Wind‐induced equatorial bulge in Venus and Titan general circulation models: Implication for the simulation of superrotation

Abstract

[1] The centrifugal force associated with the superrotation in Venus' and Titan's middle atmosphere reduces the effective gravity and thereby modifies the shape of the geopotential surface, which manifests itself as an equatorial bulge. General circulation models (GCMs) based on the hydrostatic primitive equations cannot correctly represent this dynamics since the vertical component of the centrifugal force does not appear in the hydrostatic equation. Consequently, they are likely to underestimate the poleward pressure gradient force and superrotation in gradient wind balance. This effect can be accounted for in nonhydrostatic GCMs or in quasi-hydrostatic GCMs, in which the hydrostatic equation is supplemented by the vertical component of the centrifugal and Coriolis force and which do not make the shallow-atmosphere approximation. A quasi-hydrostatic GCM is shown to predict faster superrotation than a hydrostatic GCM run under otherwise identical conditions. Citation: Tokano, T. (2013), Wind-induced equatorial bulge in Venus and Titan general circulation models: Implication for the simulation of superrotation, Geophys. Res. Lett., 40,[4538][4539][4540][4541][4542][4543]

The unified model, a fully-compressible, non-hydrostatic, deep atmosphere global circulation model, applied to hot Jupiters

“…Previous attempts have been made to isolate the effect of this approximation (see for example Cho & Polichtchouk 2011). Tokano (2013 show that GCMs adopting the primitive equations do not correctly represent the dynamics of Titan's atmosphere (as well as indicating it may be problematic for Venus's atmosphere).…”

“…Tokano (2013 show that GCMs adopting the primitive equations do not correctly represent the dynamics of Titan's atmosphere (as well as indicating it may be problematic for Venus's atmosphere). Although Tokano (2013) focus on the assumption of hydrostatic equilibrium, the term they indicate is dominant, (u 2 + v 2 )/r, is neglected as part of the traditional approximation. The lack of coupling between the vertical and horizontal momentum in the HPEs is exacerbated by the adoption of vertical hydrostatic equilibrium, which neglects the vertical acceleration of fluid parcels.…”

“…We would also like to thank Tom Melvin for his expert advice. This work is supported by the European Research Council under the European Communitys Seventh Framework Programme (FP7/2007-2013 and by the Consolidated STFC grant ST/J001627/1.This work is also partly supported by the Royal Society award WM090065. The calculations for this paper were performed on the DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS, and the University of Exeter.…”

Using the UM dynamical cores to reproduce idealised 3-D flows

“…For example, Tokano (2013) shows that GCMs adopting the primitive equations do not correctly represent the dynamics of Titan's (and Venus's) atmosphere, which has a similar aspect ratio to hot Jupiters (∼ 0.1). Although Tokano (2013) focuses on the assumption of hydrostatic equilibrium, the term they indicate is dominant, (u 2 + v 2 )/r, is neglected as part of the "traditional" approximation. Kaspi et al (2009) present models of Jupiter using an adapted form of the MITgcm (Massachusetts Institute of Technology general circulation model), including the effects of a deep atmosphere.…”

Energy‐conserving finite‐difference schemes for quasi‐hydrostatic equations

“…Colin de Verdière and Schopp, 1994;Hua et al, 1997;Gerkema et al, 2008;Stewart and Dellar, 2011;Hayashi and Itoh, 2012). It is not obvious that deep-atmosphere equations are important for high-top models, but recent work by Tokano (2013) and Mayne et al (2013) suggest that it may be on Titan's atmospheric super-rotation and the long-term atmospheric circulation of hot Jupiter, respectively. Moreover, for high-top models, solving both NTEs and QHEs should be useful to disentangle the effects due to the NT Coriolis terms from those due to deep spherical geometry.…”