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

Excitable media in open and closed chaotic flows

We investigate the response of an excitable medium to a localized perturbation in the presence of a two-dimensional smooth chaotic flow. Two distinct types of flows are numerically considered: open and closed. For both of them three distinct regimes are found, depending on the relative strengths of the stirring and the rate of the excitable reaction. In order to clarify and understand the role of the many competing mechanisms present, simplified models of the process are introduced. They are one-dimensional baker-map models for the flow and a one-dimensional approximation for the transverse profile of the filaments.Comment: 14 pages, 16 figure

Scalar Decay in Chaotic Mixing

I review the local theory of mixing, which focuses on infinitesimal blobs of scalar being advected and stretched by a random velocity field. An advantage of this theory is that it provides elegant analytical results. A disadvantage is that it is highly idealised. Nevertheless, it provides insight into the mechanism of chaotic mixing and the effect of random fluctuations on the rate of decay of the concentration field of a passive scalar.Comment: 35 pages, 15 figures. Springer-Verlag conference style svmult.cls (included). Published in "Transport in Geophysical Flows: Ten Years After," Proceedings of the Grand Combin Summer School, 14-24 June 2004, Valle d'Aosta, Italy. Fixed some typo

The uses of coherent structure (Dryden Lecture)

The concept of coherent structure in turbulent flow is a revolutionary idea which is being developed by evolutionary means. The main objective of this review is to list some solid achievements, showing what can be done by using the concept of coherent structure that cannot be done without it. The nature of structure is described in terms of some related concepts, including celerity, topology, and the phenomenon of coalescence and splitting of structure. The main emphasis is on the mixing layer, as the one flow whose structure is well enough understood so that technical applications are now being made in problems of mixing and chemistry. An attempt is made to identify some conceptual and experimental obstacles that stand in the way of progress in other technically important flows, particularly the turbulent boundary layer. A few comments are included about the role of structure in numerical simulations and in current work on manipulation and control of turbulent flow. Some recent developments are cited which suggest that the time is nearly right for corresponding advances to occur in turbulence modeling

Recent Developments in Understanding Two-dimensional Turbulence and the Nastrom-Gage Spectrum

Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent theoretical breakthroughs by various leading researchers. We also review efforts to reconcile the observed energy spectrum of the atmosphere (the spectrum) with the predictions of two-dimensional turbulence and quasi-geostrophic turbulence.Comment: Invited review; accepted by J. Low Temp. Phys.; Proceedings for Warwick Turbulence Symposium Workshop on Universal features in turbulence: from quantum to cosmological scales, 200

Initiation of a Marnoun Snowball Earth in a state-of-the-art atmosphere-ocean general circulation model

We study the initiation of a Marinoan Snowball Earth (~635 million years before present) with the state-of-the-art atmosphere-ocean general circulation model ECHAM5/MPI-OM. This is the most sophisticated model ever applied to Snowball initiation. A comparison with a pre-industrial control climate shows that the change of surface boundary conditions from present-day to Marinoan, including a shift of continents to low latitudes, induces a global-mean cooling of 4.6 K. Two thirds of this cooling can be attributed to increased planetary albedo, the remaining one third to a weaker greenhouse effect. The Marinoan Snowball Earth bifurcation point for pre-industrial atmospheric carbon dioxide is between 95.5 and 96% of the present-day total solar irradiance (TSI), whereas a previous study with the same model found that it was between 91 and 94% for present-day surface boundary conditions. A Snowball Earth for TSI set to its Marinoan value (94% of the present-day TSI) is prevented by doubling carbon dioxide with respect to its pre-industrial level. A zero-dimensional energy balance model is used to predict the Snowball Earth bifurcation point from only the equilibrium global-mean ocean potential temperature for present-day TSI. We do not find stable states with sea-ice cover above 55%, and land conditions are such that glaciers could not grow with sea-ice cover of 55%. Therefore, none of our simulations qualifies as a "slushball" solution. While uncertainties in important processes and parameters such as clouds and sea-ice albedo suggest that the Snowball Earth bifurcation point differs between climate models, our results contradict previous findings that Snowball Earth initiation would require much stronger forcings