Subharmonic capillary–gravity waves in large containers subject to horizontal vibrations

• Published in: Journal of fluid mechanics Vol. 739; pp. 196 - 228
• Main Authors: Perez-Gracia, José M., Porter, Jeff, Varas, Fernando, Vega, José M.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.01.2014
• Subjects: Boundary conditions; Containers; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Gravity waves; Hydrodynamic waves; Pattern selection; pattern formation; Physics; capillary waves; pattern formation; parametric instability; Patterning; Parametric instabilities; Capillary waves; Non viscous fluid; Theoretical study; Oscillating vessel; Surface gravity wave
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2013.606

This paper deals with nearly inviscid, capillary–gravity, modulated waves parametrically excited by monochromatic horizontal vibrations in liquid containers whose width and depth are both large compared with the wavelength of the excited waves. A general linear amplitude equation is derived with appropriate boundary conditions that provides the threshold acceleration and associated spatiotemporal patterns, which compare very well with experimental measurements and visualizations. The primary instability is associated with a pair of complex Floquet multipliers that are close to (but strictly different from) −1, meaning that the instability is not strictly (2:1) subharmonic. The resulting (quasi-periodic) waves are generally oblique, not perpendicular to the vibrating endwalls. The extension of the theory to other confined systems such as vibrating containers of arbitrary shape and vibrating drops is also considered.