The growth of wind-waves in Titan's hydrocarbon seas
Abstract
Ocean wave growth on Titan is considered. The classic Sverdrup-Munk theory for terrestrial wave growth is applied to Titan, and is compared with a simple energy balance model that exposes the effect of Titan's environmental parameters (air density, gravity, and fluid density). These approaches are compared with the only previously-published (semi-empirical) model (Ghafoor, N.A.-L., Zarnecki, J.C., Challenor, P., Srokosz, M.A. [2000] J. Geophys. Res. 105, 12,077-12,091, hereafter G2k), and allow the impact of various parameters such as atmospheric density to be transparently explored. Our model, like G2k, suggests fully-developed significant wave heights on Titan Hs = 0.2 U2, where U is the windspeed (SI units): in dimensionless terms this is rather close to Hs = 0.2 U2/g, a rule of thumb previously noted for terrestrial waves (we find various datasets where the prefactor varies by ∼2). It is noted that liquid and air densities affect the growth rate of waves, but not their fully-developed height: for 1 m/s winds wave amplitude reaches 0.15 m (75% of fully-developed) with a fetch of only 1 km, rather faster than predicted by G2k. Liquid viscosity has no major effect on gravity wave growth, but does influence the threshold windspeed at which gravity-capillary waves form in the first place. The model is used to develop predicted ranges for wave height to guide the design of the Titan Mare Explorer (TiME), a proposed Discovery-class mission to float a capsule on Ligeia Mare in 2023. For the expected maximum 1 m/s winds, a significant wave height of 0.2 m and wavelength of ∼4 m can be expected. Assuming that wave heights follow Rayleigh statistics as they do on Earth, then given the wave period of ∼4 s, individual waves of ∼0.6 m might be encountered over a 3 month period. For predicted Titan winds at Kraken Mare, significant wave heights may reach ∼0.6 m in the peak of summer but do not exceed the tidal amplitude at its northern end, consistent with the area around Mayda Insula being a tidal flat, while elsewhere on Kraken and Ligeia and at Ontario Lacus, shorelines may be wave- or tidally-dominated, depending on the specific location.
- Publication:
-
Icarus
- Pub Date:
- May 2012
- DOI:
- 10.1016/j.icarus.2012.03.002
- Bibcode:
- 2012Icar..219..468L