Abstract
It has been established that idealized western boundary currents, which encounter a gap in their supporting boundary, will assume one of two dominant steady states: a loop current state and a gap leaping state, and that transitions between these states display hysteresis. However, a question of whether the idealized geometries considered to date apply to the Gulf of Mexico Loop Current (LC) remained. Here, the nonlinear potential vorticity advection-diffusions equations are solved, for Gulf of Mexico topography, using Newton’s method. We demonstrate that, in application to the LC in the Gulf of Mexico, the original conclusions do hold and additionally describe peculiarities of the more realistic steady states. The existence of our numerically calculated steady LC states in the actual Gulf of Mexico are supported through analysis of historical sea surface height data, and implications of our results for LC modeling and forecasting are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brillouin M (1911) Les surfaces de glissement d’helmholtz et la résistance des fluides. Annal Chimie Phys 23(145)
Chelidze D., Liu M. (2008) Reconstructing slow-time dynamics from fast-time measurements. Phil Trans R Soc A 366:729–745
Chelidze D, Zhou W (2006) Smooth orthogonal decomposition-based vibration mode identification. J Sound Vib 292(3-5):461–473. https://doi.org/10.1016/j.jsv.2005.08.006. Accessed 2020-07-22
Committee on Advancing Understanding of Gulf of Mexico Loop Current Dynamics, Gulf Research Program, National Academies of Sciences, Engineering, and Medicine (2018) Understanding and predicting the Gulf of Mexico Loop Current: critical gaps and recommendations. National Academies Press, Washington, DC. https://doi.org/10.17226/24823. Pages: 24823. https://www.nap.edu/catalog/24823 Accessed 2020-07-22
Donohue KA, Watts DR, Hamilton P, Leben R, Kennelly M (2016) Loop Current eddy formation and baroclinic instability. Dyn Atmospheres Oceans 76:195–216. https://doi.org/10.1016/j.dynatmoce.2016.01.004https://doi.org/10.1016/j.dynatmoce.2016.01.004. Accessed 2019-11-09
Donohue KA, Watts DR, Hamilton P, Leben R, Kennelly M, Lugo-Fernández A (2016) Gulf of Mexico loop current path variability. Dyn Atmospheres Oceans 76:174–194. https://doi.org/10.1016/j.dynatmoce.2015.12.003https://doi.org/10.1016/j.dynatmoce.2015.12.003. Accessed 2019-11-09
Hetland RD, Hsueh Y, Leben RR, P.P N (1999) A Loop Current-induced jet along the edge of the west Florida shelf. Geophys Res Lett 26(15):2239–2242
Ierley GR, Sheremet VA (1995) Multiple solutions and advection-dominated flows in the wind-driven circulation. Part I: Slip. J Mar Res 53(5):703–737. https://doi.org/10.1357/0022240953213052. Accessed 2020-07-22
Kafatos M, Sun D, Gautam R, Boybeyi Z, Yang R, Cervone G (2006) Role of anomalous warm gulf waters in the intensification of Hurricane Katrina. Geophys Res Lett 33(17):17802. https://doi.org/10.1029/2006GL026623https://doi.org/10.1029/2006GL026623. Accessed 2019-11-21
Khan AA, Kuehl J, Chelidze D (2020) Toward a unified interpretation of the “proper’/“smooth” orthogonal decompositions and “state variable”/“dynamic mode” decompositions with application to fluid dynamics. AIP Adv 10(3):035225. https://doi.org/10.1063/1.5144429https://doi.org/10.1063/1.5144429. Accessed 2020-07-22
Koch SP, Barker JW, Vermersch JA (1991) The Gulf of Mexico Loop Current and deepwater drilling. J Pet Technol 43(09):1046–1119. https://doi.org/10.2118/20434-PA. Accessed 2019-11-21
Kuehl JJ, DiMarco SF, Spencer LJ, Guinasso NL (2014) Application of the smooth orthogonal decomposition to oceanographic data sets. Geophys Res Lett 41(11):3966–3971. https://doi.org/10.1002/2014GL060237https://doi.org/10.1002/2014GL060237. Accessed 2019-06-06
Kuehl JJ, Sheremet VA (2009) Identification of a cusp catastrophe in a gap-leaping western boundary current. J Mar Res 67(1):25–42. https://doi.org/10.1357/002224009788597908. Accessed 2019-09-05
Kuehl JJ, Sheremet VA (2014) Two-layer gap-leaping oceanic boundary currents: experimental investigation. J Fluid Mech 740:97–113. https://doi.org/10.1017/jfm.2013.645. Accessed 2019-09-05
Kuehl JJ, Sheremet VA (2022) Effect of the coastline geometry on the boundary currents intruding through the gap. Fluids 7(71):10–33907020071
Large WG, Danabasoglu G, McWilliams JC, Gent PR, Bryan FO (2001) Equatorial circulation of a global ocean climate model with anisotropic horizontal viscosity. J Phys Oceanogr 31(2):518–536
Leben RR, Born GH, Engelbrecht BR (2002) Operational altimeter data processing for mesoscale monitoring. Mar Geodesy 25:3–18
