ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Goldobin D. S. Localization of flows in a horizontal layer subject to randomly inhomogeneous heating. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 2, pp. 29-39. DOI: 10.18500/0869-6632-2007-15-2-29-39

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Language: 
Russian
Article type: 
Article
UDC: 
536.25

Localization of flows in a horizontal layer subject to randomly inhomogeneous heating

Autors: 
Goldobin Denis S., Institute of Continuum Mechanics of the Ural Branch of the Russian Academy of Sciences (IMSS UB RAS)
Abstract: 

We study localization of thermo-convective flows in a shallow horizontal layer subject to a fixed thermal flux across the layer, and the effect of advection on the localization properties. The thermal flux applied is stationary in time and randomly inhomogeneous in space (the problem considered is 2-D; the mean flux is nearly critical). The interpretation of linear results is underpinned by numerical simulation of the original nonlinear problem. The results presented in the article are relevant for thermal convection in a porous medium as well as for natural convection and some other hydrodynamical systems.  

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Reference: 
  1. Anderson PW. Absence of diffusion in certain random lattices. Phys. Rev. 1958;109:1492–1505. DOI: 10.1103/PhysRev.109.1492.
  2. Frohlich J, Spencer T. Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Commun. Math. Phys. 1983;88:151–184. DOI: 10.1007/BF01209475.
  3. Grempel DR, Fishman Sh, Prange RE. Localization in an incommensurable potential: an exactly solvable model. Phys. Rev. Lett. 1982;49:833–836.
  4. Bourgain J, Wang WM. Anderson localization for time quasi-periodic random Schrodinger and wave equations. Commun. Math. Phys. 2004;248:429–466. DOI: 10.1007/s00220-004-1099-2.
  5. Vlad MO, Ross J, Schneider FW. Long memory, fractal statistics, and Anderson localization for chemical waves and patterns with random propagation velocities. Phys. Rev. E. 1998;57(4):4003–4015.
  6. Hammele M, Schuler S, Zimmermann W. Effects of parametric disorder on a stationary bifurcation. Physica D. 2006;218:139–157. DOI: 10.1016/j.physd.2006.05.001.
  7. Lifshits IM, Gredeskul SA, Pastur LA. Introduction to the Theory of Disordered Systems. Moscow: Nauka; 1982. (in Russian)
  8. Gershuni GZ, Zhukhovitsky EM. Convective Stability of an Incompressible Fluid. Moscow: Nauka; 1972.
  9. Knobloch E. Pattern selection in long-wavelength convection. Physica D. 1990;41:450–479. DOI: 10.1016/0167-2789(90)90008-D.
  10. Aristov SN, Frik PG. Large-scale turbulence in a thin layer of nonisothermal rotating fluid. Fluid Dymamics. 1988;23(4):552–528. DOI: 10.1007/BF01055074.
  11. Klyatskin VI. The Statistical Description of Dynamic Systems with Fluctuating Parameters. Moscow: Nauka; 1975. (in Russian)
  12. Zillmer R, Pikovsky A. Continuous approach for the random-field Ising chain. Phys. Rev. E. 2005;72:056108. DOI: 10.1103/PhysRevE.72.056108.
Received: 
11.01.2007
Accepted: 
11.01.2007
Published: 
30.04.2007
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