On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular

The main part of this contribution to the special issue of EJM-B/Fluids dedicated to Patrick Huerre outlines the problem of the subcritical transition to turbulence in wall-bounded flows in its historical perspective with emphasis on plane Couette flow, the flow generated between counter-translating parallel planes. Subcritical here means discontinuous and direct, with strong hysteresis. This is due to the existence of nontrivial flow regimes between the global stability threshold Re_g, the upper bound for unconditional return to the base flow, and the linear instability threshold Re_c characterized by unconditional departure from the base flow. The transitional range around Re_g is first discussed from an empirical viewpoint ({\S}1). The recent determination of Re_g for pipe flow by Avila et al. (2011) is recalled. Plane Couette flow is next examined. In laboratory conditions, its transitional range displays an oblique pattern made of alternately laminar and turbulent bands, up to a third threshold Re_t beyond which turbulence is uniform. Our current theoretical understanding of the problem is next reviewed ({\S}2): linear theory and non-normal amplification of perturbations; nonlinear approaches and dynamical systems, basin boundaries and chaotic transients in minimal flow units; spatiotemporal chaos in extended systems and the use of concepts from statistical physics, spatiotemporal intermittency and directed percolation, large deviations and extreme values. Two appendices present some recent personal results obtained in plane Couette flow about patterning from numerical simulations and modeling attempts.Comment: 35 pages, 7 figures, to appear in Eur. J. Mech B/Fluid

Dynamical systems techniques in the analysis of neural systems

As we strive to understand the mechanisms underlying neural computation, mathematical models are increasingly being used as a counterpart to biological experimentation. Alongside building such models, there is a need for mathematical techniques to be developed to examine the often complex behaviour that can arise from even the simplest models. There are now a plethora of mathematical models to describe activity at the single neuron level, ranging from one-dimensional, phenomenological ones, to complex biophysical models with large numbers of state variables. Network models present even more of a challenge, as rich patterns of behaviour can arise due to the coupling alone. We first analyse a planar integrate-and-fire model in a piecewise-linear regime. We advocate using piecewise-linear models as caricatures of nonlinear models, owing to the fact that explicit solutions can be found in the former. Through the use of explicit solutions that are available to us, we categorise the model in terms of its bifurcation structure, noting that the non-smooth dynamics involving the reset mechanism give rise to mathematically interesting behaviour. We highlight the pitfalls in using techniques for smooth dynamical systems in the study of non-smooth models, and show how these can be overcome using non-smooth analysis. Following this, we shift our focus onto the use of phase reduction techniques in the analysis of neural oscillators. We begin by presenting concrete examples showcasing where these techniques fail to capture dynamics of the full system for both deterministic and stochastic forcing. To overcome these failures, we derive new coordinate systems which include some notion of distance from the underlying limit cycle. With these coordinates, we are able to capture the effect of phase space structures away from the limit cycle, and we go on to show how they can be used to explain complex behaviour in typical oscillatory neuron models

Dynamical systems techniques in the analysis of neural systems

As we strive to understand the mechanisms underlying neural computation, mathematical models are increasingly being used as a counterpart to biological experimentation. Alongside building such models, there is a need for mathematical techniques to be developed to examine the often complex behaviour that can arise from even the simplest models. There are now a plethora of mathematical models to describe activity at the single neuron level, ranging from one-dimensional, phenomenological ones, to complex biophysical models with large numbers of state variables. Network models present even more of a challenge, as rich patterns of behaviour can arise due to the coupling alone. We first analyse a planar integrate-and-fire model in a piecewise-linear regime. We advocate using piecewise-linear models as caricatures of nonlinear models, owing to the fact that explicit solutions can be found in the former. Through the use of explicit solutions that are available to us, we categorise the model in terms of its bifurcation structure, noting that the non-smooth dynamics involving the reset mechanism give rise to mathematically interesting behaviour. We highlight the pitfalls in using techniques for smooth dynamical systems in the study of non-smooth models, and show how these can be overcome using non-smooth analysis. Following this, we shift our focus onto the use of phase reduction techniques in the analysis of neural oscillators. We begin by presenting concrete examples showcasing where these techniques fail to capture dynamics of the full system for both deterministic and stochastic forcing. To overcome these failures, we derive new coordinate systems which include some notion of distance from the underlying limit cycle. With these coordinates, we are able to capture the effect of phase space structures away from the limit cycle, and we go on to show how they can be used to explain complex behaviour in typical oscillatory neuron models

