Simulating the footprints of mixing in stratified fluids

大多数天然存在的沃茨在一年中的至少一部分时间内是密度分层的;分层通常将流体分成界限分明的、几乎水平的层（例如，温水覆盖冷水），并且这样做改变了材料混合和能量在整个水体中分布的方式。在加拿大地盾上的中型湖泊或沿海海洋中，高能运动的规模可能从几公里到亚厘米级。描述这些运动在观测、计算和理论上都是一个挑战。后两者通常是耦合的，并且分层流体中流体运动的理论理解的很大一部分是建立在简化的概念构建块之外的，并且关键地依赖于高质量的软件来进行控制方程的模拟。例子包括相干波，称为内部孤立波，其在长距离上传输物质和能量而不改变形式和流体动力学不稳定性，例如，Kelvin-Helmholtz，Holmboe，在小规模上操作以混合层。因此，大尺度运动在混合中的主要作用是建立有利于小尺度不稳定性的条件。 拟议的研究计划将扩展到更有代表性的领域（而不是实验室）的条件下，在分层流体的内波诱导混合的模拟的最先进的。 特别关注的领域是：浅斜坡上的浅内波、三维波-波相互作用、由于热和盐引起的分层效应（即双扩散不稳定性），以及时间相关的波导（例如，由于辐射加热）。 分层混合由于热和盐将研究在墨西哥尤卡坦半岛的洞穴网络的新背景下。开源软件的开发将与科学发展同时进行，该软件将通过github提供给科学界。加拿大将从三个方面受益：1）HQP将接受高性能计算和将这种计算应用于科学问题的培训。这样的人在公共和私营部门仍然供不应求，2）高质量的开源软件将提供给加拿大科学界，包括新的工具和新的科学背景，3）新的过程研究将测试基于实验室研究的结论是否可扩展到实地规模。加拿大的海岸线横跨三个极其多样化的大洋，气候似乎每年都在加速变化，经济利益遍及地球仪，因此，加拿大在未来几十年面临着重大挑战。该提案为成功应对这些挑战的循证方法提供了重要工具。

The majority of naturally occurring waters are density stratified for at least some portion of the year; stratification often separates the fluid into well-defined, nearly horizontal layers (e.g., warm water overlying cold) and in doing this changes the manner in which material is mixed and energy is distributed throughout the body of water. In a mid-sized lake on the Canadian shield, or in the coastal ocean, energetic motions may range in scale from multiple kilometers to sub-centimeter scales. Characterizing these motions is a challenge observationally, computationally and theoretically. The latter two are often coupled, and a large portion of the theoretical understanding of fluid motions in stratified fluids is built out of simplified, conceptual building blocks and is crucially dependent on high quality software to carry out simulations of the governing equations. Examples include coherent waves, called internal solitary-like waves, that transport material and energy over long distances without changing form and hydrodynamic instabilities, e.g., Kelvin-Helmholtz, Holmboe, that operate on small scales to mix the layers. The large scale motions' primary role in mixing is thus to set up conditions that are conducive to small scale instabilities. The proposed research program will extend the state of the art for simulations of internal wave induced mixing in stratified fluids to conditions more representative of the field (as opposed to the laboratory).  Particular areas of focus are: shoaling internal waves on shallow slopes, three dimensional wave-wave interactions, the effects of stratification due to heat and salt (i.e. double diffusive instability), and time dependent wave guides (e.g., due to radiative heating).  Stratified mixing due to heat and salt will be studied in the novel context of cave networks in the Yucatan, Mexico. The development of open source software will take place concurrently with scientific developments, and this software will be made available to the scientific community through github. Benefits to Canada will be accrued in three ways: 1) HQP will be trained in high performance computing and the application of this computing to scientific problems. Such individuals continue to be in short supply in both the public and private sectors, 2) high quality, open source software will be made available to the Canadian scientific community both with new tools and new scientific contexts, 3) novel process studies will test whether conclusions based on laboratory studies scale up to field scales. With a coastline that spans three extremely diverse oceans, a climate whose changes seem to accelerate each year, and economic interests that span the globe, Canada faces significant challenges in the coming decades. This proposal provides essential tools for an evidence-based approach to successfully tackling these challenges.