Gravitational tidal waves in Titan's upper atmosphere

Tidal waves driven by Titan's orbital eccentricity through the time-dependent component of Saturn's gravitational potential attain nonlinear, saturation amplitudes (|T^′|>10 K, , and ) in the upper atmosphere (?500 km) due to the approximate exponential growth as the inverse square root of pressure. The gravitational tides, with vertical wavelengths of ∼100-150 km above 500 km altitude, carry energy fluxes sufficient in magnitude to affect the energy balance of the upper atmosphere with heating rates in the altitude range of 500-900 km.