B. Joseph, CHAOTIC ADVECTION IN LARGE-SCALE CONVECTION, International journal of bifurcation and chaos in applied sciences and engineering, 8(1), 1998, pp. 57-71
We study the kinematics of mixing and transport of ''passive'' particl
es in two-dimensional thermal convection using a low-order spectral mo
del proposed by Howard and Krishnamurti [1986]. This model allows for
a large-scale flow spanning the layer width. Mixing by chaos in the os
cillatory flow is demonstrated with the help of numerical Poincare! ma
ps. The chaos induced transport process is characterized from a relati
on of the form Delta X-2(t) similar to t(m), for large t, where Delta
X-2(t) is the mean square distance traveled by a cloud of particles. I
t is shown that the transport process can be either shear-flow dominat
ed (m = 2) or Brownian type (m = 1) or an intermediate type characteri
zed by fractional exponents (1 < m < 2), depending on the external par
ameters in the problem. The intermediate process has been found to be
intermittent in nature. The present results are compared with earlier
studies of chaotic advection and also some experimental observations.
Directions for future work are also pointed out.