The influence of periodic islands in the flow on a scalar tracer in the presence of a steady source
Turner, MR, Thuburn, J and Gilbert, AD (2009) The influence of periodic islands in the flow on a scalar tracer in the presence of a steady source Physics of Fluids, 21 (6).

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Abstract
In this paper we examine the influence of periodic islands within a time periodic chaotic flow on the evolution of a scalar tracer. The passive scalar tracer is injected into the flow field by means of a steady source term. We examine the distribution of the tracer once a periodic state is reached, in which the rate of injected scalar balances advection and diffusion with the molecular diffusion kappa. We study the twodimensional velocity field u(x, y, t) = 2 cos(2)(omega t)(0, sin x) + 2 sin(2)(omega t)(sin y, 0). As omega is reduced from an O(1) value the flow alternates through a sequence of states which are either globally chaotic, or contain islands embedded in a chaotic sea. The evolution of the scalar is examined numerically using a semiLagrangian advection scheme. By timeaveraging diagnostics measured from the scalar field we find that the timeaveraged lengths of the scalar contours in the chaotic region grow like kappa(1/2) for small kappa, for all values of omega, while the behavior of the timeaveraged maximum scalar value, (Cmax) over bar, for small kappa depends strongly on omega. In the presence of islands (Cmax) over bar similar to kappa(alpha) for some alpha between 0 and 1 and with kappa small, and we demonstrate that there is a correlation between alpha and the area of the periodic islands, at least for large omega. The limit of small omega is studied by considering a flow field that switches from u=(0, 2 sin x) to u=(2 sin y, 0) at periodic intervals. The small kappa limit for this flow is examined using the method of matched asymptotic expansions. Finally the role of islands in the flow is investigated by considering the timeaveraged effective diffusion of the scalar field. This diagnostic can distinguish between regions where the scalar is well mixed and regions where the scalar builds up. c 2009 American Institute of Physics. [DOI: 10.1063/1.3159615]
Item Type:  Article  

Divisions :  Faculty of Engineering and Physical Sciences > Mathematics  
Authors : 


Date :  1 November 2009  
Identification Number :  https://doi.org/10.1063/1.3159615  
Uncontrolled Keywords :  EFFECTIVE DIFFUSIVITY, TRANSPORT, STRATOSPHERE, COORDINATE, ADVECTION, MODELS, AREA  
Related URLs :  
Depositing User :  Symplectic Elements  
Date Deposited :  24 Jun 2011 16:28  
Last Modified :  08 Nov 2013 12:07  
URI:  http://epubs.surrey.ac.uk/id/eprint/2919 
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