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Resonance and phase solitons in spatially-forced thermal convection. (English) Zbl 0621.76043
The competition between external and internal length scales is studied theoretically, on a two-dimensional amplitude evolution model of a fluid layer heated from below. A spatially-periodic excitation is applied to the stress-free, isothermal boundaries at a wavenumber close to the critical wavenumber for the onset of the instability. Near resonance, the large-scale phase dynamics give rise to stationary phase solitons at high Prandtl numbers and propagating sine-Gordon solitons at low Prandtl numbers. The propagating solitons are associated with the external breaking of the Galilean invariance of the problem.

MSC:
76E15 Absolute and convective instability and stability in hydrodynamic stability
76R05 Forced convection
76M99 Basic methods in fluid mechanics
35Q99 Partial differential equations of mathematical physics and other areas of application
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