Normal modes and resonance in Ontario Lacus: a hydrocarbon lake of Titan

  • David VincentEmail author
  • Jonathan Lambrechts
  • Özgür Karatekin
  • Tim Van Hoolst
  • Robert H. Tyler
  • Véronique Dehant
  • Eric Deleersnijder


The natural modes of Ontario Lacus surface oscillations, the largest lake in Titan’s southern hemisphere, are simulated and analyzed as they are potentially of broad interest in a variety of dynamical researches. We found that tidal forces are too low in frequency to excite the (barotropic) normal modes. Broadband wind forcing likely spans the resonant frequencies. High wind speed, which could be encountered under episodic phenomena such as storms, would be required to significantly excite the normal modes. While the slower baroclinic normal modes could more easily be resonantly forced by the low-frequency tidal forces, addressing this issue demands unavailable information about the lake stratification.


Ontario Lacus Natural modes Titan Extraterrestrial oceanography 


Funding information

Computational resources were provided by the Consortium des Équipements de Calcul Intensif (CÉCI), funded by the Belgian Fund for Scientific Research (F.R.S.-FNRS) under Grant No. 2.5020.11. Eric Deleersnijder is an honorary Research associate with the F.R.S.-FNRS. This research is funded by the Belgian PRODEX, managed by the ESA, in collaboration with the Belgian Federal Science Policy Office.


