Stochastic Modeling of Turbulence over Rough Walls: Theory, Experiments, and Simulations

湍流在其上发展的大多数表面是流体动力学粗糙的。粗糙度的影响是非常具有挑战性的严格模拟，因为几何形状和附近的速度场必须以非常精细的分辨率再现，这是计算昂贵的。对于某些应用，包括风能，污染扩散，城市地区的冠层流动，地面区域是一个次要的，但不幸的是必要的和昂贵的，模拟的组成部分。标准的方法是绕过粗糙层的复杂性，并假设对数平均速度分布一直延伸到表面，从而失去了近表面速度场的一些可变性。可以设想更主动的壁建模策略。近年来，对数平均流速剖面的演变和推导与均匀动量带的垂直分布有关。这些是大的流动区域，它们倾向于以相同的速度相干地移动，倾向于随着离壁的距离而变厚，并且被强梯度的薄区域分开。均匀动量区和分隔它们的内部剪切层是壁湍流最简单的建模框架。该提案的外展部分包括为美国土著部落学院的本科生提供暑期课程，与澳大利亚同事进行国际合作，以及向研究界的每个人开放的实验数据共享。该项目的目标是制定并通过实验验证一个基于均匀动量区的随机模型，该模型能够再现速度场，近地表湍流的特征，保持其可变性和动态性，一直到地面。 为了建立和检验这种新的模型，需要在不同的粗糙表面上进行实验，以绘制三维均匀动量区分布并指导随机模型。一个新的接口与大规模的数值模拟也将作为一个新的，动态的边界条件。这将使研究人员能够用负担得起的合成速度场取代计算昂贵的近表面域，并改善未来对复杂大气流动或类似高雷诺数湍流边界层的模拟，如船舶或飞机周围的湍流边界层。最终目标是根据表面粗糙度几何形状和易于测量的流量变量来实现和测试随机模型的制定，以确保以最少的输入信息实现预测能力。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Most of the surfaces over which turbulent flows evolve are hydrodynamically rough. The effect of roughness is very challenging to simulate rigorously because the geometry and the nearby velocity field has to be reproduced with a very fine resolution, which is computationally expensive. For some applications, including wind energy, pollution dispersion, canopy flows in urban areas, the ground region is a minor, but unfortunately necessary and costly, component of the simulation. The standard approach is to bypass the complexity of the roughness layer and assume that the logarithmic mean velocity profile extends all the way to the surface, thus losing some of the variability of the near surface velocity field. A more active wall modeling strategy could be envisioned. Recently, the evolution and derivation of the logarithmic mean velocity profile, has been connected to the vertical distribution of Uniform Momentum Zones. These are large flow regions that tend to move coherently with the same velocity, tend to get thicker with the distance from the wall, and are separated by thin regions of intense gradients. The Uniform Momentum Zones, and these internal shear layers separating them, are the simplest modeling framework for wall turbulence. The outreach component of the proposal includes a summer program for undergrad students from Native American Tribal College, international collaboration with a colleague in Australia, and experimental data sharing, open to everyone in the research community. The goal of this project is to formulate, and validate experimentally, a Uniform Momentum Zones-based stochastic model able to reproduce the velocity field, characteristic of near-surface turbulence, preserving its variability and dynamics, all the way to the ground. To build and test this new model, experiments are needed, on different rough surfaces, to map the Uniform Momentum Zones distribution in three dimensions and guide the stochastic model. A new interface with large scale numerical simulations will be also implemented as a new, dynamic boundary condition. This will enable researchers to replace the computationally expensive, near-surface domain with an affordable synthetic velocity field, and improve future simulations of complex atmospheric flows, or similarly high Reynolds number turbulent boundary layers, like those developing around ships or planes. The ultimate goal is to enable and test the formulation of the stochastic model based on the surface roughness geometry and on easily measurable flow variables, to ensure predictive capabilities with minimal input information.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.