Collaborative Research: CMG--Anti-Turbulence, Horizontal Convection and Thermalence

合作研究：CMG--抗湍流、水平对流和热力

• 批准号: 0222109
• 负责人: Neil Balmforth
• 金额: $ 22.38万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-09-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0222109&HistoricalAwards=false
• 关键词: Collaborative; Research; CMG; Anti; Turbulence

Horizontal convection refers to horizontal motions in a fluid slab caused by spatial gradients of fluid density. Rather surprisingly, theoretical arguments show that nonuniform heating or cooling at the top surface of a fluid layer is ineffective in driving the circulation. More specifically, if the only force acting on the fluid is nonuniform surface heating, and if the kinematic viscosity and thermal diffusivity are allowed to approach zero with their ratio fixed, then it can be shown that the energy dissipation per unit mass, determined by integrating over the whole volume of the fluid, goes to zero. Because no energy dissipation implies no turbulence, this is sometimes called the "anti-turbulence theorem." This result is counterintuitive. In fact, it has been thought that the main features of the global-scale ocean circulation might be accounted for by the pole-to-equator temperature gradient, but the anti-turbulence theorem seems to imply that differential heating of the surface cannot by itself drive the circulation. This proposal is motivated by the need to understand the physical processes that account for the anti-turbulence theorem and other purely mathematical constraints on horizontal convection. Implications of these constraints are that fluid motions on the smallest scales must be closely coupled to larger-scale motions as part of a linked, multiscale system. The goal is to relate the improved understanding of horizontal convection to the problem of ocean circulation. The approach consists of a combination of analytical and numerical techniques such as upper bound theory, numerical computation of equilibrium solutions using continuation methods, linear stability analysis of these equilibria, multiscale asymptotic methods, and direct numerical simulation. The work will contribute to improved modeling of the ocean circulation and hence climate. It is supported jointly by the Division of Ocean Sciences and the Division of Mathematical Sciences through the NSF Program, Research Collaborations between the Mathematical Sciences and the Geosciences (CMG).

水平对流是指由流体密度的空间梯度引起的流体板中的水平运动。相当令人惊讶的是，理论论证表明，在流体层的顶面处的不均匀加热或冷却在驱动循环方面是无效的。更具体地说，如果作用在流体上的唯一力是不均匀的表面加热，并且如果允许运动粘度和热扩散率在它们的比率固定的情况下接近零，则可以表明，通过对流体的整个体积进行积分而确定的每单位质量的能量耗散趋于零。因为没有能量耗散就意味着没有湍流，这有时被称为“反湍流定理”。“这个结果是违反直觉的。事实上，人们一直认为全球尺度海洋环流的主要特征可以用极地到赤道的温度梯度来解释，但反湍流定理似乎意味着表面的差异加热本身不能驱动环流。这一建议的动机是需要了解的物理过程，占反湍流定理和其他纯粹的数学约束水平对流。这些限制的含义是，最小尺度上的流体运动必须紧密耦合到大尺度的运动作为一个链接的，多尺度系统的一部分。目标是将水平对流的进一步理解与海洋环流问题联系起来。该方法由分析和数值技术相结合，如上限理论，数值计算的平衡解决方案，使用连续的方法，这些平衡的线性稳定性分析，多尺度渐近方法，直接数值模拟。这项工作将有助于改进海洋环流和气候的建模。它由海洋科学部和数学科学部通过NSF计划，数学科学和地球科学之间的研究合作（CMG）共同支持。