Heirarchical Modeling of Incompressible Turbulent Flows Using Divergence-Free Vector Wavelets

CTS-9613948，John Lumley等人，康奈尔大学，将发展一种使用无散度矢量小波的不可压缩湍流的小波表示。由于湍流中的相干结构具有类似于小波的有限的空间扩展，因此可以得到比傅立叶表示更好的结果。我们还将研究Navier-Stokes方程在无散度向量小波正交基上的Galerkin投影，以及它与真正交分解(POD)方法的结合和比较。为了评估小波分解的能力和效率，将与NASA兰利研究中心在空气中进行的详细的二维粒子图像测速测量进行比较。这项研究工作将与英国牛津大学和克拉克森大学合作进行。如果成功，小波表示将为描述和分析大型湍流结构等非均匀流动提供一种全新的方法。

Abstract CTS-9613948 John Lumley et al Cornell University A wavelet representation of incompressible turbulent flows using divergence-free vector wavelets will be developed. Better results than Fourier representations are expected because the coherent structures in turbulent flows have a limited spatial extend similar to wavelet. The Galerkin projection of the Navier-Stokes equations on a divergence-free vector wavelet orthogonal basis, and its incorporation and comparison to the Proper Orthogonal Decomposition (POD) approach, will be also investigated. Comparisons to detailed two-dimensional Particle Image Velocimetry measurements in air performed at NASA Langley Research Center will be performed in order to evaluate the capabilities and efficiency of the wavelet decomposition. The research work will be performed in collaboration with Oxford University in UK and Clarkson University. If successful, the wavelet representation will offer a fundamentally new way to describe and analyze non-uniform flows such as large turbulent structures.