Collaborative Research: Inertially Unstable Currents and Internal Waves

惯性不稳定性在气象学中得到了广泛的研究，它被认为是晴空湍流、雨带、飑线和大气重力波的来源。它在海洋学中受到的关注要少得多，这可能是因为它通常被认为只发生在反气旋（顺时针）剪切的平行流或在海洋中通常观察不到的强度的反气旋中。然而，在海洋中有许多反气旋流的观测是边缘稳定的，这表明惯性不稳定性可能是反气旋切变和反气旋涡旋维持在稳定或边缘稳定值的主要机制。惯性不稳定的判据通常被引用为罗斯比数小于-1，其中负的罗斯比数意味着反气旋流动。然而，这个判据只适用于均匀流体中的流动，如没有垂直剪切的混合层。在通常情况下，垂直剪切的分层流动也可能发生惯性不稳定，罗斯比数在-1和0之间。此外，如果垂直切变足够强，即使是Ro大于零的气旋剪切流或气旋涡旋也可能是惯性不稳定的。同样有趣的是，当理查德森数远高于四分之一时，这种不稳定性就会发生，也就是说，在与开尔文亥姆霍兹不稳定性稳定的流动中，开尔文亥姆霍兹不稳定性是海洋流动的一个控制因素。换句话说，根据众所周知的理查德森数判据是稳定的流，实际上也可能是不稳定的，因为惯性不稳定。因此，惯性不稳定性可能经常是海洋流动的一个控制因素，而没有被认识到这一点。这一更新建议将继续研究惯性不稳定性，目的是为理解惯性不稳定性在世界海洋中所起的作用提供一个基本基础。在美国国家科学基金会的资助下，研究人员进行了系统的数值研究，研究了不同的基本参数对无垂直剪切和弱垂直剪切的理想模式涡的惯性不稳定性的影响。此外，所得到的基于平面平行水平剪切流的解析模型能够解释和预测许多数值研究的基本结果。从这些调查中，现在有了进一步探索的指导方针。以前的研究将扩展到更真实的海洋涡旋模型。通过一系列的数值模拟，将研究惯性不稳定性对各种模型涡的影响，这些模型涡的基本参数范围很广。智力优势：通过开展我们对惯性不稳定性的研究，我们希望提高我们对惯性不稳定性在稳定和维持海洋洋流和漩涡中的作用的理解。更广泛的影响：作为更广泛的影响，这些研究应该为那些试图开发海洋模式参数化和确定强烈内波产生和惯性不稳定可能位置的标准的人提供指导。由于惯性不稳定性固有的小垂直尺度，它通常不被海洋模式解决。因此，模拟流可以变得并保持惯性不稳定。必须纠正这种非物理行为，以使模型中的电流保持在物理上可实现的水平，但是只有通过增加理解才能获得对不稳定性影响的适当参数化。该合作研究项目将促进与罗马大学Orlandi教授及其一名研究生的国际合作。

0525776/0526033Inertial instability has been widely studied in meteorology where it is considered a source of clearair turbulence, rain bands, squall lines and atmospheric gravity waves. It has received much lessattention in oceanography probably because it is generally thought to occur only for anticyclonically (clockwise) sheared parallel flows or anticyclones of strengths not typically observed in the ocean. However, there are many observations of anticyclonic currents in the ocean that are marginally stable, and this suggests that inertial instability may be the primary mechanism by which anticyclonic shear and anticyclonic vortices are maintained at stable or marginally stable values. The criterion for inertial instability is often quoted as Rossby number less than minus one, where a negative Rossby number implies anticyclonic flow However this criterion applies only to flows in homogeneous fluids like the mixed layer with no vertical shear In stratified flow that is vertically sheared as is commonly the case inertial instability can also occur with Rossby numbers between -1 and 0. Furthermore, even cyclonically sheared flows or cyclonic vortices for which Ro is greater than zero can be inertially unstable if the vertical shear is strong enough. It is also interesting that this instability can occur when the Richardson number is well above a quarter that is, in flows that are stable to the Kelvin Helmholtz instability, a controlling factor in oceanic flows. In other words, flows that are stable with regard to the well known Richardson number criterion can, in fact, be unstable because of inertial instability. It is therefore possible that inertial instability is frequently a controlling factor in oceanic flows without having been recognized as such. This renewal proposal will continue studies of inertial instability with the object of providing a fundamental basis for understanding the role that inertial instability plays in the worlds oceans. Under prior NSF funding, the investigators have performed a systematic numerical study of the effect of varying basic parameters on the inertial instability of idealized model vortices with no vertical shear and with weak vertical shear. In addition, the resulting analytical model, based on plane parallel horizontally sheared flow, is able to explain and predict much of the fundamental results of the numerical studies. From these investigations, there are now guidelines for exploring further. The previous studies will be extended to much more realistic models of oceanic vortices. Through a series of numerical simulations the effects of inertial instability will be studied in a variety of model vortices over a wide range of the essential parameters.Intellectual Merit: By undertaking our investigation of inertial instability, we hope to improve our understanding of the role that inertial instability plays in stabilization and maintenance of oceanic currents and eddies.Broader Impacts: As a broader impact, these studies should provide guidance for those attempting to develop parameterizations for ocean models and criteria for determining likely locations for intense internal wave generation and inertial instability. Because of the intrinsically small vertical scales of inertial instability, it is usually not resolved by ocean models. Thus, the simulated flows can become and stay inertially unstable. This unphysical behavior must be corrected to maintain currents in the models at physically realizable levels, but a proper parameterization of the effects of the instability can be obtained only through increased understanding. This collaborative research project will foster an international collaboration with professor Orlandi at the University of Rome and one of his graduate students.