Advertisement

Ocean Dynamics

, Volume 66, Issue 4, pp 461–482 | Cite as

Numerical study of tides in Ontario Lacus, a hydrocarbon lake on the surface of the Saturnian moon Titan

  • David Vincent
  • Özgur Karatekin
  • Valentin Vallaeys
  • Alexander G. Hayes
  • Marco Mastrogiuseppe
  • Claudia Notarnicola
  • Véronique Dehant
  • Eric Deleersnijder
Article

Abstract

In the context of the emergence of extra-terrestrial oceanography, we adapted an existing oceanographic model, SLIM (www.climate.be/slim), to the conditions of Titan, a moon of Saturn. The tidal response of the largest southern lake at Titan’s surface, namely Ontario Lacus, is simulated. SLIM solves the 2D, depth-averaged shallow water equations on an unstructured mesh using the discontinuous Galerkin finite element method, which allows for high spatial resolution wherever needed. The impact of the wind forcing, the bathymetry, and the bottom friction is also discussed. The predicted maximum tidal range is about 0.56 m in the southern part of the lake, which is more than twice as large as the previous estimates (see Tokano, Ocean Dyn 60:(4) 803–817  10.1007/s10236-010-0285-3 (Tokano 2010)). The patterns and magnitude of the current are also markedly different from those of previous studies: the tidal motion is not aligned with the major axis of the lake and the speed is larger nearshore. Indeed, the main tidal component rotates clockwise in an exact period of one Titan day and the tidal currents can reach 0.046 ms −1 close to the shores depending on the geometry and the bathymetry. Except for these specific nearshore regions, the current speed is less than 0.02 ms −1. Circular patterns can be observed offshore, their rotational direction and size varying along the day.

Keywords

Ontario Lacus Tides Titan Finite element Numerical model Extraterrestrial oceanography 

Notes

Acknowledgments

The present study was carried out in the framework of the project “Taking up the challenge of multiscale marine modelling,” which is funded by the Communauté Française de Belgique under contract ARC 10/15-028 with the aim of developing and using SLIM (www.climate.be/slim). David Vincent is a PhD student funded by a grant of the Fonds spéciaux de recherche of the Université catholique de Louvain, Eric Deleersnijder is an honory research associate with the Belgian Fund for Scientific Research (FNRS), Özgür Karatekin is funded by the belgian PRODEX, managed by the ESA, in collaboration with th Belgian Federal Science Policy Office.

We would like to thank N. Guillaume for his previous work as a Master’s degree student at Université catholique de Louvain and the SLIM team for their support.

