Related papers: Designing a Finite-Time Mixer: Optimizing Stirring…
We consider the advection equation on $\mathbb{T}^2$ with a real analytic and time-periodic velocity field that alternates between two Hamiltonian shears. Randomness is injected by alternating the vector field randomly in time between just…
Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps…
Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario,the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice,…
This article addresses mixing and diffusion properties of passive scalars advected by rough ($C^\alpha$) shear flows. We show that in general, one cannot expect a rough shear flow to increase the rate of inviscid mixing to more than that of…
We revisit the well-known problem of multiscaling in substances passively advected by homogeneous and isotropic turbulent flows or passive scalar turbulence. To that end we propose a two-parameter continuum hydrodynamic model for an…
Phase separation between two fluids in two-dimensions is investigated by means of Direct Numerical Simulations of coupled Navier-Stokes and Cahn-Hilliard equations. We study the phase ordering process in the presence of an external stirring…
Multivariate time series forecasting is widely applied in fields such as transportation, energy, and finance. However, the data commonly suffers from issues of multi-scale characteristics, weak correlations, and noise interference, which…
Central schemes are frequently used for incompressible and compressible flow calculations. The present paper is the first in a forthcoming series where a new approach to a 2nd order accurate Finite Volume scheme operating on cartesian grids…
We prove the existence of invariant curves for a $T$--periodic Hamiltonian system which models a fluid stirring in a cylindrical tank, when $T$ is small and the assigned stirring protocol is piecewise constant. Furthermore, using the…
To analyze nonlinear dynamic systems, we developed a new technique based on the square matrix method. We propose this technique called the \convergence map" for generating particle stability diagrams similar to the frequency maps widely…
Analyzing unsteady fluid flows often requires access to the full distribution of possible temporal states, yet conventional PDE solvers are computationally prohibitive and learned time-stepping surrogates quickly accumulate error over long…
Spatial designs for monitoring stream networks, especially ephemeral systems, are typically non-standard, `sparse' and can be very complex, reflecting the complexity of the ecosystem being monitored, the scale of the population, and the…
Linear transient growth analysis is commonly used to suggest the structure of disturbances which are particularly efficient in triggering transition to turbulence in shear flows. We demonstrate that the addition of nonlinearity to the…
The computational cost of fluid simulations increases rapidly with grid resolution. This has given a hard limit on the ability of simulations to accurately resolve small scale features of complex flows. Here we use a machine learning…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
The dispersion of a passive scalar in a fluid through the combined action of advection and molecular diffusion is often described as a diffusive process, with an effective diffusivity that is enhanced compared to the molecular value.…
Direct numerical simulations are carried out to investigate scalar mixing in an isotropic turbulent flow with a time-periodic forcing. For high amplitudes of the modulation, it is shown that the average mixing rate is negatively affected at…
We consider the evolution of a passive scalar advected by a parallel shear flow in an infinite cylinder with bounded cross section, in arbitrary space dimension. The essential parameters of the problem are the molecular diffusivity $\nu$,…
We performed a numerical study of the efficiency of mixing by alternating horizontal and vertical shear ``wedge'' flows on the two-dimensional torus. Our results suggest that except in cases where each individual flow is applied for only a…
Passive scalars advected by a magnetically driven two-dimensional turbulent flow are analyzed using methods of statistical topography. The passive tracer concentration is interpreted as the height of a random surface and the scaling…