Supercritical Eckhaus Instability for Surface-Tension-Driven Hydrothermal Waves

Abstract : We study the nonlinear dynamics of hydrothermal waves produced by a surface-tension-driven convective flow in a long and thin annular channel heated from the side. Above onset, the supercritical traveling wave pattern undergoes a secondary instability: a supercritical Eckhaus instability. This leads to a small-wave-number phase-modulated nonlinear mode, and shows the first experimental evidence of a nonlinearly saturated phase instability mode for traveling wave patterns. At higher forcing level, this secondary pattern is subject to a tertiary instability. This mode is an amplitude mode characterized by traveling hole patterns, i.e., space-time defects that change the wave number
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Nathalie Mukolobwiez, Arnaud Chiffaudel, François Daviaud. Supercritical Eckhaus Instability for Surface-Tension-Driven Hydrothermal Waves. Physical Review Letters, American Physical Society, 1998, 80, pp.4661-4664. ⟨10.1103/PhysRevLett.80.4661⟩. ⟨cea-01373936⟩

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