Chaotic advection in large-scale convection

We study the kinematics of mixing and transport of "passive" particles in two-dimensional thermal convection using a low-order spectral model proposed by Howard and Krishnamurti [1986]. This model allows for a large-scale flow spanning the layer width. Mixing by chaos in the oscillatory flow is demonstrated with the help of numerical Poincare! maps. The chaos induced transport process is characterized from a relation 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. It is shown that the transport process can be either shear-flow dominated (m = 2) or Brownian type (m = 1) or an intermediate type characterized by fractional exponents (1 < m < 2), depending on the external parameters 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.