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

湍流在其上发展的大多数表面都是流体力学粗糙的。粗糙度的影响是非常具有挑战性的严格模拟，因为几何和附近的速度场必须以非常精细的分辨率再现，这是计算代价高昂的。对于一些应用，包括城市地区的风能、污染扩散、冠层流动，地面区域是模拟的次要组成部分，但不幸的是，这是必要的和昂贵的。标准的方法是绕过粗糙层的复杂性，并假设对数平均速度剖面一直延伸到地表，从而失去近地表速度场的一些可变性。可以设想一种更积极的墙建模策略。近年来，对数平均速度剖面的演化和推导与均匀动量带的垂直分布有关。这些大的流动区域倾向于以相同的速度一致地移动，往往随着距离壁面的距离而变得更厚，并且被强烈梯度的薄区域隔开。均匀动量带和分隔它们的内部剪切层是壁面湍流最简单的建模框架。该提案的外展部分包括为美洲原住民部落学院的本科生提供暑期项目，与澳大利亚的一名同事进行国际合作，以及向研究社区的所有人开放的实验数据共享。该项目的目标是建立一个统一的基于动量带的随机模型，并进行实验验证，该模型能够再现近地表湍流的速度场，保持其变异性和动力学，一直到地面。为了建立和检验这一新模型，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图，并指导随机模型。具有大规模数值模拟的新界面也将作为一种新的动态边界条件来实现。这将使研究人员能够用负担得起的合成速度场来取代计算昂贵的近表面区域，并改进未来对复杂大气流动或类似高雷诺数湍流边界层的模拟，如围绕船只或飞机发展的那些。最终目标是启用和测试基于表面粗糙度几何形状和易于测量的流动变量的随机模型的公式，以确保以最少的输入信息进行预测能力。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.