Turbulent flows are characterized by the non-linear cascades of energy and other inviscid
invariants across a huge range of scales, from where they are injected to where they are …

This work reviews the present position of and surveys future perspectives in the physics of
chaotic advection: the field that emerged three decades ago at the intersection of fluid …

Mixing of initially distinct substances plays an important role in our daily lives as well as in
ecological and technological worlds. From the continuum point of view, which we adopt …

Mixing is the operation by which a system evolves under stirring from one state of simplicity—
the initial segregation of the constituents—to another state of simplicity—their complete …

The notion of a Lagrangian Coherent Structure (LCS) is by now well established as a way to
capture transient coherent transport dynamics in unsteady and aperiodic fluid flows that are …

We study the mixing and dissipation properties of the advection–diffusion equation with
diffusivity 0< κ ≪ 1 0< κ≪ 1 and advection by a class of random velocity fields on T^ d T d …

In 1959 Batchelor predicted that the stationary statistics of passive scalars advected in fluids
with small diffusivity k should display a power spectrum along an inertial range contained in …

We construct universal mixers, incompressible flows that mix arbitrarily well general
solutions to the corresponding transport equation, in all dimensions. This mixing is …

We consider the nonlinear optimisation of the mixing of a passive scalar, initially arranged in
two layers, in a two-dimensional plane Poiseuille flow at finite Reynolds and Péclet …

Mixing and un-mixing by incompressible flows Page 1 DOI 10.4171/JEMS/709 J. Eur. Math.
Soc. 19, 1911–1948 c European Mathematical Society 2017 Yao Yao · Andrej Zlatoš Mixing …