Geophysical and Astrophysical Fluid Dynamics

Abstract:

Until recently, observations of the giant planets of our Solar System were confined to sampling relatively shallow regions of their atmospheres, leaving many uncertainties as to the dynamics of deeper layers. The Cassini and Juno missions to Saturn and Jupiter, however, have begun to address these issues, for example, by measuring their gravity and magnetic fields. The results show that the zonally coherent jets and cloud bands extend to levels where the electrical conductivity of the fluid becomes significant, whereas large-scale vortices, such as the Great Red Spot, are relatively shallow but may have deep-seated roots. The polar regions also exhibit intense cyclonic vortices that, on Jupiter, arrange themselves into remarkably regular “vortex crystals.” Numerical models seem able to capture some of this complexity, but many issues remain unresolved, suggesting a need for models that can represent both deep and shallow processes sufficiently realistically to compare with observations.

Abstract:

We investigate the characteristics of equatorial waves associated with the maintenance of superrotation in the stratosphere of a Titan general circulation model. A variety of equatorial waves are present in the model atmosphere, including equatorial Kelvin waves, equatorial Rossby waves, and mixed Rossby–gravity waves. In the upper stratosphere, acceleration of superrotation is strongest around solstice and is due to interaction between equatorial Kelvin waves and Rossby-type waves in winter hemisphere midlatitudes. The existence of this "Rossby–Kelvin"-type wave appears to depend on strong meridional shear of the background zonal wind that occurs in the upper stratosphere at times away from the equinoxes. In the lower stratosphere, acceleration of superrotation occurs throughout the year and is partially induced by equatorial Rossby waves, which we speculate are generated by quasigeostrophic barotropic instability. Acceleration of superrotation is generally due to waves with phase speeds close to the zonal velocity of the mean flow. Consequently, they have short vertical wavelengths that are close to the model's vertical grid scale and therefore likely to be not properly represented. We suggest that this may be a common issue among Titan general circulation models that should be addressed by future model development.

Abstract:

This paper examines the energetics of a convective flow subject to an oscillation with a period $t_{\rm osc}$ much smaller than the convective time-scale $t_{\rm conv}$, allowing for compressibility and uniform rotation. We show that the energy of the oscillation is exchanged with the kinetic energy of the convective flow at a rate $D_R$ that couples the Reynolds stress of the oscillation with the convective velocity gradient. For the equilibrium tide and inertial waves, this is the only energy exchange term, whereas for p modes there are also exchanges with the potential and internal energy of the convective flow. Locally, $\left| D_R \right| \sim u^{\prime 2} / t_{\rm conv}$, where $u^{\prime}$ is the oscillating velocity. If $t_{\rm conv} \ll t_{\rm osc}$ and assuming mixing length theory, $\left| D_R \right|$ is $\left( \lambda_{\rm conv} / \lambda_{\rm osc} \right)^2$ smaller, where $\lambda_{\rm conv}$ and $\lambda_{\rm osc}$ are the characteristic scales of convection and the oscillation. Assuming local dissipation, we show that the equilibrium tide lags behind the tidal potential by a phase $\delta(r) \sim r \omega_{\rm osc} / \left( g(r) t_{\rm conv}(r) \right)$, where g is the gravitational acceleration. The equilibrium tide can be described locally as a harmonic oscillator with natural frequency $\left( g/r \right)^{1/2}$ and subject to a damping force $-u^{\prime}/t_{\rm conv}$. Although $\delta(r)$ varies by orders of magnitude through the flow, it is possible to define an average phase shift $\overline{\delta }$ which is in good agreement with observations for Jupiter and some of the moons of Saturn. Finally, $1 / \overline{\delta }$ is shown to be equal to the standard tidal dissipation factor.