Geophysical and Astrophysical Fluid Dynamics

Abstract:

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh–Bénard convection in a reduced Rayleigh number range $1.3\le Ra/Ra_{c}\le 83.1$ . Under slow rotations ( $Ra\approx 80\,Ra_{c}$ ), the vortices are distributed randomly, which is manifested by the size distribution of the Voronoi cells of the vortex centres being a standard $\varGamma$ distribution. The vortices exhibit Brownian-type horizontal motion in the parameter range $Ra\gtrsim 10\,Ra_{c}$ . The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ( $4\,Ra_{c}\le Ra\lesssim 10\,Ra_{c}$ ), the centrifugal force leads to radial vortex motions, i.e. warm cyclones (cold anticyclones) moving towards (outwards from) the rotation axis. The horizontal scale of the vortices decreases with decreasing $Ra/Ra_c$ , and the size distribution of their Voronoi cells deviates from the $\varGamma$ distribution. In the rapidly rotating regime ( $1.6\,Ra_{c}\le Ra\le 4\,Ra_{c}$ ), the vortices are densely distributed. The hydrodynamic interaction of neighbouring vortices results in the formation of vortex clusters. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the outward motion of the strong anticyclones, and the radial velocity of the anticyclones is enhanced. The radial mobility of isolated vortices, scaled by their vorticity strength, is shown to be a simple power function of the Froude number. For all flow regimes studied, we show that the number of vortices with a lifespan greater than $t$ decreases exponentially as $\exp ({-t/{\tau }})$ for large time, where $\tau$ represents the characteristic lifetime of long-lived vortices.

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.