University of Illinois Urbana-Champaign

Nonlinear steady convection in rotating mushy layers

Riahi, Daniel N.; Carlson, Donald E.; Fried, Eliot; Sellers, S.; Tomkins, C D; Adrian, Ronald; Tortorelli, Daniel A.; Brown, Eric N.; Kessler, M.R.; Sottos, Nancy R.; White, Scott R.; Hill, Kimberly M.; Gioia, Gustavo; Tota, Vinay V.; Cermeli, Paolo; Gurtin, Morton E.; Amaravadi, Deepak R.; Chen, Y-C; Sellers, Shaun; Bhattacharjee Pratik

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https://hdl.handle.net/2142/112692

Description

Title
Nonlinear steady convection in rotating mushy layers
Author(s)
  • Riahi, Daniel N.
  • Carlson, Donald E.
  • Fried, Eliot
  • Sellers, S.
  • Tomkins, C D
  • Adrian, Ronald
  • Tortorelli, Daniel A.
  • Brown, Eric N.
  • Kessler, M.R.
  • Sottos, Nancy R.
  • White, Scott R.
  • Hill, Kimberly M.
  • Gioia, Gustavo
  • Tota, Vinay V.
  • Cermeli, Paolo
  • Gurtin, Morton E.
  • Amaravadi, Deepak R.
  • Chen, Y-C
  • Sellers, Shaun
  • Bhattacharjee Pratik
Issue Date
2002-03
Keyword(s)
  • Nematic-isotropic Phase Transitions
  • Liquid Crystal
  • Isotropic Phases
  • Isotropic Cores
Abstract
We consider the problem of nonlinear steady convection in a horizontal mushy layer rotating about a vertical axis. We analyze the stationary modes of convection in the form of two-dimensional oblique rolls and three-dimensional distorted patterns. Under a neareutectic approximation and the limit of large far-field temperature, we determine the twoand three-dimensional solutions to the weakly nonlinear problem by using a pe1turbation technique, and the stability of these solutions are investigated with respect to arbitrary three-dimensional disturbances. The results of the analyses in particular range of values of the amplitude of convection indicate, in particular, that, over most of the range of values of the parameters, subcritical convection in the form of down-hexagons with down-flow at the cells' centers and up-flow at the cells' boundaries can be preferred over the up-hexagonal convection, where the convective flow is upward at the cells' centers and downward at the cells' boundaries. For zero or very small values of T (T<
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 1002
  • 2002-6010
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112692
Copyright and License Information
Copyright 2002 Board of Trustees of the University of Illinois

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