The dashed line represents the effective viscosity for the respon tide, both of which are numerically-derived (see Section 4.2) using the same coefficient of obliquity tide the likely dominant contributor to the ocean energy dissipation (see Sect Average kinetic energy associated with each of the tidal responses for an ocean on calculated from scaling arguments (Section 3 and Appendices E and F) and the solid lin shaded region indicates where the Reynolds number is less than 50 for this model ocean solution value (see (29)). The obliquity for Titan is taken to be the observed value (Stiles et al., 2008) and is not a theoretical Cassini state value. The gravity coefficients for the Galiean satellites are from Galileo measurements (Schubert et al., 2004) others are calculated from a hydrostatic assumption. Calculations for the quantities on the right side of the table are described in Section 5.1 measured (as opposed to calculated) quantities are indicated with ⁄. The orbital parameters are taken from JPL satellite ephemerides (). (1992) for the uranian satellites, and Thomas (2000) and Jacobson (2009) for Triton. (2006) for the saturnian satellites, Thomas (1988) and Jacobson et al. (2004) for the Galilean satellites, Thomas (2010), Zebker et al. The physical parameters on the left half of the table are taken from Schubert et al. Table 2 Satellite specific parameters used in thermal energy calculations.Of known satellites, Triton is the most likely icy satellite to have ocean tidal heating play a role in its present day thermal budget and long-term thermal evolution. Although uncertainties such as ocean thickness and satellite obliquity remain, we find that for most satellites it is unlikely that ocean tidal dissipation is important when compared to either radiogenic or solid-body tidal heating. Using these novel scalings, we calculate the ocean contribution to the overall thermal energy budgets for many of the outer Solar System satellites. Our approach is appropriate for situations in which the ocean bottom topography is much smaller than the ocean thickness.
![tidal heating tidal heating](https://i.ytimg.com/vi/3C0Lp5OwN84/maxresdefault.jpg)
In addition, we provide new scaling relations appropriate for the inclusion of ocean tidal heating in thermal–orbital evolution models. From numerical solutions to the shallow-water equations including nonlinear bottom drag, we obtain scalings for the equivalent value of Q as a function of this drag coefficient. To address this issue we adopt an approach employed in terrestrial ocean modeling, where a significant portion of tidal dissipation arises due to bottom drag, with the drag coefficient O (0.001) being relatively well-established. The corresponding tidal dissipation spans orders of magnitude depending on the value of Q assumed. A critical unknown in this previous work is what the tidal quality factor, Q, of such an ocean should be. 36, doi:10.1029/2009GL038300) suggested that obliquity tides could drive large-scale flow in the oceans of Europa and Enceladus, leading to significant heating. Abstract: Tidal heating plays a significant role in the evolution of many satellites in the outer Solar System however, it is unclear whether tidal dissipation in a global liquid ocean can represent a significant additional heat source.