References

  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. doi: 10.1038/ngeo698 CrossRefGoogle Scholar
  2. Barnes JW, Brown RH, Soderblom JM, Soderblom LA, Jaumann R, Jackson B, Le Mouélic S, Sotin C, Buratti BJ, Pitman KM et al (2009) Shoreline features of Titan’s Ontario Lacus from Cassini/VIMS observations. Icarus 201(1):217–225. doi: 10.1016/j.icarus.2008.12.028 CrossRefGoogle Scholar
  3. Bernard PE, Chevaugeon N, Legat V, Deleersnijder E, Remacle JF (2007) High-order h-adaptive discontinuous galerkin methods for ocean modelling. Ocean Dyn 57(2):109–121. doi: 10.1007/s10236-006-0093-y CrossRefGoogle Scholar
  4. Beuthe M (2015) Tidal Love numbers of membrane worlds: europa, Titan, and Co. Icarus 258(57):239–266. doi: 10.1016/j.icarus.2015.06.008 CrossRefGoogle Scholar
  5. Brown RH, Baines KH, Bellucci G, Bibring JP, Buratti BJ, Capaccioni F, Cerroni P, Clark RN, Coradini A, Cruikshank DP et al (2004) The Cassini visual and infrared mapping spectrometer (VIMS) investigation. In: The Cassini-Huygens Mission. Springer, pp 111–168. doi: 10.1007/1-4020-3874-7_3
  6. 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. doi: 10.1038/nature07100 CrossRefGoogle Scholar
  7. De Brye B, De Brauwere A, Gourgue O, Kärnä T, Lambrechts J, Comblen R, Deleersnijder E (2010) A finite-element, multi-scale model of the Scheldt tributaries, river, estuary and ROFI. Coast Eng 57(9):850–863. doi: 10.1016/j.coastaleng.2010.04.001 CrossRefGoogle Scholar
  8. De Brye B, Schellen S, Sassi M, Vermeulen B, Kärnä T, Deleersnijder E, Hoitink T (2011) Preliminary results of a finite-element, multi-scale model of the Mahakam Delta (Indonesia). Ocean Dyn 61(8):1107–1120. doi: 10.1007/s10236-011-0410-y CrossRefGoogle Scholar
  9. 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. doi: 10.1088/0004-637X/707/2/L128 CrossRefGoogle Scholar
  10. Cordier D, Mousis O, Lunine JI, Lebonnois S, Rannou P, Lavvas P, Lobo LQ, Ferreira AGM (2012) Titan’s lakes chemical composition: sources of uncertainties and variability. Planet Space Sci 61(1):99–107. doi: 10.1016/j.pss.2011.05.009 CrossRefGoogle Scholar
  11. Cottini V, Nixon CA, Jennings DE, de Kok R, Teanby NA, Irwin PGJ, Flasar FM (2012) Spatial and temporal variations in Titan’s surface temperatures from Cassini CIRS observations. Planet Space Sci 60(1):62–71. doi: 10.1016/j.pss.2011.03.015 CrossRefGoogle Scholar
  12. Dermott SF, Sagan C (1995) Tidal effects of disconnected hydrocarbon seas on Titan. Nature 374 (6519):238–240. doi: 10.1038/374238a0  10.1038/374238a0 CrossRefGoogle Scholar
  13. Drews C (2013) Using wind setdown and storm surge on Lake Erie to calibrate the air-sea drag coefficient. PloS ONE 8(8):e72,510. doi: 10.1371/journal.pone.0072510 CrossRefGoogle Scholar
  14. Elachi C, Allison MD, Borgarelli L, Encrenaz P, Im E, Janssen MA, Johnson WTK, Kirk RL, Lorenz RD, Lunine JI et al (2004) Radar: the Cassini titan radar mapper. Space Sci Rev 115(1-4):71–110. doi: 10.1007/s11214-004-1438-9 CrossRefGoogle Scholar
  15. Flasar FM, Kunde VG, Abbas MM, Achterberg RK, Ade P, Barucci A, Bézard B, Bjoraker GL, Brasunas JC, Calcutt S et al (2004) Exploring the saturn system in the thermal infrared: The composite infrared spectrometer. In: The Cassini-Huygens Mission. doi: 10.1007/1-4020-3874-7_4. Springer, pp 169–297
  16. Friedson AJ, West RA, Wilson EH, Oyafuso F, Orton GS (2009) A global climate model of Titan’s atmosphere and surface. Planet Space Sci 57(14):1931–1949. doi: 10.1016/j.pss.2009.05.006 CrossRefGoogle Scholar
  17. Fulchignoni M, Ferri F, Angrilli F, Ball AJ, Bar-Nun A, Barucci MA, Bettanini C, Bianchini G, Borucki W, Colombatti G et al (2005) In situ measurements of the physical characteristics of Titan’s environment. Nature 438(7069):785–791. doi: 10.1038/nature04314 CrossRefGoogle Scholar
