Detecting barriers to transport: A review of different techniques

We review and discuss some different techniques for describing local dispersion properties in fluids. A recent Lagrangian diagnostics, based on the Finite Scale Lyapunov Exponent (FSLE), is presented and compared to the Finite Time Lyapunov Exponent (FTLE), and to the Okubo-Weiss (OW) and Hua-Klein (HK) criteria. We show that the OW and HK are a limiting case of the FTLE, and that the FSLE is the most efficient method for detecting the presence of cross-stream barriers. We illustrate our findings by considering two examples of geophysical interest: a kinematic meandering jet model, and Lagrangian tracers advected by stratospheric circulation.Comment: 15 pages, 9 figures, submitted to Physica

Graph-enhanced large language models in asynchronous plan reasoning

Planning is a fundamental property of human intelligence. Reasoning about asynchronous plans is challenging since it requires sequential and parallel planning to optimize time costs. Can large language models (LLMs) succeed at this task? Here, we present the first large-scale study investigating this question. We find that a representative set of closed and open-source LLMs, including GPT-4 and LLaMA-2, behave poorly when not supplied with illustrations about the task-solving process in our benchmark AsyncHow. We propose a novel technique called Plan Like a Graph (PLaG) that combines graphs with natural language prompts and achieves state-of-the-art results. We show that although PLaG can boost model performance, LLMs still suffer from drastic degradation when task complexity increases, highlighting the limits of utilizing LLMs for simulating digital devices. We see our study as an exciting step towards using LLMs as efficient autonomous agents. Our code and data are available at https://github.com/fangru-lin/graph-llm-asynchow-plan

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

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

Turbulent spectrum of the Earth's ozone field

The Total Ozone Mapping Spectrometer (TOMS) database is subjected to an analysis in terms of the Karhunen-Loeve (KL) empirical eigenfunctions. The concentration variance spectrum is transformed into a wavenumber spectrum, $E_c(k)$. In terms of wavenumber $E_c(k)$ is shown to be $O(k^{-2/3})$ in the inverse cascade regime, $O(k^{-2})$ in the enstrophy cascade regime with the spectral {\it knee} at the wavenumber of barotropic instability.The spectrum is related to known geophysical phenomena and shown to be consistent with physical dimensional reasoning for the problem. The appropriate Reynolds number for the phenomena is $Re\approx 10^{10}$.Comment: RevTeX file, 4 pages, 4 postscript figures available upon request from Richard Everson <[email protected]

Polygonal N-vortex arrays: A Stuart model

Published versio

Predictive use of the Maximum Entropy Production principle for Past and Present Climates

In this paper, we show how the MEP hypothesis may be used to build simple climate models without representing explicitly the energy transport by the atmosphere. The purpose is twofold. First, we assess the performance of the MEP hypothesis by comparing a simple model with minimal input data to a complex, state-of-the-art General Circulation Model. Next, we show how to improve the realism of MEP climate models by including climate feedbacks, focusing on the case of the water-vapour feedback. We also discuss the dependence of the entropy production rate and predicted surface temperature on the resolution of the model