Simulating the footprints of mixing in stratified fluids

大多数自然产生的水在一年中至少有一部分时间是密度分层的；分层通常将流体分成明确的、接近水平的层(例如，覆盖在冷水上的温水)，这样做会改变物质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等大小的湖泊中，或在沿海海洋中，能量运动的尺度可能从几公里到亚厘米尺度。描述这些运动在观测、计算和理论上都是一项挑战。后两者往往是耦合的，分层流体中流体运动的很大一部分理论理解是建立在简化的概念性基础上的，并且至关重要地依赖于高质量的软件来执行控制方程的模拟。例子包括相干波，称为类内孤立波，它在不改变形式的情况下长距离传输物质和能量，以及流体动力不稳定性，例如，开尔文-赫姆霍尔茨，Holmboe，它在小尺度上运行，以混合各层。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。拟议的研究计划将把分层流体中内波诱导混合的模拟技术扩展到更具现场代表性的条件(而不是实验室)。特别关注的领域包括：浅斜坡上的浅化内波、三维波波相互作用、由于热和盐引起的层化的影响(即双扩散不稳定性)，以及与时间相关的波导(例如，由于辐射加热)。由于热和盐引起的分层混合将在墨西哥尤卡坦洞穴网络的新环境中进行研究。开放源码软件的开发将与科学开发同时进行，该软件将通过GitHub向科学界提供。加拿大的收益将通过三种方式积累：1)HQP将接受高性能计算方面的培训，并将这种计算应用于科学问题。这类人员在公共和私营部门仍然供不应求，2)将向加拿大科学界提供高质量的开放源码软件，包括新的工具和新的科学背景，3)新的过程研究将检验基于实验室研究的结论是否能扩大到现场规模。加拿大的海岸线横跨三个极其不同的大洋，气候变化似乎每年都在加速，经济利益遍及全球，加拿大在未来几十年将面临重大挑战。该提案为以证据为基础的办法成功应对这些挑战提供了必要的工具。

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.