Durlofsky, L. and Brady, J. F. (1984) The spatial stability of a class of similarity solutions. Physics of Fluids, 27 (5). pp. 10681076. ISSN 10706631. http://resolver.caltech.edu/CaltechAUTHORS:20120702094236176

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Abstract
The spatial stability of a class of exact similarity solutions of the Navier–Stokes equations whose longitudinal velocity is of the form xf′(y), where x is the streamwise coordinate and f′(y) is a function of the transverse, cross‐streamwise, coordinate y only, is determined. These similarity solutions correspond to the flow in an infinitely long channel or tube whose surface is either uniformly porous or moves with a velocity linear in x. Small perturbations to the streamwise velocity of the form x^λg′(y) are assumed, resulting in an eigenvalue problem for λ which is solved numerically. For the porous wall problem, it is shown that similarity solutions in which f′(y) is a monotonic function of y are spatially stable, while those that are not monotonic are spatially unstable. For the accelerating‐wall problem, the interpretation of the stability results is not unambiguous and two interpretations are offered. In one interpretation the conclusions are the same as for the porous problem—monotonic solutions are stable; the second interpretation is more restrictive in that some of the monotonic as well as the nonmonotonic solutions are unstable.
Item Type:  Article  

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Additional Information:  © 1984 American Institute of Physics. Received 31 May 1983; accepted 4 November 1983. Discussions with Professor A. Acrivos are greatly appreciated, as is R. Reade's contribution to some of the numerical computations. This work was partially supported by the DuPont Young Faculty Grant to J. F. B.  
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Subject Keywords:  navier−stokes equations, channels, porosity, fluid flow, analytical solution, velocity distribution, surfaces, acceleration  
Classification Code:  PACS: 47.56.+r, 47.60.i  
Record Number:  CaltechAUTHORS:20120702094236176  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20120702094236176  
Official Citation:  The spatial stability of a class of similarity solutions L. Durlofsky and J. F. Brady Phys. Fluids 27, 1068 (1984); http://dx.doi.org/10.1063/1.864736  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  32225  
Collection:  CaltechAUTHORS  
Deposited By:  Ruth Sustaita  
Deposited On:  02 Jul 2012 17:22  
Last Modified:  26 Dec 2012 15:27 
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