Surface Quasigeostrophic Turbulence : The Study of an Active Scalar

We study the statistical and geometrical properties of the potential temperature (PT) field in the Surface Quasigeostrophic (SQG) system of equations. In addition to extracting information in a global sense via tools such as the power spectrum, the g-beta spectrum and the structure functions we explore the local nature of the PT field by means of the wavelet transform method. The primary indication is that an initially smooth PT field becomes rough (within specified scales), though in a qualitatively sparse fashion. Similarly, initially 1D iso-PT contours (i.e., PT level sets) are seen to acquire a fractal nature. Moreover, the dimensions of the iso-PT contours satisfy existing analytical bounds. The expectation that the roughness will manifest itself in the singular nature of the gradient fields is confirmed via the multifractal nature of the dissipation field. Following earlier work on the subject, the singular and oscillatory nature of the gradient field is investigated by examining the scaling of a probability measure and a sign singular measure respectively. A physically motivated derivation of the relations between the variety of scaling exponents is presented, the aim being to bring out some of the underlying assumptions which seem to have gone unnoticed in previous presentations. Apart from concentrating on specific properties of the SQG system, a broader theme of the paper is a comparison of the diagnostic inertial range properties of the SQG system with both the 2D and 3D Euler equations.Comment: 26 pages, 11 figures. To appear in Chao

The Decay of Passive Scalars Under the Action of Single Scale Smooth Velocity Fields in Bounded 2D Domains : From non self similar pdf's to self similar eigenmodes

We examine the decay of passive scalars with small, but non zero, diffusivity in bounded 2D domains. The velocity fields responsible for advection are smooth (i.e., they have bounded gradients) and of a single large scale. Moreover, the scale of the velocity field is taken to be similar to the size of the entire domain. The importance of the initial scale of variation of the scalar field with respect to that of the velocity field is strongly emphasized. If these scales are comparable and the velocity field is time periodic, we see the formation of a periodic scalar eigenmode. The eigenmode is numerically realized by means of a deterministic 2D map on a lattice. Analytical justification for the eigenmode is available from theorems in the dynamo literature. Weakening the notion of an eigenmode to mean statistical stationarity, we provide numerical evidence that the eigenmode solution also holds for aperiodic flows (represented by random maps). Turning to the evolution of an initially small scale scalar field, we demonstrate the transition from an evolving (i.e., {\it non} self similar) pdf to a stationary (self similar) pdf as the scale of variation of the scalar field progresses from being small to being comparable to that of the velocity field (and of the domain). Furthermore, the {\it non} self similar regime itself consists of two stages. Both the stages are examined and the coupling between diffusion and the distribution of the Finite Time Lyapunov Exponents is shown to be responsible for the pdf evolution.Comment: 21 pages (2 col. format), 11 figures. Accepted, to appear in PR

How to decarbonize? Look to Sweden

Bringing global warming to a halt requires that worldwide net emissions of carbon dioxide be brought to essentially zero, and the sooner this occurs, the less warming our descendants for the next thousand years and more will need to adapt to. The widespread fear that the actions needed to bring this about conflict with economic growth is a major impediment to efforts to protect the climate. However, much of this fear is pointless, and the magnitude of the task, while great, is no greater than challenges human ingenuity has surmounted in the past. To light the way forward, there is a need for examining success stories in which nations have greatly reduced their carbon dioxide emissions while simultaneously maintaining vigorous growth in the standard of living. In this article, the example of Sweden is showcased. Through a combination of sensible government infrastructure policies and free-market incentives, Sweden has managed to successfully decarbonize, cutting its per capita emissions by a factor of three since the 1970s, while doubling its pre capita income and providing a wide range of social benefits. This has all be accomplished within a vigorous capitalistic framework which in many ways embodies freemarket principles better than the economy of the United States

