Finite-Amplitude Upper-Ocean Baroclinic Instability

一种被广泛使用的描述局限于海洋最上部的过程的垂直构形，比如说在温跃层之上，是减重力构形。PI有助于证明，存在的自由移动的界面与静止的，无限深的流体改变了经典的水平刚性边界斜压不稳定的范例在许多方面。特别是，自由边界效应的纳入提供了理论支持，声称斜压不稳定波在控制混合层再分层和深海对流方面发挥了核心作用。哈密尔顿不稳定性理论的一个基本方面是，它提供了一种方法来设定这些波的振幅的先验界限。在构造涡旋闭合中，它们的精确性和实用性的研究还有待进一步探索。此外，它是未知的程度，关闭模型的预测同意与先验的不稳定性饱和界限，使初始扰动的性质没有假设。目标.拟议的研究工作将集中在评估基于守恒定律的不稳定饱和度严格上限的准确性上，特别是在海洋表面附近的薄层中。这项研究将探讨使用先验信息的不稳定性饱和度在建设一个瞬态涡流参数化。拟议的研究将进行使用汉密尔顿海洋模型，其中，拥有李雅普诺夫稳定平衡，允许推导的先验界限onthe增长的扰动不稳定状态。这些是系统遍历性的界限，可以用波拟能方差定义的度量来量化。将导出父无穷维Hamilton方程组的结构保持低阶近似，以执行弱（和不那么弱）非线性分析，这将对有限振幅不稳定性的基本物理有更深入的了解。“结构表示近似”被理解为保留了无限维系统的显式对称性，即通过Noether定理导致能量和动量守恒定律的那些对称性，以及尽可能好的隐式对称性，这与Casimir不变量的存在有关。“低阶近似”被理解为包括允许描述非线性不稳定性的某些方面的那些（傅立叶）分量的有限维模型。严格的界限将用于量化这些方面的表现。除了扩展低维模型分析的有效性外，还将进行直接非线性数值模拟，以评估这些饱和边界作为涡流振幅预测因子的准确性。这些模拟将使用最近提出的几何积分方法进行。超出保守理论的界限的鲁棒性将通过执行强制耗散模拟来研究。这项研究还将寻求使用的界限，以发展一个涡流封闭，预计弱非线性分析将提供指导，在执行这项任务。该项目将增加我们对海洋最上层发生的物理过程的了解，大部分生物质集中在那里，大气和海洋的耦合也通过那里发生。因此，拟议的研究对生物学和气候有影响，因此对社会有益。拟议的调查工作将有助于作为100%软钱科学家的PI的职业发展。PI是一名西班牙裔女性，这将扩大海洋科学中代表性不足的群体的参与。拟议的工作提供了有趣的可能性，以进一步研究生的教育。预算资金用于将一名博士生纳入该项目。

ABSTRACTOCE-0648284A widely used vertical configuration for describing processes confined to the uppermost part ofthe ocean, say above the thermocline, is the reduced-gravity configuration. The PI contributed to demonstrate that the presence of the freely moving interface with the quiescent, infinitely deep fluid changes the classical horizontally-rigid-boundary baroclinic instability paradigm in many respects. In particular, the incorporation of free-boundary effects provided theoretical support for the claimed central role played by baroclinic instability waves in providing controls for mixed layer re-stratification and deep-ocean convection. A fundamental aspect of Hamiltonian instability theory is that it provides means for setting a priori bounds on the amplitude of those waves. Largely unexplored remains the study of their accuracy and utility in constructing eddy closures. Furthermore, it is unknown the extent to which closure-model predictions agree with the a priori instability saturation bounds, which make no assumption on the nature of the initial perturbation. Objectives. The proposed research effort will center on making assessments of the accuracy of conservation-law-based rigorous upper bounds on instability saturation, particularly in a thin layer confined near the ocean surface. The study will explore the use of a priori information on instability saturation in the construction of a transient-eddy parametrization.Intellectual Merit. The proposed study will be carried out using Hamiltonian ocean models,which, possessing Lyapunov stable equilibria, allow the derivation of a priori bounds onthe growth of perturbations on unstable states. These are bounds on the ergodicity of thesystems, which can be quantified in terms of the metric defined by the wave-enstrophy variance.Structure-preserving low-order approximations of the parent infinite-dimensional Hamiltonianset of equations will be derived to perform weakly (and not so weakly) nonlinear analysis,which will give a deeper insight into basic physics of finite-amplitude instability. "Structurepreserving approximation" is understood to be one that preserves the explicit symmetries of the parent infinite-dimensional system, i.e. those leading to the conservation laws of energy and momentum via Noether's theorem, and as best as possible the implicit symmetries, which relate to the existence of Casimir invariants. "Low-order approximation" is understood to be a finite-dimensional model that includes those (Fourier) components that allow the description of some aspects of nonlinear instability. The rigorous bounds will be used to quantify how well these aspects are represented. In addition to extending the validity of the low-dimensional model analysis, direct nonlinear numerical simulations will be performed to make an assessment of the accuracy of these saturation bounds as predictors of eddy amplitudes. These simulations will be carried out using recently proposed geometric integration methods. The robustness of the bounds beyond conservative theory will be investigated by performing forced dissipative simulations. The study will also seek to use the bounds to develop an eddy closure; it is expected that the weakly nonlinear analysis will provide guidance in performing this task.Broader Impacts. This project will increase our knowledge of physical processes that occur inthe uppermost layer of the ocean, where most of the biomass concentrates and through whichatmosphere ocean coupling takes place. The proposed research thus has implications for biology and climate, and consequently is beneficial for society. The proposed investigation effort will contribute to the career development of the PI who is employed as a 100% soft-money scientist. The PI is a female Hispanic, which will broaden the participation of underrepresented groups in ocean sciences. The proposed work offers interesting possibilities to further the education of graduate students. Funds are budgeted to incorporate one PhD student in the project.