A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

/pdf/pattern-formation-outside-of-equilibrium-1601b9znum.pdf

Pattern formation outside of equilibrium

The goal of this survey is to review recent developments in the hydro­ dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts. We wish to dem­ onstrate how these notions can be used effectively to obtain a qualitative and quantitative description of the spatio-temporal dynamics of open shear flows, such as mixing layers, jets, wakes, boundary layers, plane Poiseuille flow, etc. In this review, we only consider open flows where fluid particles do not remain within the physical domain of interest but are advected through downstream flow boundaries. Thus, for the most part, flows in "boxes" (Rayleigh-Benard convection in finite-size cells, Taylor-Couette flow between concentric rotating cylinders, etc.) are not discussed. Further­ more, the implications of local/global and absolute/convective instability concepts for geophysical flows are only alluded to briefly. In many of the flows of interest here, the mean-velocity profile is non-

/pdf/local-and-global-instabilities-in-spatially-developing-flows-ja4x14nrk6.pdf

Local and global instabilities in spatially developing flows

Fluctuating lift on a circular cylinder: review and new measurements

Regular Article: An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries

Results are reported from a highly accurate, global numerical stability analysis of the periodic wake of a circular cylinder for Reynolds numbers between 140 and 300 The analysis shows that the two-dimensional wake becomes (absolutely) linearly unstable to three-dimensional perturbations at a critical Reynolds number of 1885±10 The critical spanwise wavelength is 396 ± 002 diameters and the critical Floquet mode corresponds to a ‘Mode A’ instability At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength 0822 diameters at onset Stability spectra and corresponding neutral stability curves are presented for Reynolds numbers up to 300

/pdf/three-dimensional-floquet-stability-analysis-of-the-wake-of-4r1lk83e37.pdf

Three-dimensional Floquet stability analysis of the wake of a circular cylinder

The wake of a circular cylinder is investigated near the oscillation threshold by means of a laser probe. Above the threshold the transient regime is studied and described by a Stuart-Landau law (already found to be relevant in explaining free-oscillating regimes). Below the critical point, impulse and resonant regimes are examined, so the coefficients of the Stuart-Landau equation are determined.Moreover, in the supercritical regime, the behaviour of the (externally forced) oscillating system is described, varying parameters such as threshold deviation, forcing frequency and amplitude. The different zones of entrainment and desynchronization are given for simple or harmonic frequency.

Bénard-von Kármán instability: transient and forced regimes

The evolution of the velocity components of the wake behind a cylinder has been investigated in the range 40 L'evolution des composantes de la vitesse dans le sillage d'un cylindre est etudiee dans la gamme 40<Re<300 par anemometrie Laser Doppler a defilement de franges. Le parametre d'ordre (amplitude de la fluctuation de vitesse perpendiculaire) suit la loi de Landau. L'existence de plusieurs modes est verifiee et des effets tridimensionnels sont observes et interpretes lorsque deux modes co-existent. La dependance des grandeurs critiques en fonction du rapport d'aspect est egalement donnee

/pdf/the-benard-von-karman-instability-an-experimental-study-near-151mxt43x5.pdf

The Benard-Von Karman instability : an experimental study near the threshold

A conical flame, in the presence of high-frequency (≈1000 Hz) and high-amplitude acoustic modulation of the cold gases, deforms to a shape which is approximately hemispherical. It is shown that the acoustic level required to produce a hemispherical flame is such that the ratio of acoustic velocity to laminar combustion velocity is about 3. This flame flattening is equivalent to the phenomenon of acoustic restabilization observed for cellular flames propagating in tubes. The transition between the conical flame and a hemispherical flame is described. The surface area of the reaction zone of the flame is found to be unmodified when the flame flattens. The velocity field at the burner outlet is examined with and without a flame. The mean flow lines are strongly deflected when the hemispherical flame is present. We show that the presence of the flame creates an unusual situation where the oscillating flow controls the geometry of the mean flow.

L. Boyer

Papers

Bénard-von Kármán instability: transient and forced regimes

The Benard-Von Karman instability : an experimental study near the threshold

On the shape of flames under strong acoustic forcing : a mean flow controlled by an oscillating flow

CO2 and H2S absorption in aqueous MDEA with ethylene glycol: Electrolyte NRTL, rate-based process model and pilot plant experimental validation