Asymptotic Solutions for Equatorial Waves on Venus

Abstract

The atmosphere of Venus exhibits equatorial planetary-scale waves that are suspected to play an important role in its complex atmospheric circulation. Due to its particularly long sidereal day (243 terrestrial days against 24 h for the Earth), the Venusian waves must be described with the momentum equations for a cyclostrophic regime, but efforts to derive analytical wave solutions have been scarce. Following a classic approach for the terrestrial quasi-geostrophic regime, I present analytical solutions for equatorial waves in the atmosphere of Venus, assuming a single layer of a homogeneous incompressible fluid with a free surface and focusing on two asymptotic cases described by the ratio of their non-dimensional frequency and zonal wavenumber. One of the dispersion relations that has been obtained describes waves on a small spatial scale propagating upstream relative to the zonal flow, which is associated with a Rossby-type wave called “centrifugal”. The solutions for the other asymptotic case were interpreted as inertio-surface waves, which describe planetary-scale waves that can propagate “upstream” and “downstream” relative to the zonal winds and have null group velocity. These new wave solutions stress relevant differences between waves in geostrophic and cyclostrophic regimes and may be applicable to Saturn’s moon, Titan, and Venus-like exoplanets.