O Oleksandr Gorodetskyi

An efficient approach for eigenmode analysis of transient distributive mixing by the mapping method

The mapping method is an efficient tool to investigate distributive mixing induced by periodic flows. Computed only once, the mapping matrix can be applied a number of times to determine the distribution of concentration inside the flow domain. Spectral analysis of the mapping matrix reveals detailed properties of the distributive mixing as all relevant information is stored in its eigenmodes. Any vector that describes a distribution of concentration can be expanded in the complete system of linearly independent eigenvectors of the mapping matrix. The rapid decay of the contribution of each mode in the eigenmode decomposition allows for a truncation of the eigenmode expansion from the whole spectrum to only the dominant eigenmodes (characterized by a decay rate significantly lower than the duration of the mixing process). This truncated decomposition adequately represents the distribution of concentration inside the flow domain already after a low number of periods, because contributions of all non-domina...

Exploiting numerical diffusion to study transport and chaotic mixing for extremely large Péclet values

We show that the purely convective mapping matrix approach provides an extremely versatile tool to study advection-diffusion processes for extremely large Peclet values (~108 and higher). This is made possible due to the coarse-grained approximation that introduces numerical diffusion, the intensity of which depends in a simple way on grid resolution. This observation permits to address fundamental physical issues associated with chaotic mixing in the presence of diffusion. Specifically, we show that in partially chaotic flows, the dominant decay exponent of the advection diffusion propagator will eventually decay as Pe−1 in the presence of quasiperiodic regions of finite measure, no matter how small they are. Examples of 2d and 3d partially chaotic flows are discussed.