Convective Generation of Equatorial Superrotation in Planetary Atmospheres

In rapidly rotating planetary atmospheres that are heated from below, equatorial superrotation can occur through convective generation of equatorial Rossby waves. If the heating from below is sufficiently strong that convection penetrates into the upper troposphere, then the convection generates equatorial Rossby waves, which can induce the equatorward angular momentum transport necessary for superrotation. This paper investigates the conditions under which the convective generation of equatorial Rossby waves and their angular momentum transport lead to superrotation. It also addresses how the strength and width of superrotating equatorial jets are controlled. In simulations with an idealized general circulation model (GCM), the relative roles of baroclinicity, heating from below, and bottom drag are explored systematically. Equatorial superrotation generally occurs when the heating from below is sufficiently strong. However, the threshold heating at which the transition to superrotation occurs increases as the baroclinicity or the bottom drag increases. The greater the baroclinicity is, the stronger the angular momentum transport out of low latitudes by baroclinic eddies of extratropical origin. This competes with the angular momentum transport toward the equator by convectively generated Rossby waves and thus can inhibit a transition to superrotation. Equatorial bottom drag damps both the mean zonal flow and convectively generated Rossby waves, weakening the equatorward angular momentum transport as the drag increases; this can also inhibit a transition to superrotation. The strength of superrotating equatorial jets scales approximately with the square of their width. When they are sufficiently strong, their width, in turn, scales with the equatorial Rossby radius and thus depends on the thermal stratification of the equatorial atmosphere. The results have broad implications for planetary atmospheres, particularly for how superrotation can be generated in giant planet atmospheres and in terrestrial atmospheres in warm climates

Contrasting responses to orbital precession on Titan and Earth

Earth and Titan exhibit contrasting atmospheric responses to orbital precession. On Earth, most (water) precipitation falls in low latitudes, and precipitation is enhanced in a hemisphere when perihelion occurs in that hemisphere's summer. On Titan, most (methane) precipitation falls in high latitudes, and precipitation is enhanced in a hemisphere when aphelion occurs in that hemisphere's summer. We use a Titan general circulation model to elucidate the dynamical reasons for these different responses to orbital precession. They arise primarily because of the different diurnal rotation rates of Titan and Earth. The slower rotation rate of Titan leads to wider Hadley cells that transport moisture into polar regions. Changes in the length of summer, rather than in the intensity of summer insolation as in Earth's tropics, then dominate the precession response of the hydrologic cycle

Scaling of Off-Equatorial Jets in Giant Planet Atmospheres

In the off-equatorial region of Jupiter’s and Saturn’s atmospheres, baroclinic eddies transport angular momentum out of retrograde and into prograde jets. In a statistically steady state, this angular momentum transfer by eddies must be balanced by dissipation, likely produced by magnetohydrodynamic (MHD) drag in the planetary interior. This paper examines systematically how an idealized representation of this drag in a general circulation model (GCM) of the upper atmosphere of giant planets modifies jet characteristics, the angular momentum budget, and the energy budget. In the GCM, Rayleigh drag at an artificial lower boundary (with mean pressure of 3 bar) is used as a simple representation of the MHD drag that the flow on giant planets experiences at depth. As the drag coefficient decreases, the eddy length scale and eddy kinetic energy increase, as they do in studies of two-dimensional turbulence. Off-equatorial jets become wider and stronger, with increased interjet spacing. Coherent vortices also become more prevalent. Generally, the jet width scales with the Rhines scale, which is of similar magnitude as the Rossby radius in the simulations. The jet strength increases primarily through strengthening of the barotropic component, which increases as the drag coefficient decreases because the overall kinetic energy dissipation remains roughly constant. The overall kinetic energy dissipation remains roughly constant presumably because it is controlled by baroclinic conversion of potential to kinetic energy in the upper troposphere, which is mainly determined by the differential solar radiation and is only weakly dependent on bottom drag and barotropic flow variations. For Jupiter and Saturn, these results suggest that the wider and stronger jets on Saturn may arise because the MHD drag on Saturn is weaker than on Jupiter, while the thermodynamic efficiencies of the atmospheres are not sensitive to the drag parameters

Constraints on Deep-seated Zonal Winds Inside Jupiter and Saturn

The atmospheres of Jupiter and Saturn exhibit strong and stable zonal winds. How deep the winds penetrate unabated into each planet is unknown. Our investigation favors shallow winds. It consists of two parts. The first part makes use of an Ohmic constraint; Ohmic dissipation associated with the planet's magnetic field cannot exceed the planet's net luminosity. Application to Jupiter (J) and Saturn (S) shows that the observed zonal winds cannot penetrate below a depth at which the electrical conductivity is about six orders of magnitude smaller than its value at the molecular-metallic transition. Measured values of the electrical conductivity of molecular hydrogen yield radii of maximum penetration of 0.96R_J and 0.86R_S, with uncertainties of a few percent of R. At these radii, the magnetic Reynolds number based on the zonal wind velocity and the scale height of the magnetic diffusivity is of order unity. These limits are insensitive to difficulties in modeling turbulent convection. They permit complete penetration along cylinders of the equatorial jets observed in the atmospheres of Jupiter and Saturn. The second part investigates how deep the observed zonal winds actually do penetrate. Truncation of the winds in the planet's convective envelope would involve breaking the Taylor-Proudman constraint on cylindrical flow. This would require a suitable nonpotential acceleration which none of the obvious candidates appears able to provide. Accelerations arising from entropy gradients, magnetic stresses, and Reynolds stresses appear to be much too weak. These considerations suggest that strong zonal winds are confined to shallow, stably stratified layers, with equatorial jets being the possible exception

Flood Routing Based on Diffusion Wave Equation Using Lattice Boltzmann Method

AbstractOne-dimensional diffusion wave equation is a simplified form of the full Saint Venant equations by neglecting the inertia terms. In this study, the Lattice Boltzmann method for the linear diffusion wave equation was developed. In order to verify the calculation accuracy of it, the analytical solution and Muskingum method were also introduced. Excellent agreement was obtained between observed data and numerical prediction. The results show that the Lattice Boltzmann method is a very competitive method for solving diffusion wave equation in terms of computational efficiency and accuracy