Convective Rolls Research Articles

THE EFFECT OF ROTATION AND PULSATING THROUGHFLOW ON THE ONSET OF LONGITUDINAL CONVECTIVE ROLLS IN A POROUS MEDIUM SATURATED BY NANOFLUID

This study accentuates the combined effect of rotation and pulsating throughflow on the onset of longitudinal convec-tive rolls in a porous medium saturated by nanofluid. Pulsating throughflow modifies the basic profiles for temperature and the volumetric fraction of nanoparticle from linear to nonlinear with layer height, which in turn affects the stability significantly. To treat this problem, Buongiorno's two-phase mathematical model is used. Using the framework of linear stability theory and the frozen profile approach, the stability equations are derived and solved analytically using the Galerkin weighted residuals method. The effect of increasing the modified diffusive ratio NA and the nanoparticle Rayleigh-Darcy number RN, and decreasing the rotation parameter TD is to accelerate the onset of convection, while the Lewis number Le and porosity parameter φ have dual effect on the stability of the system in the presence of pulsating throughflow. Moreover, the frozen profile approach shows that the effect of pulsating throughflow in both directions is stabilizing. An increased amplitude of throughflow oscillations leads to increased stability by an amount that depends on frequency.

Three dimensional flows beneath a thin layer of 2D turbulence induced by Faraday waves

Faraday waves occur on a fluid being subject to vertical shaking. Although it is well known that form and shape of the wave pattern depend on driving amplitude and frequency, only recent studies discovered the existence of a horizontal velocity field at the surface, called Faraday flow. This flow exhibits attributes of two-dimensional turbulence and is replicated in this study. Despite the increasing attention towards the inverse energy flux in the Faraday flow and other not strictly two-dimensional (2D) systems, little is known about the velocity fields developing beneath the fluid surface. In this study, planar velocity fields are measured by means of particle image velocimetry with high spatio-temporal resolution on the water surface and at different depths below it. A sudden drop in velocity and turbulent kinetic energy is observed at half a Faraday wavelength below the surface revealing that the surface flow is the main source of turbulent fluid motion. The flow structures below the surface comprise much larger spatial scales than those on the surface leading to very long-tailed temporal and spatial velocity (auto-) correlation functions. The three-dimensionality of the flow is estimated by the compressibility, which increases strongly with depth while the divergence changes its appearance from intermittent and single events to a large scale pattern resembling 2D cut-planes of convection rolls. Our findings demonstrate that the overall fluid flow beneath the surface is highly three-dimensional and that an inverse cascade and aspects of a confined 2D turbulence can coexist with a three-dimensional flow.Graphic abstract

Flow organisation in laterally unconfined Rayleigh–Bénard turbulence

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Steady Rayleigh–Bénard convection between stress-free boundaries

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Linear stability analysis of bubble-induced convection in a horizontal liquid layer.

We investigate with a linear analysis the stability of a horizontal liquid layer subjected to injection of gas bubbles through a bottom wall. The injection is assumed uniform in space and constant in time. Injected bubbles ascend in the liquid layer due to the Archimedean buoyancy force and are ejected from the top free surface of the liquid layer. Modeling this two-phase flow system as two interpenetrating liquid and gas continua, we show that homogeneous upward gas flows become unstable at large gas fluxes. We determine the critical conditions of this homogeneous-heterogeneous regime transition and show that the critical modes are made of stationary convection rolls, either multi- or whole-layered depending on liquid viscosity, the radius of bubbles, and the thickness of liquid layer. By examining the energy transfer from base to perturbation flows, we indicate that liquid convective motion is driven by the buoyancy on heterogeneously distributed bubbles. We also reveal that the lift forces on bubbles have significant stabilizing effects by homogenizing bubble distribution close to the bottom wall.

From zonal flow to convection rolls in Rayleigh–Bénard convection with free-slip plates

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Theoretical and Experimental Study of Thermal Convection in Rotating Horizontal Annulus

The paper presents the results of theoretical and experimental studies of thermal convection in a rotating horizontal cylindrical liquid layer. A layer with boundaries of different temperatures both when heating from inside and outside is considered. Steady thermal convection is determined by two mechanisms: thermovibrational and centrifugal ones. The first one appears due to oscillations of nonisothermal liquid in the cavity frame caused by gravity. Both mechanisms manifest themselves in the formation of two-dimensional convective rolls, extended along the axis of rotation. It is shown that the results of the experimental study of the layer quasiequilibrium stability are in a good agreement with the results obtained in the framework of numerical calculation and linear theory. The structure of thermal convection and heat transport in the supercritical area of parameters is studied numerically, taking into account the slow azimuthal drift of the entire liquid layer in the direction opposite to the rotation of the cavity. The results of numerical simulation and experimental studies are consistent in the area of moderate and large values of the dimensionless velocity of rotation.

