计算涡旋统计量的多分辨率普查算法 湍流

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摘要翻译：
模拟湍流流动的基本方程对观测到的湍流结构的大小和形状没有提供太多的洞察力。我们通过将统计模型直接应用于模拟的涡度场，研究了二维湍流结构的有效和准确的表示。在经典的信号加噪声模型中，我们不是从背景变化中提取图像的相干部分，而是使用非抽取离散小波变换来建立单个涡旋的模型。由用户提供的模板图像提供了要从涡度场中提取的特征。通过将涡旋模板转换到小波域，将模板中的特定特征，如尺寸和对称性分解为与空间频率相关的分量。采用多元多元线性回归方法将涡模板与小波域涡度场进行拟合。由于模板分解的所有级别都可以用于对字段分解中的每个级别建模，因此得到的模型不必与模板相同。给出了在涡度场演化过程中记录感兴趣量（如大小、峰值振幅、环流等）的涡普查算法的应用。多分辨率普查算法在模拟涡度场中提取各种形状和大小的相干结构，并能够在处理随时间演化的一组涡度场时再现已知的物理标度律。
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英文标题：
《A Multiresolution Census Algorithm for Calculating Vortex Statistics in
  Turbulent Flows》
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作者：
Brandon Whitcher, Thomas C. M. Lee, Jeffrey B. Weiss, Timothy J. Hoar,
  Douglas W. Nychka
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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一级分类：Physics        物理学
二级分类：Atmospheric and Oceanic Physics        大气与海洋物理
分类描述：Atmospheric and oceanic physics and physical chemistry, biogeophysics, and climate science
大气和海洋物理和物理化学，生物地球物理和气候科学
--

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英文摘要：
  The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude, circulation, etc.) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and is able to reproduce known physical scaling laws when processing a set of voriticity fields that evolve over time.
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PDF链接：
https://arxiv.org/pdf/710.0657

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关键词：分辨率 统计量 epidemiology Transforming Presentation into 提取 分辨率 模拟 vorticity