Modulation of Weakly Nonlinear Traveling Waves in the Presence of a Damped Large-Scale Mode

• Published in: Radiophysics and quantum electronics Vol. 64; no. 10; pp. 681 - 692
• Main Authors: Nepomnyashchy, A. A., Samoilova, A. E.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-03-2022; Springer; Springer Nature B.V
• Subjects: Astronomy; Astrophysics and Astroparticles; Dielectric films; Dynamic stability; Film thickness; Hadrons; Heavy Ions; Landau-Ginzburg equations; Lasers; Liquid levels; Marangoni convection; Mathematical analysis; Mathematical and Computational Physics; Modulation; Multiscale analysis; Nuclear Physics; Observations and Techniques; Optical Devices; Optics; Photonics; Physics; Physics and Astronomy; Quantum Optics; Stability criteria; Theoretical; Thin films; Traveling waves
• ISSN: 0033-8443; 1573-9120
• DOI: 10.1007/s11141-022-10170-7

We study the modulation of weakly nonlinear traveling waves in the presence of a damped large-scale mode. The traveling wave is generated by the Marangoni convection in a thin liquid film heated from below. Against the background of the traveling wave, an additional “soft” mode arises due to large-scale surface deformations. Using the multiscale approach, we derive a set of coupled equations that describe a modulated traveling wave near the convection threshold. One of the equations is the wave envelope equation in the form of a modified complex Ginzburg–Landau equation (CGLE) that contains an additional term of the local liquid level rise. The second equation is an evolution equation for the film thickness that is derived from liquid volume conservation. It is shown that the presence of an additional large-scale mode affects the dynamics significantly. New modulational instability criteria are obtained.