Gravity Currents and Related Phenomena: A Circulation-Based Modeling Framework

开发预测重力流前沿速度的分析模型的努力可以追溯到几十年前。最重要的先前的模型强加质量守恒和流向动量，以描述电流。然而，在这样做时，他们引入了一个额外的未知形式，即重力流锋面上的压力跳变，因此需要一个额外的方程来获得一个封闭系统，并且需要调用经验能量参数。因此，它们都含有一定程度的随意性。有趣的是，不同作者的高分辨率Navier-Stokes模拟表明，重力流的动力学仅由质量和动量守恒决定，因此不应该随意施加额外的能量约束。因此，一个物理上正确的解析重力流模型也应该仅仅基于质量和动量守恒，而不应该引用能量的论点。最近，PI？S组的研究表明，基于动量守恒方程的涡度公式，确实有可能建立这样一个模型。在这种方法中，压力变量不出现，因此它避免了基于经验能量参数的封闭假设的需要。新模型的预测结果与数值模拟结果非常吻合，比以前的模型更接近。这些比较进一步证明了所有早期的模型都违反了垂直动量守恒。该研究将使用这种基于循环的建模的新概念来研究具有界面和自由表面的重力驱动流。具体来说，它将解决诸如内部钻孔、侵入、跨越障碍的分层流动、跨越技能的交换流和粒子驱动流等流动。此外，将进行高分辨率DNS模拟，以评估这些模型的有效性范围。智力优势：提出的研究将为大范围的分层流开发一种全新的基于循环的模型。这些模型将是革命性的，因为它们避免了现有模型固有的垂直动量的违反，以及由于经验的、基于能量的封闭假设而产生的随意性。这是通过采用动量守恒方程的涡量形式来实现的，从而消除了对经验闭合假设的需要。更广泛的影响：拟议的研究将开发概念上新的、更精确的模型，用于广泛的由重力驱动的分层流。这些模式是描述从海风和雷暴流出到粉雪雪崩和浊流等广泛的大气和海洋现象的基础。此外，它们还被用于许多涉及两相流的技术应用中。在教育方面，拟议的研究项目将对研究生、本科生和高中生进行单相和两相流建模、大规模数值模拟、科学计算、并行计算机体系结构和流动可视化等概念的教育和培训。

Meiburg, Eckart 1335148 Efforts to develop analytical models that predict the front velocity of gravity currents date back over several decades. The most significant of the prior models impose the conservation of mass and streamwise momentum in order to describe the current. However, in doing so they introduce an additional unknown in the form of the pressure jump across the gravity current front, so that an additional equation is required to obtain a closed system and an empirical energy argument needs to be invoked. Hence, all of them contain a certain degree of arbitrariness. Interestingly, high-resolution Navier-Stokes simulations by various authors show that the dynamics of gravity currents are determined by the conservation of mass and momentum alone, so that one should not be free to impose an additional energy constraint. Hence, a physically correct analytical gravity current model also should be based on the conservation of mass and momentum alone, and it should not invoke an energy argument. Rececently, the PI?s group showed that it is indeed possible to develop such a model, based on the vorticity formulation of the momentum conservation equation. In this approach, the pressure variable does not appear, so that it avoids the need for a closure assumption based on an empirical energy argument. Predictions by the new model are shown to be in excellent agreement with numerical simulationresults, much closer than the earlier models. These comparisons furthermore demonstrate that all of the earlier models violate the conservation of vertical momentum. The proposed research will use this novel concept of circulation-based modeling to investigate a wide range of gravity-driven flows with interfaces and free surfaces. Specifically, it will address such flows as internal bores, intrusions, stratified flows over obstacles, exchange flows over sills and particle-driven currents. Furthermore, high-resolution DNS simulations will be conducted in order to assess the range of validity of these models.Intellectual Merit :The proposed research will develop a fundamentally new class of circulation-based models for a wide range of stratified flows. These models will be transformative in that they avoid the violation of vertical momentum inherent in existing models, along with their arbitrariness due to empirical, energy-based closure assumptions. This is accomplished by employing the vorticity form of the momentum conservation equation, thus eliminating the need for empirical closure assumptions.Broader Impacts :The proposed research will develop conceptually new, more accurate models for a broad class of stratified flows driven by gravity. Such models serve as basis for describing a wide range of atmospheric and oceanic phenomena from sea breezes and thunderstorm outflows to powder snow avalanches and turbidity currents. In addition, they are employed in numerous technical applications involving two-phase flows. On the educational side, the proposed research project will educate and train graduate, undergraduate and high school students in the concepts of single-phase and two-phase flow modeling, large-scale numerical simulations, scientific computing, parallel computer architectures and flow visualization.