Cross-waves excited by distributed forcing in the gravity-capillary regime

Abstract

Cross-wave descriptions based on a boundary forced nonlinear Schrodinger equation, which have been widely used since Jones [J. Fluid Mech. 138, 53-74 (1984)], rely on the assumption that modulations occur on a slow lengthscale compared with the extent of the forcing. This assumption does not hold for recent higher frequency (large aspect ratio) experiments. We extend the established theory of modulated cross-waves in horizontally vibrated containers by including surface tension and, most importantly, a spatially extended forcing term. The resulting amplitude equations provide predictions for onset values, spatial profiles, and temporal modulations that are compared with previous theory and with experimental measurements. The appearance of temporally modulated solutions, confirmed experimentally, is interpreted as the result of weak symmetry-breaking related to the interaction of waves generated at opposite ends.

Two-scale wave patterns on a periodically excited miscible liquid–liquid interface

“…The application of periodic excitations to a fluid system with a density gradient can lead to a wide variety of patterns and complex dynamics (Wolf 1970;Talib, Jalikop & Juel 2007;Benilov & Chugunova 2010;Shevtsova et al 2010;Borcia, Borcia & Bestehorn 2014;Tinao et al 2014;Shevtsova et al 2015a). In spite of the substantial advances in the study of Faraday waves and Kelvin-Helmholtz types of instability, their simultaneous existence in the same system has not been reported so far.…”

Dynamics of weakly coupled parametrically forced oscillators

“…Horizontally vibrated containers of fluid, in particular, are often used to study surface waves [15][16][17][18] and, if the container is relatively large compared to the decay length of the waves, then the excitation patterns generated at the left and right endwalls (or wavemakers) can be considered to be weakly interacting. This is the situation in several recent experiments [19,20].…”

“…Bifurcation sets are calculated as a function of forcing and detuning for representative sets of parameters. The detailed bifurcation scenario obtained for two coupled oscillators is compared, to the extent possible, with the recent experiments of [20] in Sec. V and with direct numerical simulations of a corresponding two-dimensional vibrated fluid system in Sec.…”

Pattern formation of parametrically driven surface waves induced by vibration

“…The calculated threshold amplitude compares very well quantitatively with the experimental observations by Porter et al (2012), the resulting patterns also agree well with the experiments qualitatively. The theory allowed to predict a different kind of pattern from the originally reported in Porter et al (2012) that was confirmed independently in Tinao et al (2014). Studying the variation of the threshold for the different parameters it was found that the obliqueness is enhanced by capillary effects and viscosity.…”

“…In short runs, instead, the visualized patterns would show activity either near the left or the right endwall, or distributed among both endwalls, depending on the (non controllable) initial condition, which could be seen as unpredictable/non repeatable. After the theoretical prediction in Perez-Gracia et al (2014), the slowly modulated patterns were experimentally reported in Tinao et al (2014).…”