Wave breaking at high wind speeds and its effects on air-sea gas transfer

Gravity waves are ubiquitous at the surface of the ocean and play a key role in the coupled ocean-atmosphere system. These wind generated waves, for which gravity provides the restoring force, influence the kinematics and dynamics of the upper ocean and lower atmosphere. Their breaking injects turbulence into the upper ocean, generates bubble plumes and sea-spray thus transferring energy, momentum, heat and mass between the atmosphere and the ocean. In the anthropocene, with CO2 driving the warming trend and the ocean acting as the main carbon sink, it is imperative to understand the complex physical controls of air-sea gas transfer. Large uncertainties still remain under high wind speed conditions where wave breaking processes are dominant. This dissertation seeks to shed light onto the dependence of wave breaking and air-sea gas transfer on environmental parameters. It further explores process based models of air-sea gas transfer that explicitly account for the breaking related processes. Air entraining breaking waves are easily detectable as bright features on the ocean surface composed of foam and subsurface bubble plumes. These features, termed whitecaps, arise at wind speed as as low as 3 m s−1 . The whitecap coverage (W) has been recognized as a useful proxy for quantifying wave breaking related processes. It can be determined from shipboard, air-borne and satellite remote sensing. W is most commonly parameterized as a function of wind speed, but previous parameterizations display over three orders of magnitude scatter. Concurrent wave field and flux measurements acquired during the Southern Ocean Gas Exchange (SO GasEx) and the High Wind Gas exchange Study (HiWinGS) projects permitted evaluation of the dependence of W on wind speed, wave age, wave steepness, mean square slope, as well as on wave-wind and breaking Reynolds numbers. W was determined from over 600 high frequency visible imagery recordings of 20 minutes each. Wave statistics were computed from in situ and remotely sensed data as well as from a WAVEWATCH-III® hind cast. The first ship-borne estimates of W under sustained wind speeds (U10N ) of 25 m s−1 were obtained during HiWinGS. These measurements suggest that W levels off at high wind speed, not exceeding 10% when averaged over 20 minutes. Combining wind speed and wave height in the form of the wave-wind Reynolds number resulted in closely agreeing models for both datasets, individually and combined. These are also in good agreement with two previous studies. When expressing W in terms of wave field statistics only or wave age, larger scatter is observed and/or there is little agreement between SO GasEx, HiWinGS, and previously published data. The wind–speed-only parameterizations deduced from the SO GasEx and HiWinGS datasets agree closely and capture more of the observed W variability than Reynolds number parameterizations. However, these wind-speed-only models do not agree as well with previous studies than the wind-wave Reynolds numbers. The ability to quantify air-sea gas transfer hinges on parameterizations of the gas transfer velocity k. k represents physical mass transfer mechanisms and is usually parameterized as a non-linear function of wind forcing. Previous eddy-covariance measurements and models based on the global radio carbon inventory led to diverging parameterizations with both cubic and quadratic wind speed dependence. At wind speeds above 10 m s−1 these parameterizations differ considerably and measurements display large scatter. In an attempt to reduce uncertainties in k, explored empirical parameterizations that incorporate both wind speed and sea state dependence via breaking and wave-wind Reynolds numbers, were explored. Analysis of concurrent eddy covariance gas transfer and measured wave field statistics supplemented by wave model hindcasts shows for the first time that wave-related Reynold numbers collapse four open ocean datasets that have a wind speed dependence of CO2 transfer velocity ranging from lower than quadratic to cubic. Wave-related Reynolds number and wind speed show comparable performance for parametrizing DMS which, because of its higher solubility, is less affected by bubble-mediated exchange associated with wave breaking. While single parameter models may be readily used in climate studies, their application is gas specific and may be limited to select environments. Physically based parameterizations that incorporate multiple forcing factors allow to model the gas transfer of gases with differing solubility for a wide range of environmental conditions. Existing mechanistic models were tested and a novel framework to model gas transfer in the open ocean in the presence of breaking waves is put forward. This analysis allowed to update NOAA’s Coupled OceanAtmosphere Response Experiment Gas transfer algorithm (COAREG) and exposed limitation of other existing physically based parameterizations. The newly proposed mechanistic model incorporates both the turbulence and bubble mediated transfer. It is based on various statistics determined from the breaking crest length distribution (Λ(c)). Λ(c) was obtained by tracking the advancing front of breaking waves in the high frequency videos taken during HiWinGS. Testing the mechanistic model with the HiWinGS dataset shows promising results for both CO2 and DMS, though it does not perform better than COAREG. Uncertainties remain in the quantification of bubble cloud which are at the core of the formulation of the bubble mediated transfer and additional field measurements are necessary to characterize bubble plume properties in the open ocean

Up in smoke? Asia and the Pacific – The threat from climate change to human development and the environment

