Response to “Comment on ‘The effect of rotation on the Rayleigh-Bénard stability
threshold’ ” [Phys. Fluids25, 059101 (2013)]
Andrea Prosperetti
Citation: Physics of Fluids 25, 059102 (2013); doi: 10.1063/1.4805091
View online: http://dx.doi.org/10.1063/1.4805091
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PHYSICS OF FLUIDS 25, 059102 (2013)
Response to “Comment on ‘The effect of rotation
on the Rayleigh-B ´enard stability threshold’ ”
[Phys. Fluids 25, 059101 (2013)]
Andrea Prosperettia)
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
(Received 27 March 2013; accepted 9 April 2013; published online 23 May 2013)
[http://dx.doi.org/10.1063/1.4805091]
I would like to thank Dr. Dawes’s for his useful comments1on my paper2with which I am in total agreement. As he points out, and as is stated in the paper itself2the error of the approximate solution presented there can be as large as 15% in certain parameter ranges.
The point of the paper is not the superiority of the numerical values which, these days, are readily made as accurate as one may wish by the use of appropriate software. Rather, this paper and the other one to which Dr. Dawes refers3demonstrate an alternative way to approach problems of this type
which is, first, of interest in itself and, second, more flexible than existing ones. The latter feature is demonstrated by its ability to produce results for the case of finite plate thermal conductivity and for modes antisymmetric about the mid-plane of the system, for neither of which exact (or better) results seem to be available. While a claim of great accuracy for these approximations would be misplaced, the parameter dependency that they exhibit is a robust feature which can be explored in a fairly straightforward manner on their basis.
1J. H. P. Dawes, “Comment on ‘The effect of rotation on the Rayleigh-B´enard stability threshold’ [Phys. Fluids 24, 114101
(2012)],”Phys. Fluids25, 059101 (2013).
2A. Prosperetti, “The effect of rotation on the Rayleigh-B´enard stability threshold,”Phys. Fluids24, 114101 (2012). 3A. Prosperetti, “A simple analytic approximation to the Rayleigh-B´enard stability threshold,”Phys. Fluids23, 124101
(2011).
a)Also at Faculty of Science and Technology and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500AE
Enschede, The Netherlands. Electronic mail:prosperetti@jhu.edu.
1070-6631/2013/25(5)/059102/1/$30.00 25, 059102-1 C 2013 AIP Publishing LLC
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