STATE FUNCTION IN UNSTABLE CONVECTIVE MEDIUM
Convection in a thin layer of liquid (gas) with temperature independent viscosity between poorly heat conducting boundaries is studied within framework of the Proctor-Sivashinsky model. We have shown by numerical simulation of the Proctor-Sivashinsky model that the state with certain topology can be described by the state function, which is the sum of squared mode of temperature spatial spectrum on the surface. The transitions between these states are characterized by splashes in time-derivative of this function and different meta-stable structures, corresponding to different values of the state function have different visually distinguishable topologies.
Busse F.H., Riahi N. Nonlinear convection in a layer with nearly insulating boundaries // J.Fluid Mech. – 1980. - Vol.96. - P.243.
Chandrasekhar S. Hydrodenamic and hydromagnetic stability. Third printing of the Clarendon Press. Oxford University Press edition, Dover Publication Inc.: New York, 1970. - 704 p.
Getling A.V. Structures in heat convection // Usp. Fiz. Nauk. – 1991. – Vol.11. – P.1-80.
Chapman J., Proctor M.R.E. Nonlinear Rayleigh-Benard convection between poorly conducting boundaries // J. Fluid Mech. – 1980. – No.101. – P.759-765.
Gertsberg V., Sivashinsky G.E. Large cells in nonlinear Rayleigh-Benard convection // Prog. Theor. Phys. – 1981. – No.66. - P.1219-1229.
Malomed B.A., Nepomniachtchi A.A., Tribel'skii M.P. Two-dimensional quasi-periodic structures in nonequilibrium systems // Zh. Eksp. Teor. Fiz. – 1989. – T.96. - P.684-700.
Kirichok A.V., Kuklin V.M. Allocated Imperfections of Developed Convective Structures // Physics and Chemistry of the Earth Part A. – 1999. – No. 6. – P.533-538.
Gushchin I.V., Kirichok А.V., Kuklin V.M. Pattern formation in convective media (review) // The Journal of Kharkiv National University, physical series “Nuclei, Particles, Fields. – 2013. – No.1040. – Issue 1/57. – Р.4-27.
Belkin E.V., Gushchin I.V., Kirichok A.V., Kuklin V.M. Structural transitions in the model of Proctor-Sivashinsky // Problems of Atomic Science and Technology. – 2010 – No.4 – Series: Plasma Electronics and New Methods of Acceleration (7) – P.296-298.
Gushchin I.V., Kirichok A.V., Kuklin V.M. Pattern formation in unstable viscous convective medium // Problems of Atomic Science and Technology. – 2013 – No.4 – Series: Plasma Electronics and New Methods of Acceleration (8) – P. 251-256.
Gushchin I.V., Belkin E.V. Modeling of noise influence on the formation of spatial structures in the Proctor-Sivashinsky model // Contemporary problems of mathematics, mechanics and computing sciences, Karazin Kharkiv National University. – 2011. - C.226-231.
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