# Pattern Formation in Convective Media

### Abstract

The several models of convection in a thin layer of liquid (gas) with poorly heat conducting boundaries are considered. These models demonstrate a rich dynamics of pattern formation and structural phase transitions. The primary analysis of pattern formation in such a system is performed with using of the well-studied Swift-Hohenberg model. The more advanced Proctor-Sivashinsky model is examined in order to study the second-order structural phase transitions both between patterns with translational invariance and between structures with broken translational invariance but keeping a long-range order. The spatial spectrum of arising structures and visual estimation of the number of defects are analyzed. The relation between the density of defects and the spectral characteristics of the structure is found. We also discuss the effect of noise on the formation of structural defects. It is shown that within the framework of the Proctor-Sivashinsky model with additional term, taking into account the inertial effects, the large-scale vortex structures arise as a result of the secondary modulation instability.

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### References

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*East European Journal of Physics*, (1040(1), 4-27. Retrieved from https://periodicals.karazin.ua/eejp/article/view/13556

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