Patterns beyond Faraday waves: observation of parametric crossover from Faraday instabilities to the formation of vortex lattices in open dual fluid strata

Abstract

Faraday first characterized the behaviour of a fluid in a container subjected to vertical periodic oscillations. His study pertaining to hydrodynamic instability, the "Faraday instability", has catalyzed a myriad of experimental, theoretical, and numerical studies shedding light on the mechanisms responsible for the transition of a system at rest to a new state of well-ordered vibrational patterns at fixed frequencies. Here we study dual strata in a shallow vessel containing distilled water and high-viscosity lubrication oil on top of it. At elevated driving power, beyond the Faraday instability, the top stratum is found to "freeze" into a rigid pattern with maxima and minima. At the same time there is a dynamic crossover into a new state in the form of a lattice of recirculating vortices in the lower layer containing the water. Instrumentation and the physics behind are analyzed in a phenomenological way together with a basic heuristic modeling of the wave field. The study, which is based on relatively low-budget equipment, stems from related art projects that have evolved over the years. The study is of value within basic research as well as in education, especially as more advanced collective project work in e.g. engineering physics, where it invites to further studies of pattern formation, the emergence of vortex lattices and complexity.

Probability Current and a Simulation of Particle Separation

“…We conclude that although different boundary conditions are used, the structure of the current is similar (Figures 2, 3, and 4). The obtained current for Neumann boundary condition (Figure 2) shows full agreement with the results in the recent experimental study by Ohlin and Berggren (2016). The findings could be used to simplify the modeling of complex structures in quantum transport calculations.…”

“…Mapping and understanding the structure of wave fields and currents is relevant to a variety of structures such as quantum structures, optical and acoustic cavities, microwave billiards and water waves in a tank (Berggren & Ljung, 2009;Berggren, Yakimenko, & Hakanen, 2010;Blümel, Davidson, Reinhardt, Lin, & Sharnoff, 1992;Stöckmann , 1999;Chen, Liu, Su, Lu, Chen, & Huang, 2007;Ohlin & Berggren, 2016;Panda & Hazra, 2014). Here, cavities and billiards stand for systems with hard walls such that a particle or a wave only scatter from the walls and there is no scattering within the system.…”

Faraday waves and droplets in quasi-one-dimensional Bose gas mixtures

“…It will be of interest to consider different modulations in the time of the scattering lengths in the framework of two-field description, which can be more accessible from the experimental point of view. One should also note that the frequency of modulations can induce heating in the condensate for long-time evolutions, with observed temperature effects on the pattern formations (on this regard, see [29]). These are kind of problems that will require separate investigations.…”

Exploring the Origin of Maximum Entropy States Relevant to Resonant Modes in Modern Chladni Plates

“…Ernst Chladni in the 18th century demonstrated a classical experiment related to acoustic phenomenon by means of vibrating a thin plate with a bow and manifesting the resonant nodal-line pattern with small sands [ 1 , 2 ]. Chladni figures have stimulated numerous scientific explorations in physics including quantum chaos [ 3 ], self-organization of granular media [ 4 , 5 ], microscale acoustofluidics [ 6 , 7 ], and pattern formation [ 8 , 9 ]. The classical Chladni figures obtained by a bow are found to considerably different from the resonant nodal-line patterns in the modern Chladni plate which is driven by a mechanical oscillator whose vibrating frequency can be precisely controlled to generate the resonant modes.…”