Spectral analysis of mixing in chaotic flows via the mapping matrix formalism : inclusion of molecular diffusion and quantitative eigenvalue estimate in the purely convective limit

摘要: This paper extends the mapping matrix formalism to include effects of molecular diffusion in analysis mixing processes chaotic flows. The approach followed is Lagrangian, by considering stochastic formulation advection-diffusion via Langevin equation for passive fluid particle motion. In addition, inclusion diffusional permits frame spectral properties matrices purely convective limit a quantitative way. Specifically, coarse graining can be quantified means an effective Peclet number that scales as second power linear lattice size. simple result sufficient predict scaling exponents characterizing behavior eigenvalue spectrum operator flows function number, exclusively from kinematic data, varying grid resolution. Simple but representative model systems and realistic physically realizable are considered under wealth different conditions–from presence large quasi-periodic islands intertwined regions, almost globally conditions, possessing “sticky islands”–providing fairly comprehensive characterization numerical phenomenologies may occur matrices, ultimately processes.