Dimotakis, Paul E. and Miller, Paul L. (1990) Some consequences of the boundedness of scalar fluctuations. Physics of Fluids A - Fluid Dynamics, 2 (11). pp. 1919-1920. ISSN 0899-8213. http://resolver.caltech.edu/CaltechAUTHORS:20120508-154933764
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Values of the scalar field c(x,t), if initially bounded, will always be bounded by the limits set by the initial conditions. This observation permits the maximum variance ∼(c′^2) to be computed as a function of the mean value c. It is argued that this maximum should be expected in the limit of infinite Schmidt numbers (zero scalar species diffusivity). This suggests that c′/c on the axis of turbulent jets, for example, may not tend to a constant, i.e., independent of x/d, in the limit of very large Schmidt numbers. It also underscores a difficulty with the k^(−1) scalar spectrum proposed by Batchelor [J. Fluid Mech. 5, 113 (1959)].
|Additional Information:||© 1990 American Institute of Physics. Received 24 August 1990; accepted 11 September 1990. We would like to acknowledge our discussions with P. Saffman, D. Meiron, and H. K. Moffatt. This work is part of a larger effort on turbulent mixing supported by AFOSR Grant No. 88-0155 and GRI Contract No. 5087-260-1467.|
|Subject Keywords:||SCALAR FIELDS, FLUCTUATIONS, INITIAL CONDITIONS, FUNCTIONS, DIFFUSIVITY, TURBULENT FLOW, JETS, BOUNDARY CONDITIONS|
|Classification Code:||PACS: 47.27.-i|
|Official Citation:||Some consequences of the boundedness of scalar fluctuations Paul E. Dimotakis and Paul L. Miller Phys. Fluids A 2, 1919 (1990); http://dx.doi.org/10.1063/1.857666|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||09 May 2012 16:56|
|Last Modified:||26 Dec 2012 15:10|
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