Analytical Solution for Waves in Planets With Atmospheric Superrotation. Ii. Lamb, Surface, and Centrifugal Waves

Abstract

This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.

Six years of Venus winds at the upper cloud level from UV, visible and near infrared observations from VIRTIS on Venus Express

“…Additionally, signatures of zonal wind variations with periods of 4-5 days and amplitudes of 5-15 m s À 1 are also present in the VMC data, confirming previous findings with Pioneer Venus . Kouyama et al (2013) found a variation of the cloud-tracked zonal velocity of $20 m s À 1 with a timescale of about 255 days (though this was not confirmed by Khatuntsev et al with a larger data sample) and recently interpreted as a centrifugal wave (Peralta et al, 2014b). Khatuntsev et al (2013) also present a preliminary analysis of near-IR images obtained over 10 orbits and measured using manual tracking resulting in a mean circulation of 70-80 m s À 1 at low latitudes and decreasing winds at latitudes higher than 451.…”

“…These features, loosely correlated with the ultraviolet details, are generally considered to lie about 5-8 km below the ultraviolet cloud top and their motions were first studied from images obtained by the Galileo orbiter on its Venus flyby (Belton et al, 1991;Peralta et al, 2007). Although the cloud motions are a good proxy for true atmospheric motions Machado et al, 2012Machado et al, , 2014 the apparent motion of clouds can be different in regions covered by atmospheric waves which seem ubiquitous in Venus atmosphere Piccialli et al, 2014) and present different scales and physical origins (Peralta et al, 2014a(Peralta et al, , 2014b. Nevertheless, studying the cloud motions is the best-suited technique at present capable to provide a systematic long-term analysis of the atmospheric winds (zonal and meridional) and disentangle the short and long time-scales variations.…”

Venus's major cloud feature as an equatorially trapped wave distorted by the wind

“…Along with other waves' solutions previously obtained [ Peralta et al , ], our wave model could potentially be extended to other slowly rotating bodies like Titan [ Flasar et al , ] and the increasing number of extrasolar planets suspected to have, globally or locally, cyclostrophic conditions. Future improvements for this model must include Venus's meridional flow (which may improve the tilt of the dark streaks at midlatitudes), midlatitude interactions with a 5 day mode at midlatitudes in terms of centrifugal waves [ Peralta et al , ], as well as exploring the sources of excitation for these equatorial waves.…”

“…Our analytical model starts from the primitive equations for a cyclostrophic regime [ Peralta et al , ] (see Appendix A), neglecting equatorward of midlatitudes the meridional shear of the zonal wind, and incorporating the vertical shear of the zonal wind [ Schubert , ; Gierasch et al , ; Peralta et al , ]. While on the Earth, what traps atmospheric waves along the equator is the meridional variation of the Coriolis parameter f ≈ β · y (with f = 2Ω · sin φ , β = d f /d y , with Ω being Earth's angular rotation velocity and y the meridional coordinate) [ Sánchez‐Lavega , ], we find that on Venus this role is played by the centrifugal force through a centrifugal frequency [ Peralta et al , ] Ψ = ( u 0 · tan φ )/ a (where φ is the latitude, u 0 is Venus background zonal wind, and a is the planetary radius of Venus). Equivalently, Ψ is found to vary linearly between the equator and midlatitudes with (Ψ≈ β * · y with β * = ∂ Ψ/ ∂ y ) [ Peralta et al , ].…”

“…Moreover, the properties of the equatorial waves in a cyclostrophic regime like the Venusian have never been studied analytically but with complex numerical models involving a difficult interpretation of the phenomenon, and in no case make a successful comparison with the time evolution of the Y feature reported with Pioneer Venus observations [ Smith et al , ; Yamamoto and Tanaka , ; Imamura , ; Lee et al , ; Kouyama et al , ]. Most of the previous works interpret the Y feature as the combination of two modes: a Rossby mode at midlatitudes and a Kelvin mode at the equatorial region [ del Genio and Rossow , ; Imamura , ; Kouyama et al , ], although classical Rossby and Kelvin waves are not possible in cyclostrophic regimes [ Peralta et al , ], and periodograms from zonal winds obtained with Venus Express observations do not show evidence of two simultaneous modes at equator and midlatitudes but a single equatorial mode extending to midlatitudes [see Kouyama et al , , Figure 9] and with periods varying between 4 and 5 days [see Khatuntsev et al , , Table 2]. For this reason, we investigate the Kelvin‐like wave that could arise as a solution in Venus's particular conditions.…”