Abstract
This study presents several new observations from the study of a numerically simulated warm-core ring (WCR) in the Gulf of Mexico based on the ECCO2 global ocean simulation. Using Lagrangian coherent structures (LCS) techniques to investigate this flow reveals a pattern of transversely intersecting LCS in the mixed layer of the WCR which experiences consistent stretching behavior over a large region of space and time. A detailed analysis of this flow region leads to an analytical model of the velocity field which captures the essential elements that generate the transversely intersecting LCS. The model parameters are determined from the simulated WCR and the resulting LCS show excellent agreement with those observed in the WCR. The three-dimensional transport behavior that creates these structures relies on the small radial outflow that is present in the mixed layer and is not seen below the pycnocline, leading to a sharp change in the character of the LCS at the bottom of the mixed layer. The flow behavior revealed by the LCS limits fluid exchange between the WCR and the surrounding ocean, contributing to the long life of WCRs. Further study of these structures and their associated transport behavior may lead to further insights into the development and persistence of such geophysical vortices as well as their transport behavior.
Similar content being viewed by others
References
Beron-Vera F, Olascoaga M, Goni G (2008) Oceanic mesoscale eddies as revealed by Lagrangian coherent structures. Geophys Res Lett 35(12):L12603
Biggs D (1992) Nutrients, plankton, and productivity in a warm-core ring in the western Gulf of Mexico. J Geophys Res: Oceans 97(C2):2143–2154
Cardwell B, Mohseni K (2008) Vortex shedding over two-dimensional airfoil: where do the particles come from?AIAA J 46(3):545–547
Chen R (2013) Energy pathways and structures of oceanic eddies from the ecco2 state estimate and simplified models. PhD thesis, Massachusetts Institute of Technology
Coulliette C, Wiggins S (2001) Intergyre transport in a wind-driven, quasigeostrophic double gyre: an application of lobe dynamics. Nonlinear Process Geophys 8(1/2):69–94
Coulliette C, Lekien F, Haller G, Paduan J, Marsden J (2007) Optimal pollution mitigation in Monterey Bay based on coastal radar data and nonlinear dynamics. Environ Sci Technol 41(18):6562–6572
Cushman-Roisin B, Heil WH, Nof D (1985) Oscillations and rotations of elliptical warm-core rings. J Geophys Res: Oceans (1978–2012) 90(C6):11756–11764
Dellnitz M, Grubits K, Marsden JE, Padberg K, Thiere B (2005) Set-oriented computation of transport rates in 3-degree of freedom systems: the Rydberg atom in crossed fields. Regul Chaotic Dyn 10(2):173–192
Elliott B (1979) Anticyclonic rings and the energetics of the circulation of the gulf of mexico. PhD thesis, Texas A&M Univ
Farazmand M, Haller G (2012) Computing Lagrangian coherent structures from variational theory. Chaos 22(1):013128–013128
Flierl GR, Mied RP (1985) Frictionally induced circulations and spin down of a warm-core ring. J Geophys Res: Oceans (1978–2012) 90(C5):8917–8927
Franks PJ, Wroblewski J, Flierl GR (1986) Prediction of phytoplankton growth in response to the frictional decay of a warm-core ring. J Geophys Res 91(C6):7603–7610
Froyland G, Padberg K (2009) Almost-invariant sets and invariant manifolds—connecting probabilistic and geometric descriptions of coherent structures in flows. Phys D 238:1507–1523
Fu LL (2009) Pattern and velocity of propagation of the global ocean eddy variability. J Geophys Res 114(C11):C11017
Green M, Rowley C, Haller G (2007) Detection of Lagrangian coherent structures in three-dimensional turbulence. J Fluid Mech 572(1):111–120
Haller G (2002) Lagrangian coherent structures from approximate velocity data. Phys Fluids 14(6):1851–1861
Haller G (2004) Exact theory of unsteady separation for two-dimensional flows. J Fluid Mech 512:257–311
Haller G (2011) A variational theory of hyperbolic Lagrangian coherent structures. Phys D 240:574–598
Haller G, Yuan G (2000) Lagrangian coherent structures and mixing in two dimensional turbulence. Phys D 147:352–370
Hong X, Chang SW, Raman S, Shay LK, Hodur R (2000) The interaction between Hurricane Opal (1995) and a warm core ring in the Gulf of Mexico. Mon Weather Rev 128(5):1347–1365
Huntley H, Lipphardt B, Kirwan A, Hogan P (2013) Surface drift predictions of the Deepwater Horizon spill: the Lagrangian perspective. In: Liu Y, Macfadyen A, Ji ZG, Weisberg RH (eds) Monitoring and modeling the deepwater horizon oil spill: a record-breaking enterprise. American Geophysical Union, Washington, D.C., pp 179–195
