Complex-ordered patterns in shaken convection

Symmetry properties and bifurcations of viscoelastic thermovibrational convection in a square cavity

To fill a gap in the literature about the specific dynamics of thermovibrational flow in a square cavity filled with a viscoelastic fluid when vibrations and the imposed temperature gradient are concurrent, a parametric investigation has been conducted to investigate the response of this system over a relatively wide subregion of the space of parameters (Pr_{g}=10; viscosity ratio ξ=0.5; nondimensional frequency Ω=25, 50, 75, and 100; and Ra_{ω}∈[Ra_{ω,cr},3.3×10^{4}], where Ra_{ω,cr} is the critical vibrational Rayleigh number). Through solution of the governing nonlinear equations formulated in the framework of the finitely extensible nonlinear elastic Chilcott-Rallison paradigm, it is shown that the flow is prone to develop a unique hierarchy of bifurcations where initially subharmonic spatiotemporal regimes can be taken over by more complex states driven by the competition of disturbances with different symmetries if certain conditions are considered. What drives a wedge between the cases with parallel and perpendicular vibrations is essentially the existence of a threshold to be exceeded to produce convection in the former case. Nevertheless, these two configurations share some interesting properties, which are reminiscent of the resonances and antiresonances typical of multicomponent mechanical structures. Additional insights into these behaviors are gained through consideration of quantities representative of the kinetic and elastic energy globally possessed by the system and its sensitivity to the initial conditions.

Competition of overstability and stabilizing effects in viscoelastic thermovibrational flow

Attention is paid to a specific form of thermal convection which encompasses viscoelastic and thermovibrational effects in a single problem or framework. The main objective is understanding the relationship between the phenomenon of overstability and periodic forcing through numerical solution of the governing equations in their complete, time-dependent, and nonlinear form. Fluid motion is found for values of the control parameter one order of magnitude smaller than the threshold to be exceeded in the equivalent Newtonian case. When the disturbances saturate their amplitude, patterns emerge that are reminiscent of the superlattice structures typical of complex order. In the present case, such peculiar modes of convection are driven by the coexistence of two distinct spatial scales, each displaying a different temporal dependence, driven by the interplay of the time-varying (stabilizing or destabilizing) acceleration induced by vibrations and the ability of the fluid to store and release elastic energy.

Viscoelastic Thermovibrational Flow Driven by Sinusoidal and Pulse (Square) Waves

The present study aims to probe the role of an influential factor heretofore scarcely considered in earlier studies in the field of thermovibrational convection, that is, the specific time-varying shape of the forcing used to produce fluid motion under the effect of an imposed temperature gradient. Towards this end, two different temporal profiles of acceleration are considered: a classical (sinusoidal) and a pulse (square) wave. Their effects are analyzed in conjunction with the ability of a specific category of fluids to accumulate and release elastic energy, i.e., that of Chilcott–Rallison finitely extensible nonlinear elastic (FENE-CR) liquids. Through solution of the related governing equations in time-dependent, three-dimensional, and nonlinear form for a representative set of parameters (generalized Prandtl number Prg=8, normalized frequency Ω=25, solvent-to-total viscosity ratio ξ=0.5, elasticity number ϑ=0.1, and vibrational Rayleigh number Raω=4000), it is shown that while the system responds to a sinusoidal acceleration in a way that is reminiscent of modulated Rayleigh–Bénard (RB) convection in a Newtonian fluid (i.e., producing a superlattice), with a pulse wave acceleration, the flow displays a peculiar breaking-roll mode of convection that is in between classical (un-modulated) RB in viscoelastic fluids and purely thermovibrational flows. Besides these differences, these cases share important properties, namely, a temporal subharmonic response and the tendency to produce spatially standing waves.

Dynamic stabilization of the Rayleigh-Bénard instability by acceleration modulation

This paper presents the results of an experimental investigation of the parametric stabilization of Rayleigh-Bénard convection through the imposition of sinusoidal vibration. The ability to dynamically stabilize Rayleigh-Bénard convection using acceleration modulation is of interest to groups who design and study thermoacoustic machines as the introduction of parasitic convection can have deleterious effects on the desired operation and thermodynamic efficiency of the device. These performance issues caused by suspected convective instability have been seen both in traveling wave thermoacoustic refrigerators and cryogenic pulse tube chillers. This paper reports the results of an experiment intended to determine the vibratory, fluidic, and geometric conditions under which a small, rectangular container of statically unstable fluid may be stabilized by vertical vibration with comparison to the computational methods of R. M. Carbo [J. Acoust. Soc. Am. 135, 654-668 (2014)]. Measurements are obtained using a large-displacement kinematic shaker of an original design with the convecting gas characterized using both thermal transport measurements and flow visualization employing tracer particles illuminated by a diode laser light sheet phase-locked to the shaker. These experiments are believed to be the first demonstrating the suppression of convection through vibration in rectangular containers.

Emergence of Chirality from Isotropic Interactions of Three Length Scales

Chirality is known to play a pivotal role in determining material properties and functionalities. However, it remains a great challenge to understand and control the emergence of chirality and the related enantioselective process particularly when the building components of the system are achiral. Here we explore the generic mechanisms driving the formation of two-dimensional chiral structures in systems characterized by isotropic interactions and three competing length scales. We demonstrate that starting from isotropic and rotationally invariant interactions, a variety of chiral ordered patterns and superlattices with anisotropic but achiral units can self-assemble. The mechanisms for selecting specific states are related to the length-scale coupling and the selection of resonant density wave vectors. Sample phase diagrams and chiral elastic properties are identified. These findings provide a viable route for predicting chiral phases and selecting the desired handedness.

Three-wave interactions and spatiotemporal chaos

Three-wave interactions form the basis of our understanding of many pattern-forming systems because they encapsulate the most basic nonlinear interactions. In problems with two comparable length scales, it is possible for two waves of the shorter wavelength to interact with one wave of the longer, as well as for two waves of the longer wavelength to interact with one wave of the shorter. Consideration of both types of three-wave interactions can generically explain the presence of complex patterns and spatiotemporal chaos. Two length scales arise naturally in the Faraday wave experiment, and our results enable some previously unexplained experimental observations of spatiotemporal chaos to be interpreted in a new light. Our predictions are illustrated with numerical simulations of a model partial differential equation.

Turing patterns beyond hexagons and stripes

The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. Until recently, Turing patterns with other geometries have been observed only rarely. Here we present experimental studies and mathematical modeling of the formation and stability of hexagonal and square Turing superlattice patterns in a photosensitive reaction-diffusion system. The superlattices develop from initial conditions created by illuminating the system through a mask consisting of a simple hexagonal or square lattice with a wavelength close to a multiple of the intrinsic Turing pattern's wavelength. We show that interaction of the photochemical periodic forcing with the Turing instability generates multiple spatial harmonics of the forcing patterns. The harmonics situated within the Turing instability band survive after the illumination is switched off and form superlattices. The square superlattices are the first examples of time-independent square Turing patterns. We also demonstrate that in a system where the Turing band is slightly below criticality, spatially uniform internal or external oscillations can create oscillating square patterns.