Lipphardt BL, Poje AC, Kirwan AD, Kantha L, Zweng M (2008) Death of three Loop Current rings. J Mar Res 66:25–60
Liu G, Falasca F, Bracco A (2021) Dynamical characterization of the loop current attractor. Geophys Res Lett 48(24):10–10292021096731
McMahon CW, Kuehl JJ, Sheremet VA (2020) A viscous, two-layer western boundary current structure function. Fluids 5(2):63. https://doi.org/10.3390/fluids5020063. Accessed 2020-07-22
Mei H, Qi Y, Qiu B, Cheng X, Wu X (2019) Influence of an island on hysteresis of a western boundary current flowing across a gap. J Phys Oceanogr 49(5):1353–1366. https://doi.org/10.1175/JPO-D-18-0116.1https://doi.org/10.1175/JPO-D-18-0116.1. Accessed 2019-09-05
Pichevin T., Nof D. (1996) The eddy cannon. Deep-Sea Research 1 43(9):1475–1507
Pichevin T, Nof D (1997) The momentum imbalance paradox. Tellus A 49 (2):298–319. https://doi.org/10.1034/j.1600-0870.1997.t01-1-00009.xhttps://doi.org/10.1034/j.1600-0870.1997.t01-1-00009.x. Accessed 2019-11-01
Pierini S, de Ruggiero P, Negretti ME, Schiller-Weiss I, Weiffenbach J, Viboud S, Valran T, Dijkstra HA, Sommeria J (2022) Laboratory experiments reveal intrinsic self-sustained oscillations in ocean relevant rotating fluid flows. Sci Rep 12(1):1–11
Reid RO (1972) A simple dynamic model of the Loop Current (1972):157–159
Sheremet VA (2001) Hysteresis of a western boundary current leaping across a gap. J Phys Oceanogr 31(5):1247–1259
Sheremet VA (2002) A method of finding unstable steady solutions by forward time integration: relaxation to a running mean. Ocean Model 5:77–89
Sheremet VA, Kuehl J (2007) Gap-leaping western boundary current in a circular tank model. J Phys Oceanogr 37(6):1488–1495. https://doi.org/10.1175/JPO3069.1. Accessed 2019-06-11
Song X, Yuan D, Wang Z (2019) Hysteresis of a periodic or leaking western boundary current flowing by a gap. Acta Oceanol Sin 38(4):90–96. https://doi.org/10.1007/s13131-018-1251-z. Accessed 2019-09-05
Thom A (1933) The flow past circular cylinders at low speeds. Proc R Soc Lond A 141:651–669
Vanden-Broeck J-M, Keller JB (1989) Pouring flows with separation. Physics of Fluids A Fluid Dynamics 1(1):156–158
Villat H (1914) Sur la validité des solutions de certains problèmes d’hydrodynamique. J Math Pures Appl 10(231)
Wang Z, Yuan D, Hou Y (2010) Effect of meridional wind on gap-leaping western boundary current. Chin J Oceanol Limnol 28(2):354–358. https://doi.org/10.1007/s00343-010-9281-1. Accessed 2019-11-04
Weisberg RH, Lianyuan Z, Liu Y (2017) On the movement of Deepwater Horizon Oil to northern Gulf beaches. Ocean Model 111:81–97. https://doi.org/10.1016/j.ocemod.2017.02.002. Accessed 2020-07-16
Weisberg RH, Liu Y (2017) On the loop current penetration into the gulf of mexico. J Geophys Res 122(12):9679–9694. https://doi.org/10.1002/2017JC013330. Accessed 2020-07-22
Weisberg RH, Zheng L, Liu Y, Lembke C, Lenes JM, Walsh JJ (2014) Why no red tide was observed on the West Florida Continental Shelf in 2010. Harmful Algae 38:119–126. https://doi.org/10.1016/j.hal.2014.04.010. Accessed 2020-07-22
Yuan D, Song X, Yang Y, Dewar WK (2019) Dynamics of mesoscale eddies interacting with a western boundary current flowing by a gap. Journal of Geophysical Research: Oceans, 2019–014949. https://doi.org/10.1029/2019JC014949. Accessed 2019-09-04
Yuan D, Wang Z (2011) Hysteresis and dynamics of a western boundary current flowing by a gap forced by impingement of mesoscale eddies. J Phys Oceanogr 41(5):878–888. https://doi.org/10.1175/2010JPO4489.1. Accessed 2019-09-04
Funding
The authors are thankful to the National Science Foundation, USA, for funding this research via grant number 1823452, and to the National Academies of Sciences, Engineering and Medicine (NASEM) UGOS-1 via grant number 2000009918 and UGOS-2 via grant number 200011071.
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible Editor: Alejandro Orfila
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
Code availability
The numerical code used in this work can be found at http://sites.udel.edu/kuehl-group/software/.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Vitalii A. Sheremet, Arham Amin Khan, and Joseph Kuehl contributed equally to this work.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sheremet, V.A., Khan, A.A. & Kuehl, J. Multiple equilibrium states of the Gulf of Mexico Loop Current. Ocean Dynamics 72, 731–740 (2022). https://doi.org/10.1007/s10236-022-01534-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10236-022-01534-8