Hurlburt H, Thompson J (1980) A numerical study of loop current intrusions and eddy shedding. J Phys Oceanogr 10(10):1611–1651
Ide K, Small D, Wiggins S (2002) Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets. Nonlinear Process Geophys 9:237–263
Joyce T, Kennelly M (1985) Upper-ocean velocity structure of Gulf Stream warm-core ring 82B. J Geophys Res: Oceans (1978–2012) 90(C5):8839–8844
Kanamitsu M, Ebisuzaki W, Woollen J, Yang SK, Hnilo J, Fiorino M, Potter G (2002) NCEP-DOE AMIP-II reanalysis (R-2). Bull Am Meteorol Soc 83(11):1631–1643
Kishi MJ (1994) Prediction of phytoplankton growth in a warm-core ring using three dimensional ecosystem model. J Oceanogr 50(5):489–498. doi:10.1007/BF02235419
Lekien F, Ross S (2010) The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds. Chaos 20:017504. doi:10.1063/1.3278516
Lewis JK, Kirwan A, Forristall GZ (1989) Evolution of a warm-core ring in the Gulf of Mexico: Lagrangian observations. J Geophys Res: Oceans 94(C6):8163–8178
Lipinski D, Mohseni K (2009) A numerical investigation of flow structures and fluid transport with applications to feeding for the hydromedusae Aequorea victoria and Sarsia tubulosa. J Exp Biol 212:2436–2447
Lipinski D, Mohseni K (2012) A 3D fast algorithm for computing Lagrangian coherent structures via ridge tracking. arXiv preprint arXiv:1202.5236
Madrid J, Mancho A (2009) Distinguished trajectories in time dependent vector fields. Chaos 19:013111(18 pp)
Marshall J, Adcroft A, Hill C, Perelman L, Heisey C (1997) A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J Geophys Res: Oceans (1978–2012) 102(C3):5753–5766
Menemenlis D, Campin JM, Heimbach P, Hill C, Lee T, Nguyen A, Schodlok M, Zhang H (2008) ECCO2: high resolution global ocean and sea ice data synthesis. Mercator Ocean Q Newsl 31:13–21
Mezić I, Loire S, Fonoberov VA, Hogan P (2010) A new mixing diagnostic and Gulf oil spill movement. Science 330(6003):486–489
Oey L (2008) Loop current and deep eddies. J Phys Oceanogr 38(7):1426–1449
Olascoaga M, Haller G (2012) Forecasting sudden changes in environmental pollution patterns. Proc Natl Acad Sci 109:4738–4743. doi:10.1073/pnas.1118574109
Olson DB, Backus RH (1985) The concentrating of organisms at fronts: a cold-water fish and a warm-core gulf stream ring. J Mar Res 43:113–137
Olson D, Schmitt R, Kennelly M, Joyce T (1985) A two-layer diagnostic model of the long-term physical evolution of warm-core ring 82B. J Geophys Res: Oceans (1978–2012) 90(C5):8813–8822
Peng J, Dabiri J (2009) Transport of inertial particles by Lagrangian coherent structures: application to predator-prey interaction in jellyfish feeding. J Fluid Mech 623:75–84. doi:10.1017/S0022112008005089
Scharroo R, Smith WH, Lillibridge JL (2005) Satellite altimetry and the intensification of Hurricane Katrina. Eos, Trans Am Geophys Union 86(40):366
Shadden S, Lekien F, Marsden J (2005) Definition and properties of Lagrangian coherent structures from finite time Lyapunov exponents in two-dimensional aperiodic flows. Phys D 212:271–304
Shay LK, Goni GJ, Black PG (2000) Effects of a warm oceanic feature on Hurricane Opal. Mon Weather Rev 128(5):1366–1383
Sturges W, Leben R (2000) Frequency of ring separations from the loop current in the Gulf of Mexico: a revised estimate. J Phys Oceanogr 30(7):1814–1819
Sulman MH, Huntley HS, Lipphardt B Jr, Kirwan A Jr (2013) Leaving flatland: diagnostics for Lagrangian coherent structures in three-dimensional flows. Phys D Nonlinear Phenom 258:77–92
Volkov DL, Fu LL (2008) The role of vorticity fluxes in the dynamics of the Zapiola Anticyclone. J Geophys Res: Oceans (1978–2012) 113(C11). doi:10.1029/2008JC004841
Volkov DL, Lee T, Fu LL (2008) Eddy-induced meridional heat transport in the ocean. Geophys Res Lett 35(20). doi:10.1029/2008GL035490
Acknowledgments
The authors gratefully acknowledge the support of the Office of Naval Research in conducting this work.
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible Editor: Tal Ezer
Rights and permissions
About this article
Cite this article
Lipinski, D., Mohseni, K. Observations on the flow structures and transport in a simulated warm-core ring in the Gulf of Mexico. Ocean Dynamics 64, 79–88 (2014). https://doi.org/10.1007/s10236-013-0674-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10236-013-0674-5