  18. 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. doi: 10.1002/nme.2579 CrossRefGoogle Scholar
  19. Glein CR, Shock EL (2013) A geochemical model of non-ideal solutions in the methane-ethane-propane-nitrogen-acetylene system on Titan. Geochim Cosmochim Ac 115:217–240. doi: 10.1016/j.gca.2013.03.030 CrossRefGoogle Scholar
  20. Hamblin PF (1982) On the free surface oscillations of Lake Ontario. Limnol Oceanogr 27(6):1039–1049. doi: 10.4319/lo.1982.27.6.1039 CrossRefGoogle Scholar
  21. Hanel R, Conrath B, Flasar FM, Kunde V, Maguire W, Pearl J, Pirraglia J, Samuelson R, Herath L, Allison M, Cruikshank D, Gautier D, Gierasch P, Horn L, Koppany R, Ponnamperuma C (1981) Infrared observations of the saturnian system from Voyager-1. Science 212:192–200. doi: 10.1126/science.212.4491.192 CrossRefGoogle Scholar
  22. Hayes AG (2016) The lakes and seas of Titan. Ann Rev Earth Planet Sci:44. doi: 10.1146/annurev-earth-060115-012247
  23. 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). doi: 10.1029/2008GL033409
  24. 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):E09, 009. doi: 10.1029/2009JE003557 CrossRefGoogle Scholar
  25. 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. doi: 10.1016/j.icarus.2010.08.017 CrossRefGoogle Scholar
  26. Hayes AG, Michaelides RJ, Turtle EP, Barnes JW, Soderblom JM, Masrtogiuseppe M, Lorenz RD, Kirk RL, Lunine JI (2014) The distribution and volume of Titan’s hydrocarbon lakes and seas. In: Lunar and planetary institute science conference abstracts, vol 45, p 2341Google Scholar
  27. Howarth MJ (2005) Hydrography of the Irish sea Sea6 technical report. Department of Trade and Industry offshore energy Strategic Assessment programme, UKGoogle Scholar
  28. Iess L, Jacobson RA, Ducci M, Stevenson DJ, Lunine JI, Armstrong JW, Asmar SW, Racioppa P, Rappaport NJ, Tortora P (2012) The tides of Titan. Science 337(6093):457–459. doi: 10.1126/science.1219631 CrossRefGoogle Scholar
  29. Jennings DE, Flasar FM, Kunde VG, Samuelson RE, Pearl JC, Nixon CA, Carlson RC, Mamoutkine AA, Brasunas JC, Guandique E et al (2009) Titan’s surface brightness temperatures. Astrophys J Lett 691(2):L103. doi: 10.1088/0004-637X/691/2/L103 CrossRefGoogle Scholar
  30. Jennings DE, Cottini V, Nixon CA, Flasar FM, Kunde VG, Samuelson RE, Romani PN, Hesman BE, Carlson RC, Gorius NJP et al (2011) Seasonal changes in Titan’s surface temperatures. Astrophys J Lett 737(1):L15. doi: 10.1088/2041-8205/737/1/L15 CrossRefGoogle Scholar
  31. Kärnä T, De Brye B, Gourgue O, Lambrechts J, Comblen R, Legat V, Deleersnijder E (2011) A fully implicit wetting-drying method for DG-FEM shallow water models, with an application to the Scheldt Estuary. Comput Method Appl M 200(5):509–524. doi: 10.1016/j.cma.2010.07.001 CrossRefGoogle Scholar
  32. Lambrechts J, Comblen R, Legat V, Geuzaine C, Remacle JF (2008a) Multiscale mesh generation on the sphere. Ocean Dyn 58(5-6):461–473. doi: 10.1007/s10236-008-0148-3 CrossRefGoogle Scholar
  33. Lambrechts J, Hanert E, Deleersnijder E, Bernard PE, Legat V, Remacle JF, Wolanski E (2008b) A multi-scale model of the hydrodynamics of the whole Great Barrier Reef. Estuar Coast Shelf S 79(1):143–151. doi: 10.1016/j.ecss.2008.03.016 CrossRefGoogle Scholar
  34. 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. doi: 10.1016/j.icarus.2011.11.032 CrossRefGoogle Scholar
  35. Legrand S, Deleersnijder E, Hanert E, Legat V, Wolanski E (2006) High-resolution, unstructured meshes for hydrodynamic models of the great barrier reef, Australia. Estuar, Coastal Shelf Sci 68(1):36–46. doi: 10.1016/j.ecss.2005.08.017 CrossRefGoogle Scholar
  36. Lopez Gonzalez T, Bourgeois O, Le Mouélic S, Rodriguez S, Lopez Gonzalez T, Sotin C, Tobie G, Fleurant C, Barnes JW, Brown RH 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. doi: 10.1016/j.icarus.2012.01.013 CrossRefGoogle Scholar
