Collaborative Research: Inertially Unstable Currents and Internal Waves

0525776/0526033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、广场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，可能是因为人们通常认为它只发生在反气旋(顺时针)切变的平行流或海洋中通常观察不到的强度的反气旋。然而，在海洋中有许多观测到的反气旋流是边缘稳定的，这表明惯性不稳定可能是反气旋切变和反气旋涡旋保持稳定或边缘稳定的主要机制。惯性不稳定的判据通常被引用为Rossby数小于负1，其中负的Rossby数表示反气旋流动，但该判据仅适用于均匀流体中的流动，如分层流动中没有垂直剪切的混合层，通常情况下，当Rossby数在-1和0之间时，也可以发生惯性不稳定。此外，如果垂直切变足够强，即使是Ro大于零的气旋切变流动或气旋涡旋也可能是惯性不稳定的。同样有趣的是，当理查森数远高于四分之一时，也就是说，在与开尔文亥姆霍兹不稳定性稳定的气流中，这种不稳定性可能发生，开尔文亥姆霍兹不稳定性是大洋气流中的一个控制因素。换句话说，根据众所周知的理查森数准则是稳定的，实际上，由于惯性不稳定，流动可能是不稳定的。因此，在没有认识到惯性不稳定的情况下，惯性不稳定常常是海洋流动的一个控制因素。这一更新提案将继续研究惯性不稳定，目的是为理解惯性不稳定在世界海洋中所起的作用提供一个基本基础。在NSF以前的资助下，研究人员已经对不同基本参数对无垂直切变和弱垂直切变的理想化模型涡的惯性不稳定性的影响进行了系统的数值研究。此外，所得到的基于平面平行水平剪切流动的分析模型能够解释和预测数值研究的大部分基本结果。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。通过一系列数值模拟，将在各种基本参数范围内的各种模型涡中研究惯性不稳定的影响。智力上的优点：通过开展惯性不稳定的研究，我们希望提高我们对惯性不稳定在稳定和维持洋流和涡旋中所起作用的理解。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型的参数化和确定强烈内波产生和惯性不稳定的可能位置的人提供指导。由于惯性不稳定固有的小垂直尺度，海洋模型通常不能解决这一问题。因此，模拟的流动可能会变得并保持惯性不稳定。必须纠正这种非物理行为，以将模型中的电流保持在物理上可实现的水平，但只有通过增加理解，才能获得对不稳定影响的适当参数化。这个合作研究项目将促进与罗马大学的奥兰迪教授和他的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.