Differential rotation in cholesteric pillars under a temperature gradient

Steady rotation is induced in cholesteric droplets dispersed in a specific liquid solvent under a temperature gradient. In this phenomenon, two rotational modes have been considered: (1) collective rotation of the local director field and (2) rigid-body rotation of the whole droplet structure. However, here we present another rotational mode induced in a pillar-shaped cholesteric droplet confined between substrates under a temperature gradient, that is, a differential rotation where the angular velocity varies as a function of the radial coordinate in the pillar. A detailed flow field analysis revealed that every pillar under a temperature gradient involves a double convection roll. These results suggested that the differential rotation in the cholesteric pillars was driven by the inhomogeneous material flow induced by a temperature gradient. The present experimental study indicates that the coupling between the flow and the director motion plays a key role in the rotation of the cholesteric droplets under the temperature gradient.

Emerging frontiers in wind engineering: Computing, stochastics, machine learning and beyond

Over the last several decades, wind engineering a multi-disciplinary subject involving engineering meteorology, fluid dynamics, structural dynamics, structural engineering, probabilistic methods, and design has addressed the challenges posed by winds of synoptic and non-synoptic origins. Combined computational approaches and laboratory to full-scale experiments have enhanced our ability to design and construct wind-resistant structures that range from low-rise to supertall buildings, footbridges to super long-span bridges and, wind turbines on the ground and floating foundations and floating offshore drilling and production systems. During this period, we have seen extraordinary advances in experimental facilities, instrumentation and data acquisition and management. At the laboratory scale, new wind tunnels have emerged with added features like extra-wide cross-sections, from passive to active driving systems, from boundary layer to flow simulators with vortical flows mimicking non-synoptic winds features. While at full-scale, we have been able to use deployable sensing networks in the path of landfalling hurricanes/typhoons to monitoring in real-time the performance of tall buildings and long-span bridges during extreme wind events. Advanced technologies like aerial surveying using drones and satellite imagery have been employed to enhance the post-storm surveillance capabilities. These advances have enabled us to build a cadre of civil infrastructure that meets some of the challenges posed by the extreme winds. Yet there remain several frontiers that still need to be addressed for example the three “Nons,” the triple emerging fronts, i.e., non-stationarity, non-Gaussianity, non-linearity prevalent in the changing dynamic of winds prevailing in gust fronts, vortical and convective systems, rolls, meso-scale features and intermittent turbulence. In the face of these challenges, increasing heights, spans, and depths of structures exposed to these winds pose additional challenges as their performance becomes more sensitive to their dynamics, thus necessitating new tools and perspectives that go beyond customary analysis and modeling norms. Fortunately, amidst these challenges, there are new opportunities to complement our existing capabilities as the burgeoning growth in computational resources and parallel computational advances coupled with data analytics and AI-based schemes, e.g., machine learning hold the promise of expanding our modeling and simulation capacity far beyond our current conventional schemes offer. All these advances can be couched in a Generalized Wind Loading Chain to capture the three “Nons” by building upon the wind loading chain proposed by Davenport based on linear and stationary conditions. An example of the Gust Front Factor in this framework is an effective means for designing under non-synoptic winds. This paper expands on these new computational opportunities and ways to take advantage of their added capabilities to address emerging challenges in building a resilient and sustainable civil infrastructure and beyond to stability and safety of high-speed trains.

Supergravitational turbulent thermal convection.

High-Rayleigh number convective turbulence is ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. In this work, we present a novel approach to boost the Rayleigh number in thermal convection by exploiting centrifugal acceleration and rapidly rotating a cylindrical annulus to reach an effective gravity of 60 times Earth's gravity. We show that in the regime where the Coriolis effect is strong, the scaling exponent of Nusselt number versus Rayleigh number exceeds one-third once the Rayleigh number is large enough. The convective rolls revolve in prograde direction, signifying the emergence of zonal flow. The present findings open a new avenue on the exploration of high-Rayleigh number turbulent thermal convection and will improve the understanding of the flow dynamics and heat transfer processes in geophysical and astrophysical flows and other strongly rotating systems.

Exit times of a Brownian particle out of a convection roll

We numerically investigated the transient dynamics of a passive colloidal particle in a periodic array of planar counter-rotating convection rolls at high Péclet numbers. We discovered that the distributions of first-exit times out of a single convection roll exhibit distinct regimes: an exponential tail, due to the noise-assisted diffusion of the trapped particle from the center toward the edge of the roll, and a peak structure emerging from a power-law background, associated with the transverse and longitudinal Brownian diffusion of the particle within the rolls’ flow boundary layers. These results are interpreted analytically and related to the earlier literature on the topic.