  37. Lorenz RD, Lunine JL, Neish CD (2011) Cyanide soap? Dissolved materials in Titan’s seas. EPSC-DPS2011 6:488Google Scholar
  38. Lorenz RD (2013) Oceanography on Saturn’s moon, Titan. In: Oceans-san diego, 2013. IEEE, pp 1–7Google Scholar
  39. Lorenz RD, Newman C, Lunine JI (2010) Threshold of wave generation on Titan’s lakes and seas: effect of viscosity and implications for Cassini observations. Icarus 207(2):932–937. doi: 10.1016/j.icarus.2009.12.004 CrossRefGoogle Scholar
  40. Lorenz RD, Tokano T, Newman CE (2012) Winds and tides of Ligeia Mare, with application to the drift of the proposed TiME (Titan Mare Explorer) capsule. Planet Space Sci 60(1):72–85. doi: 10.1016/j.pss.2010.12.009 CrossRefGoogle Scholar
  41. Lorenz RD, Kirk RL, Hayes AG, Cassini AG, Anderson YZ, Lunine JI, Tokano T, Turtle EP, Malaska MJ, Soderblom JM, Lucas A, et al (2014) A radar map of Titan seas: Tidal dissipation and ocean mixing through the throat of Kraken. Icarus 237:9–15. doi: 10.1016/j.icarus.2014.04.005 CrossRefGoogle Scholar
  42. Lunine JI, Hayes A, Aharonson O, Mitri G, Lorenz R, Stofan E, Wall S, Elachi C, Cassini Radar Team 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
  43. Luspay-Kuti A, Chevrier VF, Cordier D, Rivera-Valentin EG, Singh S, Wagner A, Wasiak FC (2015) Experimental constraints on the composition and dynamics of Titan’s polar lakes. Earth Planet Sc Lett 410:75–83. doi: 10.1016/j.epsl.2014.11.023 CrossRefGoogle Scholar
  44. 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. doi: 10.1002/2013GL058618 CrossRefGoogle Scholar
  45. McEwen A, Turtle E, Perry J, Dawson D, Fussner S, Collins G, Porco C, Johnson T, Soderblom L (2005) Mapping and monitoring the surface of Titan Bulletin of the american astronomical society, vol 37, p 739Google Scholar
  46. Mitchell KL, Barmatz MB, Jamieson CS, Lorenz RD, Lunine JI (2015) Laboratory measurements of cryogenic liquid alkane microwave absorptivity and implications for the composition of ligeia mare, titan. Geophys Res Lett 42(5):1340–1345. doi: 10.1002/2014GL059475 CrossRefGoogle Scholar
  47. National Oceanic and Atmospheric Administration (2014) Do the Great Lakes have tides. http://oceanservice.noaa.gov/facts/gltides.html, accessed: 2015-08-21
  48. Niemann HB, Atreya SK, Bauer SJ, Carignan GR, Demick JE, Frost RL, Gautier D, Haberman JA, Harpold DN, Hunten DM et al (2005) The abundances of constituents of Titan’s atmosphere from the GCMS instrument on the Huygens probe. Nature 438(7069):779–784. doi: 10.1038/nature04122 CrossRefGoogle Scholar
  49. Otto L, Zimmerman JTF, Furnes GK, Mork M, Saetre R, Becker G (1990) Review of the physical oceanography of the North Sea. Neth J Sea Res 26(2):161–238. doi: 10.1016/0077-7579(90)90091-T CrossRefGoogle Scholar
  50. 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. doi: 10.1007/s11214-004-1456-7 CrossRefGoogle Scholar
  51. Sagan C, Dermott SF (1982) The tide in the seas of Titan. Nature 300(5894):731–733. doi: 10.1038/300731a0 CrossRefGoogle Scholar
  52. Samuelson RE, Hanel RA, Kunde VG, Maguire WC (1981) Mean molecular weight and hydrogen abundance of titan’s atmosphere. Nature 292:688–693CrossRefGoogle Scholar
  53. Schneider T, Graves SDB, Schaller EL, Brown ME (2012) Polar methane accumulation and rainstorms on Titan from simulations of the methane cycle. Nature 481(7379):58–61. doi: 10.1038/nature10666 CrossRefGoogle Scholar
  54. Sears WD (1995) Tidal dissipation in oceans on Titan. Icarus 113(1):39–56. doi: 10.1006/icar.1995.1004 CrossRefGoogle Scholar
  55. Seny B, Lambrechts J, Comblen R, Legat V, Remacle JF (2013) Multirate time stepping for accelerating explicit discontinuous Galerkin computations with application to geophysical flows. Int J Numer Meth Fl 71(1):41–64. doi: 10.1002/fld.3646 CrossRefGoogle Scholar
