M. & Huhn, F. 2016 Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136–173.Google Scholar
Haller, G. & Iacono, R. 2003 Stretching, alignment, and shear in slowly varying velocity fields. Phys. Rev. E 68, 056304.Google Scholar
Henson, S. A. & Thomas, A. C. 2008 A census of oceanic anticyclonic eddies in the Gulf of Alaska. Deep-Sea Res. 55, 163–176.CrossRefGoogle Scholar
Isern-Fontanet, J., Font, J., García-Ladona, E., Emelianov, M., Millot, C. & Taupier-Letage, I. 2004 Spatial structure of anticyclonic eddies in the Algerian basin (Mediterranean Sea) analyzed using the Okubo–Weiss parameter. Deep-Sea Res. 51, 3009–3028.Google Scholar
Isern-Fontanet, J., García-Ladona, E. & Font, J. 2003 Identification of marine eddies from altimetric maps. J. Atmos. Ocean. Technol. 20, 772–778.Google Scholar
Isern-Fontanet, J., García-Ladona, E. & Font, J. 2006 Vortices of the Mediterranean Sea: an altimetric perspective. J. Phys. Oceanogr. 36, 87–103.Google Scholar
Karrasch, D., Huhn, F. & Haller, G. 2015 Automated detection of coherent Lagrangian vortices in two-dimensional unsteady flows. Proc. R. Soc. Lond. A 471, 20140639.Google Scholar
Koszalka, I., Bracco, A., McWilliams, J. C. & Provenzale, A. 2009 Dynamics of wind-forced coherent anticyclones in the open ocean. J. Geophys. Res. 114 (C8).Google Scholar
Lapeyre, G. 2009 What vertical mode does the altimeter reflect? On the decomposition in baroclinic modes and on a surface-trapped mode. J. Phys. Oceanogr. 39 (11), 2857–2874.Google Scholar
Okubo, A. 1970 Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences. Deep-Sea Res. 17, 445–454.Google Scholar
Perko, L. M. 1990 Global families of limit cycles of planar analytic systems. Trans. Am. Math. Soc. 322, 627–656.Google Scholar
Serra, M. & Haller, G. 2016 Objective Eulerian coherent structures. Chaos 26 (5), 053110.Google Scholar
Truesdell, C. & Noll, W. 2004 The Non-Linear Field Theories of Mechanics. Springer.Google Scholar
Wang, P. & Özgökmen, T. M. 2015 How do hydrodynamic instabilities affect 3D transport in geophysical vortices? Ocean Model. 87, 48–66.Google Scholar
Wang, Y., Beron-Vera, F. J. & Olascoaga, M. J. 2016 The life cycle of a coherent Lagrangian Agulhas ring. J. Geophys. Res. Oceans 121, 3944–3954.CrossRefGoogle Scholar
Waugh, D. W., Abraham, E. R. & Bowen, M. M. 2006 Spatial variations of stirring in the surface ocean: a case study of the Tasman Sea. J. Phys. Oceanogr. 36, 526–542.Google Scholar
Weiss, J. 1991 The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica D 48, 273–294.Google Scholar
Wunsch, C. 1997 The vertical partition of oceanic horizontal kinetic energy. J. Phys. Oceanogr. 27 (8), 1770–1794.Google Scholar