Global-mean Vertical Tracer Mixing in Planetary Atmospheres II: Tidally Locked Planets

In Zhang $\&$ Showman (2018, hereafter Paper I), we developed an analytical theory of 1D eddy diffusivity $K_{zz}$ for global-mean vertical tracer transport in a 3D atmosphere. We also presented 2D numerical simulations on fast-rotating planets to validate our theory. On a slowly rotating planet such as Venus or a tidally locked planet (not necessarily a slow-rotator) such as a hot Jupiter, the tracer distribution could exhibit significant longitudinal inhomogeneity and tracer transport is intrinsically 3D. Here we study the global-mean vertical tracer transport on tidally locked planets using 3D tracer-transport simulations. We find that our analytical $K_{zz}$ theory in Paper I is validated on tidally locked planets over a wide parameter space. $K_{zz}$ strongly depends on the large-scale circulation strength, horizontal mixing due to eddies and waves and local tracer sources and sinks due to chemistry and microphysics. As our analytical theory predicted, $K_{zz}$ on tidally locked planets also exhibit three regimes In Regime I where the chemical and microphysical processes are uniformly distributed across the globe, different chemical species should be transported via different eddy diffusivity. In Regime II where the chemical and microphysical processes are non-uniform---for example, photochemistry or cloud formation that exhibits strong day-night contrast---the global-mean vertical tracer mixing does not always behave diffusively. In the third regime where the tracer is long-lived, non-diffusive effects are significant. Using species-dependent eddy diffusivity, we provide a new analytical theory of the dynamical quench points for disequilibrium tracers on tidally locked planets from first principles.Comment: Accepted at ApJ, 16 pages, 12 figures. This is the part II. Part I is "Global-mean Vertical Tracer Mixing in Planetary Atmospheres I: Theory and Fast-rotating Planets

Solute Transport In Heterogeneous Porous Media

Solute mass transport in porous media is strongly correlated with pore fluid flow. The analysis of solute transport is an effective means for studying medium heterogeneities. In this study, we discuss the effects of heterogeneity on the tracer transport. Assuming steady fluid flow, we have simulated tracer transport in various permeability heterogeneities. The results show that the tracer distribution is very closely correlated with the medium heterogeneity, and anisotropy in tracer transport exists when there is permeability lineation and large permeability contrast between low- and high-permeability regions. An important feature by which the tracer transport differs from the fluid flow field is that the tracer transport tends to smear the effects of a thin non-permeable layer (or small permeability barriers) through diffusion into the low-permeability layer, while the fluid flow cannot penetrate the low-permeability layer. In addition, the modeling results also show that the tracer transport strongly depends on the tracer source dimension, as well as the flow source dimension.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumUnited States. Dept. of Energy (Grant DE-FG02-86ER13636

Models of Passive and Reactive Tracer Motion: an Application of Ito Calculus

By means of Ito calculus it is possible to find, in a straight-forward way, the analytical solution to some equations related to the passive tracer transport problem in a velocity field that obeys the multidimensional Burgers equation and to a simple model of reactive tracer motion.Comment: revised version 7 pages, Latex, to appear as a letter to J. of Physics

Ozone and Tracer Transport Variations in the Summer Northern Hemisphere Stratosphere

Constituent observations from the Upper Atmosphere Research Satellite (UARS) in combination with estimates of the residual circulation are used to examine the transport and chemical budgets of HF, CH4 and O3 in the summer Northern Hemisphere. Budget calculations of HF, CH4 and O3 show that the transport tendency due to the residual circulation increases in magnitude and is largely opposed by eddy motions through the summer months. Ozone budget analyses show that between 100 and 31 hPa, the magnitudes of the mean circulation and eddy transport terms increase through the summer months, producing tendencies that are factors of 2 to 3 times larger than the observed ozone change in the stratosphere. Chemical loss dominates the observed ozone decrease only at the highest latitudes, poleward of about 70°N. A comparison of observations from the Total Ozone Mapping Spectrometer with UARS-calculated total ozone suggests that poleward of 50°N, between 35% and 55% of the seasonal ozone decline during the summer occurs at altitudes below 100 hPa. The overall uncertainties, associated primarily with calculations of the residual circulation and eddy transport, are relatively large, and thus prevent accurate and useful constraints on the ozone chemical rate in the lower stratosphere

Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow

Finite Larmor radius (FLR) effects on non-diffusive transport in a prototypical zonal flow with drift waves are studied in the context of a simplified chaotic transport model. The model consists of a superposition of drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. High frequency FLR effects are incorporated by gyroaveraging the ExB velocity. Transport in the direction of the density gradient is negligible and we therefore focus on transport parallel to the zonal flows. A prescribed asymmetry produces strongly asymmetric non- Gaussian PDFs of particle displacements, with L\'evy flights in one direction but not the other. For zero Larmor radius, a transition is observed in the scaling of the second moment of particle displacements. However, FLR effects seem to eliminate this transition. The PDFs of trapping and flight events show clear evidence of algebraic scaling with decay exponents depending on the value of the Larmor radii. The shape and spatio-temporal self-similar anomalous scaling of the PDFs of particle displacements are reproduced accurately with a neutral, asymmetric effective fractional diffusion model.Comment: 14 pages, 13 figures, submitted to Physics of Plasma

Enhanced tracer transport by the spiral defect chaos state of a convecting fluid

To understand how spatiotemporal chaos may modify material transport, we use direct numerical simulations of the three-dimensional Boussinesq equations and of an advection-diffusion equation to study the transport of a passive tracer by the spiral defect chaos state of a convecting fluid. The simulations show that the transport is diffusive and is enhanced by the spatiotemporal chaos. The enhancement in tracer diffusivity follows two regimes. For large Peclet numbers (that is, small molecular diffusivities of the tracer), we find that the enhancement is proportional to the Peclet number. For small Peclet numbers, the enhancement is proportional to the square root of the Peclet number. We explain the presence of these two regimes in terms of how the local transport depends on the local wave numbers of the convection rolls. For large Peclet numbers, we further find that defects cause the tracer diffusivity to be enhanced locally in the direction orthogonal to the local wave vector but suppressed in the direction of the local wave vector.Comment: 11 pages, 12 figure