Predicting the outcome of inertial instability in ocean currents and eddies

涡流的惯性不稳定性会迅速加剧径向速度梯度，引发不稳定，然后将涡流撕裂。最终，流动平衡为一组新的稳定涡流。这个过程通常会经历一个强烈的动荡阶段，从表面上看，这似乎排除了预测最终状态的任何可能性。然而，基于绝对角动量守恒，可以推导出规则，准确地显示惯性不稳定性单独作用将如何改变任何不稳定的正压流。惯性不稳定的稳定最终需要将初始不稳定区域的位涡降低至零。先前的工作已经得出了角动量混合的简单规则，可用于预测不稳定的正压涡旋将如何演化。该项目将把这些结果扩展到：包括惯性和正压不稳定性的综合影响，并考虑分层流。 将设计一种方法来预测由于惯性不稳定而导致的湍流破坏的影响以及随后由于正压不稳定而产生的曲流和涡流。这些方法将涉及一种新方法，其中速度场的微小增量变化与等密度线形状的变化以模仿不稳定性自然进展的方式联系起来。目标是能够预测任何惯性不稳定速度剖面（正压或斜压）的最终命运。这将包括不稳定性中将出现多少漩涡、它们的漩涡轮廓是什么样子、它们将带走多少能量，以及在此过程中将消散多少能量。智力价值：这项工作将增进对惯性不稳定在洋流和涡流的产生、转变和维持中所起的作用的理解。这里正在开发的方法是新的和基本的。它们应该适用于旋转流体动力学的任何分支。更广泛的影响：通过这项研究获得的结果可以对海洋模型的发展产生重要影响。小尺度不稳定性在海洋模型中并未得到解决，但它们在发展和维持大尺度洋流方面的作用非常重要。通过研究这些不稳定性，可以预测它们的影响，并可能导致海洋模型的参数化。由于海洋在控制气候方面发挥着重要作用，海洋建模的改进可以对气候研究产生重要影响。

Inertial instability of a vortex can rapidly intensify radial velocity gradients, triggering an instability that then tears the vortex apart. Eventually the flow equilibrates as a set of new stable vortices. This process often proceeds through a strong turbulent phase that on the surface, might seem to preclude any possibility of predicting the final state. However, based on absolute angular momentum conservation, it is possible to deduce rules that show exactly how inertial instability acting alone would transform any unstable barotropic flow. Stabilization of inertial instability ultimately requires reducing potential vorticity to zero in the initially unstable region. Previous work has resulted in simple rules for angular momentum mixing which can be used to predict how an unstable barotropic vortex will evolve. This project will extend these results to: include the combined effects of inertial and barotropic instabilities, and to account for stratified flows. A method will be devised to predict the effect of the turbulent breakdown due to inertial instability and the subsequent production of meanders and vortices due to barotropic instability. The approaches will involve a new method in which small incremental changes in the velocity field are linked with changes in the shape of the isopycnals in a way that mimics the natural progression of the instability. The goal is to be able to predict the ultimate fate of any inertially unstable velocity profile, barotropic or baroclinic. This will include how many vortices will emerge from the instability, what their vorticity profiles will look like, how much energy they will carry away, and how much energy will be dissipated in the process. Intellectual Merit: This work will improve understanding of the role that inertial instability plays in production, transformation and maintenance of oceanic currents and eddies. The methods being developed here are new and fundamental. They should be applicable to any branch of rotating fluid dynamics. Broader Impacts: Results obtained through this research can have an important impact on the development of ocean models. Small-scale instabilities are not resolved in ocean models, but their role in developing and maintaining large-scale currents is very important. By studying these instabilities, their effects can be predicted, and could lead to parameterizations for ocean models. Improvement in ocean modeling can have an important impact on climate research because of the essential role that the ocean plays in controlling the climate.