Spectral Analysis and Computation of Effective Diffusivities in Space-time Periodic Incompressible Flows
Abstract
The enhancement in diffusive transport of passive tracer particles by incompressible, turbulent flow fields 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 diffusive 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, with possibly chaotic dynamics, providing rigorous integral representations for D* involving spectral measures of unbounded self-adjoint operators. We prove that 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 2015
- Accession Number
- AD1003384
Entities
People
- Elena Cherkaev
- Jack Xin
- Junqin Zhu
- Kenneth M. Golden
- N. B. Murphy
Organizations
- University of California