  1. Aharonson O, Hayes AG, Lunine JI, Lorenz RD, Allison MD, Elachi C (2009) An asymmetric distribution of lakes on Titan as a possible consequence of orbital forcing. Nat Geosci 2(12):851–854. CrossRefGoogle Scholar
  2. Atreya SK, Adams EY, Niemann HB, Demick-Montelara JE, Owen TC, Fulchignoni M, Ferri F, Wilson EH (2006) Titan’s methane cycle. Planet Space Sci 54(12):1177–1187. CrossRefGoogle Scholar
  3. Baretta-Bekker HJ, Duursma EK, Kuipers BR (1998) Encyclopedia of marine sciences. Springer Science & Business MediaGoogle Scholar
  4. Bernard PE, Deleersnijder E, Legat V, Remacle JF (2008) Dispersion analysis of discontinuous Galerkin schemes applied to Poincaré, Kelvin and Rossby waves. J Sci Comput 34(1):26–47. CrossRefGoogle Scholar
  5. Brown RH, Soderblom LA, Soderblom JM, Clark RN, Jaumann R, Barnes JW, Sotin C, Buratti B, Baines KH, Nicholson PD (2008) The identification of liquid ethane in Titan’s Ontario Lacus. Nature 454 (7204):607–610. CrossRefGoogle Scholar
  6. Charnay B, Barth E, Rafkin S, Narteau C, Lebonnois S, Rodriguez S, Du Pont SC, Lucas A (2015) Methane storms as a driver of Titan’s dune orientation. Nat Geosci 8(5):362. CrossRefGoogle Scholar
  7. Cordier D, Mousis O, Lunine JI, Lavvas P, Vuitton V (2009) An estimate of the chemical composition of Titan’s lakes. Astrophys J Lett 707(2):L128. CrossRefGoogle Scholar
  8. Cornet T, Bourgeois O, Le Mouélic S, Rodriguez S, Gonzalez TL, Sotin C, Tobie G, Fleurant C, Barnes J, Brown R et al (2012) Geomorphological significance of Ontario Lacus on Titan: integrated interpretation of cassini VIMS, ISS and RADAR data and comparison with the Etosha Pan (Namibia). Icarus 218 (2):788–806. CrossRefGoogle Scholar
  9. Coyette A, Baland RM, Van Hoolst T (2018) Variations in rotation rate and polar motion of a non-hydrostatic Titan. Icarus 307:83–105. CrossRefGoogle Scholar
  10. De Jong M, Battjes J (2004) Low-frequency sea waves generated by atmospheric convection cells. J Geophys Res-Oceans 109:C1. Google Scholar
  11. Dermott SF, Sagan C (1995) Tidal effects of disconnected hydrocarbon seas on Titan. Nature 374 (6519):238–240. CrossRefGoogle Scholar
  12. Geuzaine C, Remacle JF (2009) Gmsh: a 3-d finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Methods Eng 79(11):1309–1331. CrossRefGoogle Scholar
  13. Hartwig JW, Colozza A, Lorenz RD, Oleson S, Landis G, Schmitz P, Paul M, Walsh J (2016) Exploring the depths of Kraken Mare–power, thermal analysis, and ballast control for the Saturn Titan submarine. Cryogenics 74:31–46. CrossRefGoogle Scholar
  14. Hayes AG (2016) The lakes and seas of Titan. Annu Rev Earth Pl Sc, 44Google Scholar
  15. Hayes AG, Aharonson O, Callahan P, Elachi C, Gim Y, Kirk RL, Lewis K, Lopes R, Lorenz RD, Lunine JI et al (2008) Hydrocarbon lakes on Titan: distribution and interaction with a porous regolith. Geophys Res Lett 35:9. CrossRefGoogle Scholar
  16. Hayes AG, Wolf AS, Aharonson O, Zebker H, Lorenz RD, Kirk RL, Paillou P, Lunine JI, Wye L, Callahan P et al (2010) Bathymetry and absorptivity of Titan’s Ontario Lacus. J Geophys Res-Planet 115:E9. CrossRefGoogle Scholar
  17. Hayes AG, Aharonson O, Lunine JI, Kirk RL, Zebker HA, Wye LC, Lorenz RD, Turtle EP, Paillou P, Mitri G et al (2011) Transient surface liquid in Titan’s polar regions from Cassini. Icarus 211 (1):655–671. CrossRefGoogle Scholar
  18. Hayes AG, Lorenz RD, Lunine JI (2018) A post-cassini view of Titan’s methane-based hydrologic cycle. Nat Geosci 11:306–313. CrossRefGoogle Scholar
  19. Hussmann H, Choblet G, Lainey V, Matson DL, Sotin C, Tobie G, Van Hoolst T (2010) Implications of rotation, orbital states, energy sources, and heat transport for internal processes in icy satellites. Space Sci Rev 153(1–4):317–348. CrossRefGoogle Scholar
  20. Jones E, Oliphant T, Peterson P, et al. (2001) SciPy: open source scientific tools for Python. [Online; accessed May 2018]
  21. Lebonnois S, Burgalat J, Rannou P, Charnay B (2012) Titan global climate model: a new 3-dimensional version of the IPSL Titan GCM. Icarus 218(1):707–722. CrossRefGoogle Scholar
  22. Lorenz RD (1994) Crater lakes on Titan: rings, horseshoes and bullseyes. Planet Space Sci 42(1):1–4. CrossRefGoogle Scholar
  23. Lorenz RD, Tokano T, Newman CE (2012) Winds and tides of Ligeia Mare, with application to the drift of the proposed time TiME (Titan Mare Explorer) capsule. Planet Space Sci 60(1):72–85. CrossRefGoogle Scholar
  24. Lorenz RD, Turtle EP, Barnes JW, Trainer MG, Adams DS, Hibbard KE, Sheldon CZ, Zacny K, Peplowski PN, Lawrence DJ et al (2018) Dragonfly: a rotorcraft lander concept for scientific exploration at Titan. Johns Hopkins APL Technical DigestGoogle Scholar
  25. Lunine JI, Hayes A, Aharonson O, Mitri G, Lorenz R, Stofan E, Wall S, Elachi C, Team CR et al (2009) Evidence for liquid in Ontario Lacus (Titan) from Cassini-observed changes. In: AAS/Division for planetary sciences meeting abstracts# 41, vol 41Google Scholar
  26. Mastrogiuseppe M, Poggiali V, Hayes A, Lorenz R, Lunine J, Picardi G, Seu R, Flamini E, Mitri G, Notarnicola C et al (2014) The bathymetry of a Titan sea. Geophys Res Lett 41(5):1432–1437. CrossRefGoogle Scholar
  27. Mastrogiuseppe M, Hayes A, Poggiali V, Seu R, Lunine JI, Hofgartner J (2016) Radar sounding using the Cassini altimeter: waveform modeling and Monte Carlo approach for data inversion of observations of Titan’s seas. IEEE T Geosci Remote 54(10):5646–5656. CrossRefGoogle Scholar
