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

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.

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Notes

  1. 1.

    Imaging Science Subsystem: it takes pictures in visible, near-ultraviolet, and near-infrared light. (see Porco et al, 2004).

  2. 2.

    Radar: it maps the surface of Titan using a radar imager to pierce the veil of haze. It is also used to measure heights of surface features. The synthetic aperture radar observed Titan in 13.78 GHz Ku-band with a resolution ranging from 0.35 to 1.7 km (see Elachi et al, 2004).

  3. 3.

    The largest lakes are referred to as seas (Mare) and the others as lakes (Lacus), according to the nomenclature of the International Astronomical Union. It only reflects the size of the lake.

  4. 4.

    The true anomaly of Titan, L s , is the angle between the direction of the perikron and the current position of Titan as seen from Saturn.

  5. 5.

    Visible and Infrared Mapping Spectrometer: it identifies the chemical compositions of the surfaces, atmospheres, and rings of Saturn and its moons by measuring colors of visible light and infrared energy emitted or reflected (Brown et al. 2004).

  6. 6.

    Composite Infrared Spectromter : it measures infrared energy from the surfaces, atmospheres, and rings of Saturn and its moons to study their temperature and compositions (Flasar et al. 2004).

  7. 7.

    The loss tangent is the tangent of the loss angle. It is used to parametrise the electromagnetic energy dissipation inherent to a dielectric material.

  8. 8.

    This composition is shown in Table 3 of Cordier et al. (2009). The main constituents and their lake mole fraction are C 2 H 6 (7.64 × 10−1), CH 4 (9.69 × 10−2), C 3 H 8 (7.42 × 10−2), C 4 H 8 (1.39 × 10−2), N 2 (4.9 × 10−3), Ar (5.01 × 10−6), CO (4.21 × 10−7), and H 2 (3.99 × 10−11).

  9. 9.

    In this paper, the words “maximum depth” refer to the maximum depth of the implemented bathymetry and not the maximum depth on the lake which is a function of the resolution of the data.

  10. 10.

    For interpretation of the references to color, the reader is referred to the web version of this article.

  11. 11.

    Such a wind speed is strong in comparison with Titan standards: the wind is lower than 0.7 ms −1 most of the time.

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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.

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Vincent, D., Karatekin, Ö., Vallaeys, V. et al. Numerical study of tides in Ontario Lacus, a hydrocarbon lake on the surface of the Saturnian moon Titan. Ocean Dynamics 66, 461–482 (2016). https://doi.org/10.1007/s10236-016-0926-2

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Keywords

  • Ontario Lacus
  • Tides
  • Titan
  • Finite element
  • Numerical model
  • Extraterrestrial oceanography