Spectral analysis and computation of effective diffusivities in space-time periodic incompressible flows

N. Benjamin Murphy University of California at Irvine Elena Cherkaev University of Utah Jack Xin University of California at Irvine Jingyi Zhu University of Utah Kenneth M. Golden University of Utah

Analysis of PDEs mathscidoc:1608.03002

Annals of Mathematical Sciences and Applications, 0, (0), 2014.1
The diffusive transport of passive tracers or particles can be enhanced by incompressible, turbulent flow fields. Analyzing the effective behavior is a challenging problem with theoretical and practical importance in many areas of science and engineering, ranging from the transport of mass, heat, and pollutants in geophysical flows to sea ice dynamics and turbulent combustion. The long time, large scale behavior of such systems is equivalent to an enhanced diffusion process with an effective diffusivity tensor D*. Two different formulations of integral representations for D* were developed for the case of time-independent fluid velocity fields, involving spectral measures of bounded self-adjoint operators acting on vector fields and scalar fields, respectively. Here, we extend both of these approaches to the case of space-time periodic velocity fields, allowing for chaotic dynamics, providing rigorous integral representations for D* involving spectral measures of unbounded self-adjoint operators.We prove the different formulations are equivalent. Their correspondence follows from a one-to-one isometry between the underlying Hilbert spaces. We also develop a Fourier method for computing D*, which captures the phenomenon of residual diffusion related to Lagrangian chaos of a model flow. This is reflected in the spectral measure by a concentration of mass near the spectral origin.
advective diffusion, homogenization, effective diffusivity, spectral measure, integral formula, Fourier method, generalized eigenvalue computation, residual diffusion.
[ Download ] [ 2016-08-18 11:11:23 uploaded by admin ] [ 805 downloads ] [ 0 comments ]
@inproceedings{n.2014spectral,
  title={Spectral analysis and computation of effective diffusivities in space-time periodic incompressible flows},
  author={N. Benjamin Murphy, Elena Cherkaev, Jack Xin, Jingyi Zhu, and Kenneth M. Golden},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160818111123595932225},
  booktitle={Annals of Mathematical Sciences and Applications},
  volume={0},
  number={0},
  year={2014},
}
N. Benjamin Murphy, Elena Cherkaev, Jack Xin, Jingyi Zhu, and Kenneth M. Golden. Spectral analysis and computation of effective diffusivities in space-time periodic incompressible flows. 2014. Vol. 0. In Annals of Mathematical Sciences and Applications. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160818111123595932225.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved