Geophysical and Astrophysical Fluid Dynamics

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.

Abstract:

Recent Juno microwave observations have revealed puzzling features of Jupiter’s ammonia distribution, including an ammonia-poor layer extending down to levels of tens of bars outside the equatorial region to at least ±40° [Li et al. 2017]. Guillot et al. [2020] showed that ammonia-rich hail, or “mushballs”, formed during a powerful thunderstorm, can efficiently transport ammonia to the deeper atmosphere and hence could cause the observed ammonia depletion. However, this mechanism has not been tested in numerical simulations in which convective events are self-consistently determined. We have developed a simple parameterization scheme for the mushball process and implemented it into a Jupiter GCM [Young et al. 2019] that includes the following relevant parameterizations: a simple cloud microphysics model for water and ammonia, a water moist convection scheme that transports ammonia as a passive tracer, a dry convection scheme, and a two-stream, semi-grey radiative transfer scheme. In the two-dimensional setup of the aforementioned GCM, we show that mushball precipitation can produce an ammonia depletion qualitatively similar to the Juno observations.We present our preliminary results in three-dimensional simulations, in which a Jupiter-like zonal jet profile emerges spontaneously. We will show the role of different processes, including the mushball process, moist convection and meridional circulation in shaping ammonia distribution. Further, we compare our model output with Juno MWR result, and discuss the implication to future observations.

Abstract:

We measure baroclinic eddy heat transport in a differentially heated rotating annulus laboratory experiment to test mesoscale ocean eddy parameterization frameworks. The differentially heated rotating annulus comprises a fluid placed between two upright coaxial cylinders which are maintained at different temperatures, usually with a cooled inner cylinder and a heated outer.  The annular tank is placed on a rotating table which provides conditions for baroclinic eddies to develop and equilibrate in different flow regimes, depending upon the imposed conditions. As the rotation speed is increased, the equilibrated flow changes from a steady or periodically varying low wavenumber pattern to a more complex, time-varying flow dominated by higher wavenumbers. With a topographic beta effect produced by conically sloping upper boundary, more complex flow regimes are observed combining zonal jets and eddies forming one or more parallel storm tracks. With this possibility to explore varied flow regimes, our experimental approach combines laboratory calorimetry and visualization measurements along with numerical simulations to derive the eddy heat transport properties. In the following, we focus on the visualisation measurement to test related assumptions and parametric dependencies for eddy transport. We first test the assumptions of a down-gradient temperature flux-gradient relationship, determining coefficients of the eddy transport tensor, and exploring scaling relations for the eddy coefficients. A clear statistical scaling is found between eddy heat fluxes and physical variables such as eddy energy, the beta effect, and the temperature contrast.