Average Vibrational–Convective Fluid Flows in Two-Layer Systems of Different Permeability under Zero Gravity

Roll convection developed under vibrations in the two-layer fluid system with homogeneous porous zone of different permeability is investigated. The system performs high-frequency oscillations directed transversely to the vertical temperature gradient in weightlessness. The convection problem is simulated on the basis of the averaging technique. The ranges of vibration frequencies and permeabilities of the porous zone characteristic of the short- and long-wave rolls are determined. Under zero gravity, sharp change in the form of rolls occurring with increase in the permeability, which is typical for free thermal convection in layered systems under the ordinary Earth’s conditions, is revealed. The minimum Darcy number below which there is no sharp transition from short- to long-wave convection with increase in the vibration frequency is found.

Multiple States in Turbulent Large-Aspect-Ratio Thermal Convection: What Determines the Number of Convection Rolls?

Wall-bounded turbulent flows can take different statistically stationary turbulent states, with different transport properties, even for the very same values of the control parameters. What state the system takes depends on the initial conditions. Here we analyze the multiple states in large-aspect ratio (Γ) two-dimensional turbulent Rayleigh-Bénard flow with no-slip plates and horizontally periodic boundary conditions as model system. We determine the number n of convection rolls, their mean aspect ratios Γ_{r}=Γ/n, and the corresponding transport properties of the flow (i.e., the Nusselt number Nu), as function of the control parameters Rayleigh (Ra) and Prandtl number. The effective scaling exponent β in Nu∼Ra^{β} is found to depend on the realized state and thus Γ_{r}, with a larger value for the smaller Γ_{r}. By making use of a generalized Friedrichs inequality, we show that the elliptical shape of the rolls and viscous damping determine the Γ_{r} window for the realizable turbulent states. The theoretical results are in excellent agreement with our numerical finding 2/3≤Γ_{r}≤4/3, where the lower threshold is approached for the larger Ra. Finally, we show that the theoretical approach to frame Γ_{r} also works for free-slip boundary conditions.

Café latte: spontaneous layer formation in laterally cooled double diffusive convection

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Elliptical Instability and Multiple-Roll Flow Modes of the Large-Scale Circulation in Confined Turbulent Rayleigh-Bénard Convection

The large-scale circulation (LSC) of fluid is one of the main concepts in turbulent thermal convection as it is known to be important in global heat and mass transport in the system. In turbulent Rayleigh-Bénard convection (RBC) in slender containers, the LSC is formed of several dynamically changing convective rolls that are stacked on top of each other. The present study reveals the following two important facts: (i)the mechanism which causes the twisting and breaking of a single-roll LSC into multiple rolls is the elliptical instability and (ii)the heat and momentum transport in RBC, represented by the Nusselt (Nu) and Reynolds (Re) numbers, is always stronger (weaker) for smaller (larger) number n of the rolls in the LSC structure. Direct numerical simulations support the findings for n=1,…,4 and the diameter-to-height aspect ratio of the cylindrical container Γ=1/5, the Prandtl number Pr=0.1 and Rayleigh number Ra=5×10^{5}. Thus, Nu and Re are, respectively, 2.5 and 1.5 times larger for a single-roll LSC (n=1) than for a LSC with n=4 rolls.

Two Modes of Vibrational Double-Diffusive Instability in a Superposed Fluid-Porous Layer Heated from Below: The Effect of Buoyancy Ratio

The convective double-diffusive instability in a two-layer system consisting of a binary fluid layer overlaying a fluid-saturated porous layer is investigated numerically. The system moves periodically in a vertical direction under the conditions of gravity field. The layers are heated from below and oscillate with high frequency and small amplitude. The instability threshold for the convection onset and the wavelength of convective rolls, which induce as soon as the fluid equilibrium state has lost its stability, are found. The buoyancy ratio and vibrational parameter effects are studied. A region of parameters for the bimodal marginal stability curves is obtained and divided it into parts for the local and large-scale convection onset values. It is revealed that wavelength of stationary convection rolls varies non-monotonically as the buoyancy ratio decreases. The longitudinal scale of rolls reduces sharply at first and then increases gradually. Vibration produces the greatest stabilizing effect on the fluid equilibrium state in a narrow range of small negative and positive buoyancy ratios, which are responsible for a considerable change in the wavelength of rolls. The buoyancy ratio effect on the oscillatory convection rolls is rather weak. The vibration effect on their marginal stability threshold and wavelength is more pronounced.

