The growth of wind-waves in Titan’s hydrocarbon seas

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.

► Examines effect of atmospheric density, gravity on ocean wave growth.
► Applies Sverdrup–Munk and a first-principles model to explore wave growth on Titan.
► Presents probabilities of waves of a given height at Ligeia Mare.
► Provides basis for expectations for the Titan Mare Explorer (TiME) mission.
► Reviews historical development of wind-wave relationships.