Synchronization and predictability in experimental fluids and climate dynamics

要彻底了解地球的环境和气候，并制定方法来预测地球未来的行为和对大气成分和外部强迫等因素变化的反应，就需要对整个地球系统进行全面考虑。这种方法将地球视为一个复杂的不同子系统的集合（例如对流层、平流层、海洋、冰冻层、陆地表面和生物圈），所有这些都通过复杂的反馈过程相互作用，并受到随时间变化的外力的影响（如日周期和年周期，以及其他较长时间尺度上的外部过程），并导致非常难以预测的复杂行为。地球系统的这种观点支撑了模拟地球现在和过去气候的现代方法，以及最近评估对这种变化的社会经济和生态反应的方法，例如NERC的QUEST计划。在像地球这样复杂的系统中，子系统之间的相互作用本身可能是高度复杂的、间歇性的和非线性的，这对建模界提出了巨大的挑战，要求准确和现实地表示。在这种情况下，知识和理解的各种动力系统之间的相互作用可能存在的非线性是至关重要的，以指导未来的发展建模策略。近年来，对非线性系统同步现象的研究在物理学、工程学和生命科学的各个领域取得了重大进展。早在1665年，克里斯蒂安·惠更斯（Christiaan Huygens）就报道了同步的第一个有记载的例子，他注意到一对摆钟，安装在一个共同的支架上，最终会以同步运动的方式一起摆动，即使它们在彼此孤立的情况下会以稍微不同的速度摆动。最近，对这种非线性频率夹带和同步的研究已经扩展到对同步的性质的更定量的理解，各种形式的不完美同步现象的识别（例如，同步发生一小段时间，然后中断，稍后才重新同步），并推广到研究耦合混沌系统的同步效应。在这个项目中，我们将在实验室中研究地球中纬度大气环流的流体动力学模拟中同步化的复杂形式的范围。放置在圆柱形容器中的流体，在围绕圆柱体的轴线旋转的同时受到内外半径之间的差异加热，将自发地产生复杂的射流和波浪状不稳定性，其在动力学上类似于组织地球上中纬度天气的射流和旋风。我们最近开发了一种装置，使我们能够将其中两个实验耦合在一起，这样我们就可以研究它们的相互作用和可能的同步行为。这在某些方面类似于气候系统中的某些反馈过程。我们计划进行广泛的研究，该系统的可能行为的范围内，测量的形式和强度的同步效应和开发新的方法来分析这些影响的时间序列的测量。然后将这些方法应用于真实的气候数据，试图探测和量化过去50-100年期间大气和海洋中的类似同步现象。在研究的后半部分，我们将集中研究已知的周期现象，时间尺度从20-60天到年际周期（大约1-3年）。

A thorough understanding of the environment and climate of the Earth, and the development of methods to predict its future behaviour and responses to changes in factors such as atmospheric composition and external forcing, requires a holistic consideration of the entire Earth system. Such an approach views the Earth in terms of a complicated collection of distinct sub-systems (the troposphere, stratosphere, oceans, cryosphere, land surface and biosphere, for example), all mutually interacting via complex feedback processes and subject to time-varying external forces (such as the diurnal and annual cycles, and other external processes on longer timescales), and leading to complex behaviour that is very difficult to predict. Such a view of the Earth System underpins modern approaches to modelling the Earth's present and past climates, and more recently also to evaluating socio-economic and ecological responses to such changes, such as in NERC's QUEST programme. In a system as complex as the Earth, interactions between sub-systems are likely themselves to be highly complex, intermittent and nonlinear, presenting enormous challenges to the modelling community to represent accurately and realistically. In this context, a knowledge and understanding of the kinds of interactions possible between dynamical systems in the presence of nonlinearity is vital to guide the future development of modelling strategies. In recent years, the study of synchronization phenomena in nonlinear systems has made a number of significant advances in various areas of physics, engineering and the life sciences. The first documented example of synchronization was reported as long ago as 1665 by Christiaan Huygens, who noted the tendency of a pair of pendulum clocks, mounted on a common support, eventually to swing together in synchronized motion, even if they would tend to swing at slightly different speeds if isolated from each other. More recently, the study of such nonlinear frequency entrainment and synchronization has been extended to a much more quantitative understanding of the nature of synchronization, the identification of various forms of imperfect synchronization phenomena (e.g. where synchronization happens for a short while and then breaks up, only to resynchronize a little later), and the generalisation to the study of synchronization effects manifest in coupled chaotic systems. In this project, we will study the range of complex forms of synchronization in a fluid dynamical analogue of the Earth's mid-latitude atmospheric circulation in the laboratory. A fluid placed in a cylindrical tank, and subject to differential heating between the inner and outer radius whilst being rotated about the axis of the cylinder, will spontaneously generate complicated jet streams and wave-like instabilities that are dynamically similar to the jet stream and cyclones that organize mid-latitude weather on the Earth. We have recently developed an apparatus that allows us to couple two of these experiments together in such a way that we can study their interaction and possible synchronization behaviour. This is analogous in some respects to certain kinds of feedback process in the climate system. We plan to carry out an extensive study of the range of possible behaviour of this system, measuring the form and strength of synchronization effects and developing new methods for analysing these effects from timeseries of measurements. These methods will then be applied to real climate data in an attempt to detect and quantify similar synchronization phenomena in the atmosphere and oceans during the past 50-100 years. For the latter part of the study we will concentrate on known cyclic phenomena on timescales ranging from 20-60 days to interannual periods (around 1-3 years).