Universality of Probability Distributions Among Two-Dimensional Turbulent Flows

We study statistical properties of two-dimensional turbulent flows. Three systems are considered: the Navier-Stokes equation, surface quasi-geostrophic flow, and a model equation for thermal convection in the Earth's mantle. Direct numerical simulations are used to determine 1-point fluctuation properties. Comparative study shows universality of probability density functions (PDFs) across different types of flow. Especially for the derivatives of the ``advected'' quantity, the shapes of the PDFs are the same for the three flows, once normalized by the average size of fluctuations. Theoretical models for the shape of PDFs are briefly discussed.Comment: 5 pages, 7 figure

CO2 Ocean Bistability on Terrestrial Exoplanets

Cycling of carbon dioxide between the atmosphere and interior of rocky planets can stabilize global climate and enable planetary surface temperatures above freezing over geologic time. However, variations in global carbon budget and unstable feedback cycles between planetary sub‐systems may destabilize the climate of rocky exoplanets toward regimes unknown in the Solar System. Here, we perform clear‐sky atmospheric radiative transfer and surface weathering simulations to probe the stability of climate equilibria for rocky, ocean‐bearing exoplanets at instellations relevant for planetary systems in the outer regions of the circumstellar habitable zone. Our simulations suggest that planets orbiting G‐ and F‐type stars (but not M‐type stars) may display bistability between an Earth‐like climate state with efficient carbon sequestration and an alternative stable climate equilibrium where CO(2) condenses at the surface and forms a blanket of either clathrate hydrate or liquid CO(2). At increasing instellation and with ineffective weathering, the latter state oscillates between cool, surface CO(2)‐condensing and hot, non‐condensing climates. CO(2) bistable climates may emerge early in planetary history and remain stable for billions of years. The carbon dioxide‐condensing climates follow an opposite trend in pCO(2) versus instellation compared to the weathering‐stabilized planet population, suggesting the possibility of observational discrimination between these distinct climate categories

CO2 ocean bistability on terrestrial exoplanets

Cycling of carbon dioxide between the atmosphere and interior of rocky planets can stabilize global climate and enable planetary surface temperatures above freezing over geologic time. However, variations in global carbon budget and unstable feedback cycles between planetary sub-systems may destabilize the climate of rocky exoplanets toward regimes unknown in the Solar System. Here, we perform clear-sky atmospheric radiative transfer and surface weathering simulations to probe the stability of climate equilibria for rocky, ocean-bearing exoplanets at instellations relevant for planetary systems in the outer regions of the circumstellar habitable zone. Our simulations suggest that planets orbiting G- and F-type stars (but not M-type stars) may display bistability between an Earth-like climate state with efficient carbon sequestration and an alternative stable climate equilibrium where CO2 condenses at the surface and forms a blanket of either clathrate hydrate or liquid CO2. At increasing instellation and with ineffective weathering, the latter state oscillates between cool, surface CO2-condensing and hot, non-condensing climates. CO2 bistable climates may emerge early in planetary history and remain stable for billions of years. The carbon dioxide-condensing climates follow an opposite trend in pCO2 versus instellation compared to the weathering-stabilized planet population, suggesting the possibility of observational discrimination between these distinct climate categories

Indication of insensitivity of planetary weathering behavior and habitable zone to surface land fraction

It is likely that unambiguous habitable zone terrestrial planets of unknown water content will soon be discovered. Water content helps determine surface land fraction, which influences planetary weathering behavior. This is important because the silicate weathering feedback determines the width of the habitable zone in space and time. Here a low-order model of weathering and climate, useful for gaining qualitative understanding, is developed to examine climate evolution for planets of various land-ocean fractions. It is pointed out that, if seafloor weathering does not depend directly on surface temperature, there can be no weathering-climate feedback on a waterworld. This would dramatically narrow the habitable zone of a waterworld. Results from our model indicate that weathering behavior does not depend strongly on land fraction for partially ocean-covered planets. This is powerful because it suggests that previous habitable zone theory is robust to changes in land fraction, as long as there is some land. Finally, a mechanism is proposed for a waterworld to prevent complete water loss during a moist greenhouse through rapid weathering of exposed continents. This process is named a "waterworld self-arrest," and it implies that waterworlds can go through a moist greenhouse stage and end up as planets like Earth with partial ocean coverage. This work stresses the importance of surface and geologic effects, in addition to the usual incident stellar flux, for habitability.Comment: 15 pages, 6 figures, accepted at Ap

Cluster Dynamics of Planetary Waves

The dynamics of nonlinear atmospheric planetary waves is determined by a small number of independent wave clusters consisting of a few connected resonant triads. We classified the different types of connections between neighboring triads that determine the general dynamics of a cluster. Each connection type corresponds to substantially different scenarios of energy flux among the modes. The general approach can be applied directly to various mesoscopic systems with 3-mode interactions, encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.Comment: 6 pages, 3 figs, EPL, publishe

Conceptual models of the climate : 2001 program of studies in geophysical fluid dynamics

In 2001, the Geophysical Fluid Dynamics Summer Study Program grappled with Conceptual Models of the Climate. Eli Tziperman (Weizman Institute), Paola Cessi (Scripps Institution of Oceanography) and Ray Pierre- Humbert (University of Chicago) provided the principal lectures. This introduction gave us all a glimpse into the complex problem of the climate, both in the present, past and future, and even on other planets. As always, the next weeks of the program were filled with many seminars from the visitors, and culminated in the fellow's reports

Increased insolation threshold for runaway greenhouse processes on Earth like planets

Because the solar luminosity increases over geological timescales, Earth climate is expected to warm, increasing water evaporation which, in turn, enhances the atmospheric greenhouse effect. Above a certain critical insolation, this destabilizing greenhouse feedback can "runaway" until all the oceans are evaporated. Through increases in stratospheric humidity, warming may also cause oceans to escape to space before the runaway greenhouse occurs. The critical insolation thresholds for these processes, however, remain uncertain because they have so far been evaluated with unidimensional models that cannot account for the dynamical and cloud feedback effects that are key stabilizing features of Earth's climate. Here we use a 3D global climate model to show that the threshold for the runaway greenhouse is about 375 W/m$^2$, significantly higher than previously thought. Our model is specifically developed to quantify the climate response of Earth-like planets to increased insolation in hot and extremely moist atmospheres. In contrast with previous studies, we find that clouds have a destabilizing feedback on the long term warming. However, subsident, unsaturated regions created by the Hadley circulation have a stabilizing effect that is strong enough to defer the runaway greenhouse limit to higher insolation than inferred from 1D models. Furthermore, because of wavelength-dependent radiative effects, the stratosphere remains cold and dry enough to hamper atmospheric water escape, even at large fluxes. This has strong implications for Venus early water history and extends the size of the habitable zone around other stars.Comment: Published in Nature. Online publication date: December 12, 2013. Accepted version before journal editing and with Supplementary Informatio

Precision Measurements of Stretching and Compression in Fluid Mixing

The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of nonlinear dynamics provide a deep theoretical basis for understanding mixing. Unfortunately, the building blocks of this theory, i.e. the fixed points and invariant manifolds of the associated Poincare map, have remained inaccessible to direct experimental study, thus limiting the insight that could be obtained. Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching and compression fields. These quantities, previously available only numerically, attain local maxima along lines coinciding with the stable and unstable manifolds, thus revealing the dynamical structures that control mixing. Contours or level sets of a passive impurity field are found to be aligned parallel to the lines of large compression (unstable manifolds) at each instant. This connection appears to persist as the onset of turbulence is approached.Comment: 5 pages, 5 figure