Onset of thermal convection in a superposed fluid-porous layer subjected to high-frequency longitudinal vibration in weightlessness

The onset of thermal vibrational convection in a fluid layer overlaying a fluid-saturated porous layer is studied in zero gravity. A thermal gradient is imposed transverse to the layers. The two-layer system performs high-frequency small-amplitude oscillations perpendicular to the thermal gradient. We solve a linear stability problem with respect to the fluid quasi-equilibrium state. The basic closed-looped oscillatory flow with zero average velocity characterizes the quasi-equilibrium state. The average roll convection is generated if the Rayleigh number exceeds its threshold value. The bimodal marginal stability curves are revealed at different ratios of the fluid layer thickness to that of the porous layer. They are somewhat similar to the curves first obtained by Chen and Chen for the onset of thermal convection in a superposed fluid-porous layer in a gravity field. We find that short-wave convection replaces the long-wave one with an increase in the ratio of layer thicknesses. The transition is accompanied by a jump-wise increase in the wave number of the most dangerous convective rolls. However, the critical wave number of the vibrational convection rolls can change by several orders of magnitude in contrast to that of the gravitational convection rolls. So, one can have super short-wave convection in zero gravity. A value of the instability threshold varies non-monotonically. The convection onset delays rather weakly at small thickness ratios. On the contrary, sufficiently high thickness ratios make the convection onset speed up strongly.

Numerical Investigation of the Effects of Particle Density and Dimensionless Acceleration on Segregation in 2D Vertically Vibrated Binary Granular Mixtures

The present work aims to investigate the influences of particle density and dimensionless acceleration on segregation phenomena in 2D binary granular mixtures by using contact dynamics method. The granular samples were prepared by randomly depositing two species of regular pentagonal particles inside a rectangular container. These two particle species are the same in size, but differ in terms of particle density. Different levels of vertical vibration were then applied to the mixtures. The simulation results were systematically analyzed by using segregation coefficient (H), segregation pattern, and velocity field related to convection mechanism. It was found that segregation phenomena are not observed in this study. This could be explained by the fact that a value of friction coefficient between interparticle and that value between wall and particle is set to be the same, that is why no segregation was found in the present study. Due to the friction, only convection rolls were observed for all the density ratios when dimensionless acceleration is greater than 2.

Penetrative Convection for Rotating Boussinesq Flow in Tilted f-planes

Abstract In this paper, we have performed linear instability analysis of the penetrative convection for the Boussinesq flow on a tilted f-plane. We have discussed the onset of instability as stationary and oscillatory convection. For the stationary convection, it has been shown that the penetration of convection is hindered by the stability of the upper, less unstable layer. For the oscillatory convection, however, the conclusion is different. We have computed the penetrative convection for both prograde and retrograde waves. The result indicates that for the prograde wave, under certain circumstances, the penetrative convection in the upper layer can be more vigorous than that in the lower unstable layer. For the retrograde wave, on the other hand, the stability in the upper layer always has a negative effect on the penetrative convection. Our calculation on the tilted f-plane has reproduced many features, such as teleconvection and multilayer roll convection, previously discovered on the penetrative convection in the spherical geometry. The dependence of penetrative distance on the Ekman number, the Prandtl number, and the stability parameter has been analyzed.

Local Discontinuous Galerkin Method for Nonlinear Time-Space Fractional Subdiffusion/Superdiffusion Equations

Fractional partial differential equations with time-space fractional derivatives describe some important physical phenomena. For example, the subdiffusion equation (time order 0<α<1) is more suitable to describe the phenomena of charge carrier transport in amorphous semiconductors, nuclear magnetic resonance (NMR) diffusometry in percolative, Rouse, or reptation dynamics in polymeric systems, the diffusion of a scalar tracer in an array of convection rolls, or the dynamics of a bead in a polymeric network, and so on. However, the superdiffusion case (1<α<2) is more accurate to depict the special domains of rotating flows, collective slip diffusion on solid surfaces, layered velocity fields, Richardson turbulent diffusion, bulk-surface exchange controlled dynamics in porous glasses, the transport in micelle systems and heterogeneous rocks, quantum optics, single molecule spectroscopy, the transport in turbulent plasma, bacterial motion, and even for the flight of an albatross (for more physical applications of fractional sub-super diffusion equations, one can see Metzler and Klafter in 2000). In this work, we establish two fully discrete numerical schemes for solving a class of nonlinear time-space fractional subdiffusion/superdiffusion equations by using backward Euler difference 1<α<2 or second-order central difference 1<α<2/local discontinuous Galerkin finite element mixed method. By introducing the mathematical induction method, we show the concrete analysis for the stability and the convergence rate under the L2 norm of the two LDG schemes. In the end, we adopt several numerical experiments to validate the proposed model and demonstrate the features of the two numerical schemes, such as the optimal convergence rate in space direction is close to Ohk+1. The convergence rate in time direction can arrive at Oτ2−α when the fractional derivative is 0<α<1. If the fractional derivative parameter is 1<α<2 and we choose the relationship as h=C′τ (h denotes the space step size, C′ is a constant, and τ is the time step size), then the time convergence rate can reach to Oτ3−α. The experiment results illustrate that the proposed method is effective in solving nonlinear time-space fractional subdiffusion/superdiffusion equations.