The human drama of climate change will largely be played out in Asia, where over 60 per cent of the world’s population, around four billion people, live. Over half of those live near the coast, making them directly vulnerable to sea-level rise. Disruption to the region’s water cycle caused by climate change also threatens the security and productivity of the food systems upon which they depend. This report looks at positive measures that are being taken – by governments, by civil society and by people themselves – to reduce the causes of climate change and to overcome its effects. Summary and overview The human drama of climate change will largely be played out in Asia, where over 60 per cent of the world’s population, around four billion people, live. Over half of those live near the coast, making them directly vulnerable to sea-level rise. Disruption to the region’s water cycle caused by climate change also threatens the security and productivity of the food systems upon which they depend. In acknowledgement, both of the key meetings in 2007 and 2008 to secure a global climate agreement will be in Asia. The latest global scientific consensus from the Intergovernmental Panel on Climate Change (IPCC) indicates that all of Asia is very likely to warm during this century. Warming will be accompanied by less predictable and more extreme patterns of rainfall, including droughts and more extreme inundations. Tropical cyclones are projected to increase in magnitude and frequency, while monsoons, around which farming systems are designed, are expected to become more temperamental in their strength and time of onset. Ironically, if certain types of industrial pollution are reduced, the temporary cooling effect that results from having blankets of smog, could lead to very rapid warming. But existing projections are already bad enough. There is growing consensus about the current challenges facing Asia and what is needed to tackle them. Many of these are elaborated in this report. There is reason to hope. There is already enough knowledge and understanding to know what the main causes of climate change are, how to reduce future climate change, and how to begin to adapt. This report looks at positive measures that are being taken – by governments, by civil society and by people themselves – to reduce the causes of climate change and to overcome its effects. It gives examples of emissions reduction; alternative water and energy supply systems; preservation of strategic ecosystems and protected areas; increasing capacity, awareness and skills for risk and disaster management; and the employment of effective regulatory and policy instruments. The challenge is clear and many of the solutions are known: the point is, to act

Complex Patterns in Extended Oscillatory Systems

Ausgedehnte dissipative Systeme können fernab vom thermodynamischen Gleichgewicht instabil gegenüber Oszillationen bzw. Wellen oder raumzeitlichem Chaos werden. Die komplexe Ginzburg-Landau Gleichung (CGLE) stellt ein universelles Modell zur Beschreibung dieser raumzeitlichen Strukturen dar. Diese Arbeit ist der theoretischen Analyse komplexer Muster gewidmet. Mittels numerischer Bifurkations- und Stabilitätsanalyse werden Instabilitäten einfacher Muster identifiziert und neuartige Lösungen der CGLE bestimmt. Modulierte Amplitudenwellen (MAW) und Super-Spiralwellen sind Beispiele solcher komplexer Muster. MAWs können in hydrodynamischen Experimenten und Super-Spiralwellen in der Belousov-Zhabotinsky-Reaktion beobachtet werden. Der Grenzübergang von Phasen- zu Defektchaos wird durch den Existenzbereich der MAWs erklärt. Mittels der selben numerischen Methoden wird Bursting vom Fold-Hopf-Typ in einem Modell der Kalziumsignalübertragung in Zellen identifiziert

From sweetwater to seawater: An environmental history of Narragansett Bay, 1636--1849

This dissertation examines environmental change on and around Narragansett Bay from first European settlement in 1636 to the dissolution of the Blackstone Canal Company in 1849. It uses one of the largest estuaries on the East Coast and one situated at the heart of early English settlement in New England as a means to write estuaries into Atlantic history. Examining the ecological and epistemological complexities that arose at the nexus of land and sea, where improvable space and the push of progress met an eternal or profound ocean, this study reframes estuaries as watery borderlands that people used but never fully subdued. In this sense, this work challenges an older historiographical tradition of progress, while it advances environmental historiography by examining not terrestrial or oceanic environments but the soggy spaces in between. A closer look at the boundary between land and sea, this study shows, provides new insights into the ways Early Modern people envisioned the boundary between humans and nature. By rewriting the history of an estuary from the ground up, so to speak, this work explores the ways people shaped a watery world and how it shaped them in return. It argues that at the confluence of sweetwater and seawater, in the mixing, muddy margins of an estuary, there developed a whole host of political, legal, and cultural ambiguities that shaped patterns of settlement, trade, resource use, and ultimately the Bay itself But much more than the passive recipient of human action, the Bay became a cultural manifestation of the people who lived along its shores, and in consequence it was shaped and reshaped to meet the changing demands of human desire

Agricultural aviation research

A compilation of papers, comments, and results is provided during a workshop session. The purpose of the workshop was to review and evaluate the current state of the art of agricultural aviation, to identify and rank potentially productive short and long range research and development areas, and to strengthen communications between research scientists and engineers involved in agricultural research. Approximately 71 individuals actively engaged in agricultural aviation research were invited to participate in the workshop. These were persons familiar with problems related to agricultural aviation and processing expertise which are of value for identifying and proposing beneficial research