Numerical Methods for Layered Models of Ocean Circulation

该项目的目标是发展一般海洋环流分层（等环流）模式的数值方法。在这种模型中，纵坐标不是线性距离，而是势密度或其他相关量。当一个等压模式在垂直方向上离散化时，其效果是将海洋表示为一堆近似不混相的层。这与观测结果相一致，即海洋的上部和下部在热力学上是相互隔离的。然而，这种隔离是不完全的，并且在同型模型中，发生的交换是在建模者的控制之下的。这种类型的模型在表现海洋动力学的长期行为方面显示出很大的希望。在目前的项目中，首席研究员将开发和整合以通量形式求解动量方程的方法，其中动量而不是速度是因变量。动量公式似乎可以给出更可靠的结果，例如在层厚度趋于零的情况下，因为层界面与流体域的顶部或底部相交。这种方法在模拟海洋中的垂直输送方面也很有价值。非振荡或近非振荡平流算法将用于求解动量方程。这些方法将被分析并纳入研究者最近为控制方程的公式开发的两级时间步进算法中，其中快速和慢速时间尺度被分成单独的子系统。结果算法将在已知解行为的模型问题上进行测试。在时间允许的情况下，PI将继续在现有的海洋环流操作模型中实施和测试这些方法。在这个项目中，PI将与俄勒冈州立大学和洛斯阿拉莫斯国家实验室的海洋建模师保持定期联系。这项工作的长期目标是促进对全球气候系统的了解。了解这一系统的一个重要工具是计算机模拟，包括大气、海洋、海冰和陆地效应的耦合模型。通过这样的模拟，人们可以测试地球气候对外部强迫变化的反应，比如温室气体排放的增加。世界上的海洋储存和运输着大量的热能，因此海洋在我们的气候系统中起着至关重要的作用。当在计算机上模拟海洋环流时，人们是在用计算机获得描述流体流动演变的数学方程的近似解。本项目的目标是改进用于求解这些方程的方法。

The goal of this project is to develop numerical methods for layered (isopycnal) models of the general ocean circulation. In such models, the vertical coordinate is not linear distance, but instead is potential density or some other related quantity. When an isopycnal model is discretized in the vertical, the effect is to represent the ocean as a stack of layers that are approximately immiscible. This corresponds to the observation that the upper and lower regions of the ocean are approximately isolated thermodynamically from each other. However, this isolation is not complete, and in an isopycnal model the exchanges that do occur are under the control of the modeler. This type of model shows great promise for representing the long-term behavior of ocean dynamics. In the present project, the principal investigator will develop and incorporate methods for solving the momentum equation in a flux form for which momentum, not velocity, is the dependent variable. It appears that the momentum formulation may give more reliable results, such as in situations where layer thicknesses tend to zero because of layer interfaces intersecting the top or bottom of the fluid domain. This approach may also be valuable in modeling vertical transport in the ocean. Non-oscillatory or nearly non-oscillatory advection algorithms will be used to solve the momentum equation. Such methods will be analyzed and incorporated into a two-level time-stepping algorithm that the investigator has recently developed for formulations of the governing equations in which the fast and slow time scales are split into separate subsystems. The resulting algorithms will be tested on model problems for which the solution behavior is known. As time permits, the PI will then pursue the implementation and testing of these methods in existing, operational models of ocean circulation. During this project the PI will be in regular contact with ocean modelers at Oregon State University and at Los Alamos National Laboratory.The long-term objective of this work is to contribute to an understanding of the global climate system. An important tool towards understanding this system consists of computer simulations involving coupled models of the atmosphere, ocean, sea ice, and terrestrial effects. With such simulations one can test the response of the earth's climate to changes in external forcing, such as increased emissions of greenhouse gases. The world's oceans store and transport tremendous amounts of heat energy, so the oceans play a crucial role in our climate system. When the circulation of the ocean is simulated on a computer, one is using the computer to obtain approximate solutions to mathematical equations that describe the evolution of fluid flows. The goal of the present project is to improve the methods that are used to solve those equations.