Nonlinear Equilibration and Turbulent Cascades in Laboratory Studies of Baroclinic Turbulence

在背景旋转的情况下，湍流对流和稳定分层流之间的复杂相互作用对于各种工程背景、大气和海洋科学以及恒星和行星天体物理学中的广泛问题都是重要的。该项目将研究热源和散热器之间流动的性质，在强背景旋转的情况下，热源和散热器在垂直和水平方向上相互位移。在没有背景旋转的情况下，如果热源位于比汇低的高度，一般可以预期会产生强对流环流，将热量从热源直接而有力地输送到汇。然而，在背景旋转中，来自实验、模拟和地球物理流动的证据表明，由此产生的环流可能自发地分裂成对流不稳定/中性区域（温度混合得很好，并且随高度变化不大），该区域与静态稳定的所谓斜压区域相互作用（温度随高度升高，并从一侧到另一侧形成热梯度）。波浪状的不稳定性可能在斜压区内发展，这可能在稳定垂直分层和控制热量和动量的传递方面起着至关重要的作用。此外，有证据表明，如果不稳定的热量传输比其他热交换过程更快，这种稳定效应可能在非线性反馈回路中起作用，有点像恒温器，将流量调整回弱非线性/不稳定的“临界”状态-有时被称为“自组织临界”。然而，这种强烈的非线性和对流运动很难精确地建模，因此，尽管在某些工程系统和自然界中可能普遍存在，但所涉及的机制尚未得到很好的理解。因此，我们建议建立一个实验配置，该配置需要沿着水箱底部靠近外半径的环形环在旋转平台上加热圆柱形容器中的流体体，并通过靠近水箱上表面中心的圆形圆盘冷却。初步的数值模拟和实验（在我的小组以及在美国和西班牙的拟议合作者中进行）已经表明，这种流动很容易在加热或冷却边界上方/下方的对流不稳定区域之间形成静态稳定（尽管临床压力不稳定）区域。因此，我们计划通过原位热传感器和颗粒图像测速（PIV）技术的组合来测量所产生的流动的特性，包括使用热致变色液晶颗粒来同时确定流动中的速度和温度的创新可能性。这将有助于确定流动结构，流动中的热量和动量传输，并描述随着更多湍流状态的探索可能出现的任何动能级联的发展特征。这些实验的理想性质应确保所获得的结果将适用于各种学科的各种各样的问题。这样的结构可以被看作是各种工业过程的理想化（例如，在旋转半导体晶体生长熔体中，化学工程中的过程混合技术，涡轮机械中的对流流动等），以及许多地球物理和天体物理问题，在这些问题中，稳定和不稳定分层流动在背景旋转的存在下相互作用。这些包括地球的大气和气候系统及其对其辐射加热和冷却变化的响应，其他行星的大气（特别是火星、金星和气态巨行星），以及恒星内部（例如太阳内部的速斜区）。

Complex interactions between turbulent convection and stably-stratified flows in the presence of background rotation are important for a wide range of problems in various engineering contexts, in atmospheric and oceanic science, and in stellar and planetary astrophysics. This project will investigate the nature of flows between a heat source and a heat sink that are displaced both vertically and horizontally relative to each other, in the presence of strong background rotation. In the absence of background rotation, if a heat source is located at a lower altitude than the sink, one would generally expect a strongly convective circulation to result, carrying heat directly and vigorously from the source to the sink. With background rotation, however, evidence from experiments, simulations and in geophysical flows suggest that the resulting circulation may spontaneously partition itself into a convectively unstable/neutral region (where temperature becomes well mixed and doesn't vary much with height) that interacts with a statically stable, so-called baroclinic region (where temperature increases with height and develops a thermal gradient from one side to the other). Wave-like instabilities may develop within this baroclinic zone that may play a crucial role in stabilising the vertical stratification and dominating the transfer of heat and momentum where they occur. Moreover, there is evidence to suggest that if the transport of heat by the instability acts more rapidly than other heat exchange processes, this stabilizing effect may act within a nonlinear feedback loop, somewhat like a thermostat, adjusting the flow back towards a weakly nonlinear/unstable 'critical' state - sometimes referred to as 'self-organized criticality'. Such strongly nonlinear and convective motions are difficult to model accurately, however, so the mechanisms involved, though probably ubiquitous in certain engineering systems and in nature, are not well understood.We therefore propose to set up an experimental configuration which entails heating a body of fluid in a cylindrical container on a rotating platform along an annular ring at the bottom of the tank close to the outer radius, and cooling it through a circular disk near the centre of the tank at the upper surface. Preliminary numerical simulations and experiments (carried out in my group and with proposed collaborators in the USA and Spain) already suggest that such flows will readily form a statically stable (though baroclinically unstable) zone between convectively unstable regions over/underlying the heated or cooled boundaries. We therefore plan to measure the characteristics of the resulting flows through combinations of in situ thermal sensors and particle image velocimetry (PIV) techniques, including the innovative possibility of using thermochromic liquid crystal particles to determine velocities and temperatures simultaneously within the flow. This will facilitate the determination of flow structures, heat and momentum transports within the flow, and to characterize the development of any kinetic energy cascades that may emerge as more turbulent regimes are explored. The idealised nature of these experiments should ensure that the results obtained will be applicable to a wide variety of problems in various disciplines.Such a configuration may be seen as an idealisation of a variety of industrial processes (e.g. in rotating semiconductor crystal growth melts, process mixing techniques in chemical engineering, convective flows in turbomachinery etc.), and of a number of geophysical and astrophysical problems in which stably and unstably stratified flows interact in the presence of background rotation. These include the Earth's atmosphere and climate system and its response to variations in its radiative heating and cooling, other planetary atmospheres (notably Mars, Venus and the gas giant planets), and in stellar interiors (e.g. the tachocline region within the Sun).