The Importance of Ice Vertical Resolution for Snowball Climate and Deglaciation

Sea ice schemes with a few vertical levels are typically used to simulate the thermodynamic evolution of sea ice in global climate models. Here it is shown that these schemes overestimate the magnitude of the diurnal surface temperature cycle by a factor of 2–3 when they are used to simulate tropical ice in a Snowball earth event. This could strongly influence our understanding of Snowball termination, which occurs in global climate models when the midday surface temperature in the tropics reaches the melting point. A hierarchy of models is used to show that accurate simulation of surface temperature variation on a given time scale requires that a sea ice model resolve the e-folding depth to which a periodic signal on that time scale penetrates. This is used to suggest modifications to the sea ice schemes used in global climate models that would allow more accurate simulation of Snowball deglaciation

The runaway greenhouse on subNeptune waterworlds

The implications of the water vapor runaway greenhouse phenomenon for water-rich subNeptunes are developed. In particular, the nature of the post-runaway equilibration process for planets that have an extremely high water inventory is addressed. Crossing the threshold from sub-runaway to super-runaway conditions leads to a transition from equilibrated states with cold deep liquid oceans and deep interior ice-X phases to states with hot supercritical fluid interiors. There is a corresponding marked inflation of radius for a given mass, similar to the runaway greenhouse radius inflation effect noted earlier for terrestrial planets, but in the present case the inflation involves the entire interior of the planet. The calculation employs the AQUA equation of state database to simplify the internal structure calculation. Some speculations concerning the effect of $\mathrm{H_2}$ admixture, silicate cores and hot vs. cold start evolution trajectories are offered. Observational implications are discussed, though the search for the mass-radius signature of the phenomena considered is limited by degeneracies and by lack of data.Comment: Submitted to Astrophysical Journa

Wave-mean flow interactions in the atmospheric circulation of tidally locked planets

We use a linear shallow-water model to investigate the global circulation of the atmospheres of tidally locked planets. Simulations, observations, and simple models show that if these planets are sufficiently rapidly rotating, their atmospheres have an eastward equatorial jet and a hot-spot east of the substellar point. We linearize the shallow-water model about this eastward flow and its associated geostrophic height perturbation. The forced solutions of this system show that the shear flow explains the form of the global circulation, particularly the hot-spot shift and the positions of the cold standing waves on the night-side. We suggest that the eastward hot-spot shift in observations and 3D simulations of these atmospheres is caused by the zonal flow Doppler-shifting the stationary wave response eastwards, summed with the geostrophic height perturbation from the flow itself. This differs from other studies which explained the hot-spot shift as pure advection of heat from air flowing eastward from the substellar point, or as equatorial waves travelling eastwards. We compare our solutions to simulations in our climate model Exo-FMS and show that they matched the position of the eastward-shifted hot-spot, and the global wind pattern. We discuss how planetary properties affect the global circulation, and how they change observables such as the hot-spot shift or day-night contrast. We conclude that the wave-mean flow interaction be tween the stationary planetary waves and the equatorial jet is a vital part of the equilibrium circulation on tidally locked planets

Climate impact of beef: an analysis considering multiple time scales and production methods without use of global warming potentials

An analysis of the climate impact of various forms of beef production is carried out, with a particular eye to the comparison between systems relying primarily on grasses grown in pasture (‘grass-fed’ or ‘pastured’beef) and systems involving substantial use of manufactured feed requiring significant external inputs in the form of synthetic fertilizer and mechanized agriculture (‘feedlot’beef). The climate impact is evaluated without employing metrics such asCO e 2 or global warming potentials. The analysis evaluates the impact at all time scales out to 1000 years. It is concluded that certain forms of pastured beef production have substantially lower climate impact than feedlot systems. However, pastured systems that require significant synthetic fertilization, inputs from supplemental feed, or deforestation to create pasture, have substantially greater climate impact at all time scales than the feedlot and dairy-associated systems analyzed. Even the best pastured system analyzed has enough climate impact to justify efforts to limit future growth of beef production, which in any event would be necessary if climate and other ecological concerns were met by a transition to primarily pasture-based systems. Alternate mitigation options are discussed, but barring unforseen technological breakthroughs worldwide consumption at current North American per capita rates appears incompatible with a 2 °C warming target