  56. Smagorinsky J (1963) General circulation experiments with the primitive equations: I. the basic experiment. Mon Weather Rev 91(3):99–164. doi: 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2 CrossRefGoogle Scholar
  57. Sohl F, Sears WD, Lorenz RD (1995) Tidal dissipation on Titan. Icarus 115(2):278–294CrossRefGoogle Scholar
  58. Sohl F, Hussmann H, Schwentker B, Spohn T, Lorenz RD (2003) Interior structure models and tidal Love numbers of Titan. J Geophys Res-Planet 108(E12). doi: 10.1029/2003JE002044
  59. 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. doi: 10.1038/nature05438 CrossRefGoogle Scholar
  60. Tan SP, Kargel JS, Marion GM (2013) Titan’s atmosphere and surface liquid: new calculation using statistical associating fluid theory. Icarus 222(1):53–72. doi: 10.1016/j.icarus.2012.10.032 CrossRefGoogle Scholar
  61. Tan SP, Kargel JS, Jennings DE, Mastrogiuseppe M, Adidharma H, Marion GM (2015) Titan’s liquids: exotic behavior and its implications on global fluid circulation. Icarus 250:64–75. doi: 10.1016/j.icarus.2014.11.029 CrossRefGoogle Scholar
  62. Tokano T (2008) Dune-forming winds on Titan and the influence of topography. Icarus 194(1):243–262. doi: 10.1016/j.icarus.2007.10.007 CrossRefGoogle Scholar
  63. Tokano T (2009) Impact of seas/lakes on polar meteorology of Titan: simulation by a coupled GCM-sea model. Icarus 204(2):619–636. doi: 10.1016/j.icarus.2009.07.032 CrossRefGoogle Scholar
  64. Tokano T (2010) Simulation of tides in hydrocarbon lakes on Saturn’s moon Titan. Ocean Dyn 60(4):803–817. doi: 10.1007/s10236-010-0285-3 CrossRefGoogle Scholar
  65. Tokano T, Lorenz RD (2015) Wind-driven circulation in Titan’s seas. J Geophys Res-Planet 120(1):20–33. doi: 10.1002/2014JE004751 CrossRefGoogle Scholar
  66. 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. doi: 10.1016/j.icarus.2014.08.021 CrossRefGoogle Scholar
  67. 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. doi: 10.1016/j.icarus.2011.02.005 CrossRefGoogle Scholar
  68. Tyler RH (2008) Strong ocean tidal flow and heating on moons of the outer planets. Nature 456(7223):770–772. doi: 10.1038/nature07571 CrossRefGoogle Scholar
  69. 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. doi: 10.1016/j.icarus.2012.09.011 CrossRefGoogle Scholar
  70. Volkov VA, Johannessen OM, Borodachev VE, Voinov GN, Pettersson LH, Bobylev LP, Kouraev AV (2002) Polar seas oceanography: an integrated case study of the Kara Sea. Springer Science & Business MediaGoogle Scholar
  71. 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. doi: 10.1029/2009GL041821 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • David Vincent
    • 1
  • Özgur Karatekin
    • 2
  • Valentin Vallaeys
    • 1
  • Alexander G. Hayes
    • 3
  • Marco Mastrogiuseppe
    • 4
  • Claudia Notarnicola
    • 5
  • Véronique Dehant
    • 2
    • 6
  • Eric Deleersnijder
    • 7
    • 8
  1. 1.Institute of Mechanics, Materials and Civil Engineering (IMMC)Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Royal observatory of BelgiumBruxellesBelgium
  3. 3.Cornell Center for Astrophysics and Planetary ScienceCornell UniversityIthacaUSA
  4. 4.Cornell Center for Astrophysics and Planetary ScienceCornell UniversityIthacaUSA
  5. 5.Institute for Applied Remote Sensing, EURACBolzanoItaly
  6. 6.Earth and Life Institute (ELI)Université catholique de LouvainLouvain-la-NeuveBelgium
  7. 7.Institute of Mechanics, Materials and Civil Engineering (IMMC) & Earth and Life Institute (ELI)Université catholique de LouvainLouvain-la-NeuveBelgium
  8. 8.Delft Institute of Applied Mathematics (DIAM)Delft University of TechnologyDelftThe Netherlands

Personalised recommendations