Threshold of wave generation on Titan’s lakes and seas: Effect of viscosity and implications for Cassini observations

Motivated by radar and near-infrared data indicating that Titan’s polar lakes are extremely smooth, we consider the conditions under which a lake surface will be ruffled by wind to form capillary waves. We evaluate laboratory data on wind generation and derive, without scaling for surface tension effects, a threshold for pure methane/ethane of ~0.5–1 m/s. However, we compute the physical properties of predicted Titan lake compositions using the National Institute for Standards Technology (NIST) code and note that dissolved amounts of C3 and C4 compounds are likely to make Titan lakes much more viscous than pure ethane or methane, even without allowing for suspended particulates which would increase the viscosity further. Wind tunnel experiments show a strong dependence of capillary wave growth on liquid viscosity, and this effect may explain the apparent absence so far of waves, contrary to prior expectations that generation of gravity waves by wind should be easy on Titan. On the other hand, we note that winds over Titan lakes predicted with the TitanWRF Global Circulation Model indicate radar observations so far have in any case been when winds have been low (~0.5–0.7 m/s), possibly below the wave generation threshold, while peak winds during summer may reach 1–2 m/s. Thus observations of Titan’s northern lakes during the coming years by the Cassini Solstice mission offer the highest probability of observing wind-roughening of lake surfaces, while observations of Ontario Lacus in the south will likely continue to show it to be flat and smooth