Chaotic advection in a Rayleigh-Bénard flow
Reads0
Chats0
TLDR
By modeling the flow with a stream function, it is shown how to construct and identify invariant structures in the flow that act as a ‘‘template’’ for the motion of fluid particles, in the absence of molecular diffusivity.Abstract:
We consider the problem of transport of a passive tracer in the time-dependent flow corresponding to a Rayleigh number scrR slightly above the scrRt at the onset of the even oscillatory instability for Rayleigh-Benard convection rolls. By modeling the flow with a stream function, we show how to construct and identify invariant structures in the flow that act as a ‘‘template’’ for the motion of fluid particles, in the absence of molecular diffusivity. This approach and symmetry considerations allow us to write explicit formulas that describe the tracer transport for finite times. In the limit of small amplitude of the oscillation, i.e., when (scrR-scrRt)1/2 is small, we show that the amount of fluid transported across a roll boundary grows linearly with the amplitude, in agreement with the experimental and numerical findings of Solomon and Gollub [Phys. Rev. A 38, 6280 (1988)]. The presence of molecular diffusivity introduces a (long) time scale into the problem. We discuss the applicability of the theory in this situation, by introducing a simple rule for determining when the effects of diffusivity are negligible, and perform numerical simulations of the flow in this case to provide an example.read more
Citations
More filters
Journal ArticleDOI
Lagrangian coherent structures and mixing in two-dimensional turbulence
George Haller,Guo-Cheng Yuan +1 more
TL;DR: In this paper, a Lagrangian definition for the boundaries of coherent structures in two-dimensional turbulence is introduced, defined as material lines that are linearly stable or unstable for longer times than any of their neighbors.
Journal ArticleDOI
Autonomous Movement and Self‐Assembly
TL;DR: In this article, the authors used a combination of two processes: motion of individual objects powered by the catalytic decomposition of hydrogen peroxide, and relative motion caused by capillary interactions at the fluid/air interface.
Journal ArticleDOI
Foundations of chaotic mixing.
Stephen Wiggins,Julio M. Ottino +1 more
TL;DR: Most importantly for the design process, it is shown how the so–called linked twist maps function as a minimal picture of mixing, provide a mathematical structure for understanding the type of 2D flows that arise in many micromixers already built, and give conditions guaranteeing the best quality mixing.
Journal ArticleDOI
Finite time transport in aperiodic flows
George Haller,Andrew C. Poje +1 more
TL;DR: In this paper, the authors studied the transport of particles in a general, two-dimensional, incompressible flow in the presence of a transient eddy, i.e., a bounded set of closed streamlines with a finite time of existence.
Journal ArticleDOI
Experimental and computational studies of mixing in complex Stokes flows: the vortex mixing flow and multicellular cavity flows
TL;DR: In this article, the authors present experimental and computational studies of two new complex Stokes flows: a vortex mixing flow and multicell flows in slender cavities, using a variety of dynamical tools, comparisons of boundary integral equation numerical computations to dye advection experiments are made throughout.