  28. Mastrogiuseppe M, Hayes AG, Poggiali V, Lunine JI, Lorenz R, Seu R, Le Gall A, Notarnicola C, Mitchell KL, Malaska M et al (2018) Bathymetry and composition of Titan’s Ontario Lacus derived from Monte Carlo-based waveform inversion of Cassini RADAR altimetry data. Icarus 300:203–209. CrossRefGoogle Scholar
  29. Merian J (1828) Ueber die bewegung tropfbarer flüssigkeiten in gefässen [on the motion of drippable liquids in containers]. PhD thesis PhD thesis. Basel, SchweighauserGoogle Scholar
  30. Mitchell JL, Ádámkovics M, Caballero R, Turtle EP (2011) Locally enhanced precipitation organized by planetary-scale waves on Titan. Nat Geosci 4:589–592. CrossRefGoogle Scholar
  31. Mitri G, Coustenis A, Fanchini G, Hayes AG, Iess L, Khurana K, Lebreton JP, Lopes RM, Lorenz RD, Meriggiola R et al (2014) The exploration of Titan with an orbiter and a lake probe. Planet Space Sci 104:78–92. CrossRefGoogle Scholar
  32. Porco CC, West RA, Squyres S, Mcewen A, Thomas P, Murray CD, Delgenio A, Ingersoll AP, Johnson TV, Neukum G et al (2004) Cassini imaging science: instrument characteristics and anticipated scientific investigations at Saturn. Space Sci Rev 115(1-4):363–497. CrossRefGoogle Scholar
  33. Rodriguez S, Le Mouélic S, Rannou P, Sotin C, Brown R (2013) Six years of continuous observation of Titan cloud activity with Cassini/VIMS. In: SF2A-2013: Proceedings of the annual meeting of the French society of astronomy and astrophysics, pp 71–74Google Scholar
  34. Sagan C, Dermott SF (1982) The tide in the seas of Titan. Nature 300(5894):731–733. CrossRefGoogle Scholar
  35. Sauter S, Wittum G (1992) A multigrid method for the computation of eigenmodes of closed water basins. Impact Comput Sci Eng 4(2):124–152. CrossRefGoogle Scholar
  36. Sotin C, Hayes AG, Malaska MJ, Nimmo F, Trainer M, Mastrogiuseppe M, Soderblom JM, Tortora P, Hofgartner JD, Aharonson O, Barnes JW, Hodyss R, Iess L, Kirk RL, Lavvas P, Lorenz RD, Lunine JI, Mazarico E, McEwen AS, Neish C, Nixon CA, Turtle EP, Vuitton V, Yelle R (2017) Oceanus: a new frontiers orbiter to study Titan’s potential habitability. In: 48th Lunar and planetary science conference, lunar and planetary science conference, vol 48, p 2306Google Scholar
  37. Stofan ER, Elachi C, Lunine JI, Lorenz RD, Stiles B, Mitchell KL, Ostro S, Soderblom L, Wood C, Zebker H et al (2007) The lakes of Titan. Nature 445(7123):61–64. CrossRefGoogle Scholar
  38. Tokano T (2010) Simulation of tides in hydrocarbon lakes on Saturn’s moon Titan. Ocean Dyn 60(4):803–817. CrossRefGoogle Scholar
  39. Tokano T, Lorenz RD (2015) Wind-driven circulation in Titan’s seas. J Geophys Res-Planet 120(1):20–33. CrossRefGoogle Scholar
  40. Tokano T, Lorenz RD, Van Hoolst T (2014) Numerical simulation of tides and oceanic angular momentum of Titan’s hydrocarbon seas. Icarus 242:188–201. CrossRefGoogle Scholar
  41. Turtle E, Perry J, Barbara J, Del Genio A, Rodriguez S, Le Mouélic S, Sotin C, Lora J, Faulk S, Corlies P et al (2018) Titan’s meteorology over the Cassini mission: evidence for extensive subsurface methane reservoirs. Geophys Res Lett 45(11):5320–5328. CrossRefGoogle Scholar
  42. Turtle EP, Perry JE, Hayes AG, McEwen AS (2011) Shoreline retreat at Titan’s Ontario Lacus and Arrakis Planitia from Cassini imaging science subsystem observations. Icarus 212(2):957–959. CrossRefGoogle Scholar
  43. Ventura B, Notarnicola C, Casarano D, Posa F, Hayes AG, Wye L (2012) Electromagnetic models and inversion techniques for Titan’s Ontario Lacus depth estimation from Cassini RADAR data. Icarus 221 (2):960–969. CrossRefGoogle Scholar
  44. Vienne A, Duriez L (1991) A general theory of motion for the eight major satellites of Saturn. II-Short-period perturbations. Astron Astrophys 246:619–633Google Scholar
  45. Vienne A, Duriez L (1992) A general theory of motion for the eight major satellites of Saturn. III-Long-period perturbations. Astron Astrophys 257:331–352Google Scholar
  46. Vienne A, Duriez L (1995) TASS1 6: Ephemerides of the major Saturnian satellites. Astron Astrophys 297:588Google Scholar
  47. Vincent D, Karatekin Ö, Vallaeys V, Hayes AG, Mastrogiuseppe M, Notarnicola C, Dehant V, Deleersnijder E (2016) Numerical study of tides in Ontario Lacus, a hydrocarbon lake on the surface of the Saturnian moon Titan. Ocean Dyn 66(4):461–482. CrossRefGoogle Scholar
  48. Vincent D, Karatekin Ö, Lambrechts J, Lorenz RD, Dehant V, Deleersnijder É (2018) A numerical study of tides in Titan’s northern seas, Kraken and Ligeia Maria. Icarus 310:105–126. CrossRefGoogle Scholar
  49. Wall S, Hayes AG, Bristow C, Lorenz RD, Stofan ER, Lunine JI, Le Gall A, Janssen M, Lopes R, Wye L et al (2010) Active shoreline of Ontario Lacus, Titan: a morphological study of the lake and its surroundings. Geophys Res Lett 37(5):L05, 202. CrossRefGoogle Scholar
  50. Webb D (2013) On the shelf resonances of the English Channel and Irish Sea. Ocean Sci 9(4):731–744. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Mechanics, Materials and Civil Engineering (IMMC)Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Royal Observatory of BelgiumBruxellesBelgium
  3. 3.Department of AstronomyUniversity of MarylandCollege ParkUSA
  4. 4.Earth and Life Institute (ELI)Université catholique de LouvainLouvain-la-NeuveBelgium
  5. 5.Institute of Mechanics, Materials and Civil Engineering (IMMC) & Earth and Life Institute (ELI)Université catholique de LouvainLouvain-la-NeuveBelgium
  6. 6.Delft Institute of Applied Mathematics (DIAM)Delft University of TechnologyDelftThe Netherlands

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