1
|
Hazra S, Kumar K, Mitra S. Rayleigh-Bénard magnetoconvection with temperature modulation. Proc Math Phys Eng Sci 2020; 476:20200289. [PMID: 33223933 DOI: 10.1098/rspa.2020.0289] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2020] [Accepted: 09/17/2020] [Indexed: 11/12/2022] Open
Abstract
Floquet analysis of modulated magnetoconvection in Rayleigh-Bénard geometry is performed. A sinusoidally varying temperature is imposed on the lower plate. As Rayleigh number Ra is increased above a critical value Rao, the oscillatory magnetoconvection begins. The flow at the onset of magnetoconvection may oscillate either subhar- monically or harmonically with the external modulation. The critical Rayleigh number Rao varies non-monotonically with the modulation frequency ω for appreciable value of the modulation amplitude a. The temperature modulation may either postpone or prepone the appearance of magnetoconvection. The magnetoconvective flow always oscillates harmonically at larger values of ω. The threshold Rao and the corresponding wavenumber k o approach to their values for the stationary magnetoconvection in the absence of modulation (a = 0), as ω → ∞. Two different zones of harmonic instability merge to form a single instability zone with two local minima for higher values of Chandrasekhar's number Q, which is qualitatively new. We have also observed a new type of bicritical point, which involves two different sets of harmonic oscillations. The effects of variation of Q and Pr on the threshold Rao and critical wavenumber k o are also investigated.
Collapse
Affiliation(s)
- Suparna Hazra
- Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302, West Bengal, India
| | - Krishna Kumar
- Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302, West Bengal, India
| | - Saheli Mitra
- Laboratoire de Physique des Solides, Université Paris-Saclay, CNRS, 91405 Orsay, France
| |
Collapse
|
2
|
Thermodynamic Analysis of Bistability in Rayleigh-Bénard Convection. ENTROPY 2020; 22:e22080800. [PMID: 33286571 PMCID: PMC7517371 DOI: 10.3390/e22080800] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Revised: 07/09/2020] [Accepted: 07/15/2020] [Indexed: 11/16/2022]
Abstract
Bistability is often encountered in association with dissipative systems far from equilibrium, such as biological, physical, and chemical phenomena. There have been various attempts to theoretically analyze the bistabilities of dissipative systems. However, there is no universal theoretical approach to determine the development of a bistable system far from equilibrium. This study shows that thermodynamic analysis based on entropy production can be used to predict the transition point in the bistable region during Rayleigh–Bénard convection using the experimental relationship between the thermodynamic flux and driving force. The bistable region is characterized by two distinct features: the flux of the second state is higher than that of the first state, and the entropy production of the second state is lower than that of the first state. This thermodynamic interpretation provides new insights that can be used to predict bistable behaviors in various dissipative systems.
Collapse
|
3
|
Ban T, Shigeta K. Thermodynamic analysis of thermal convection based on entropy production. Sci Rep 2019; 9:10368. [PMID: 31316153 PMCID: PMC6637266 DOI: 10.1038/s41598-019-46921-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2018] [Accepted: 07/03/2019] [Indexed: 11/08/2022] Open
Abstract
Flow patterns have a tendency to break the symmetry of an initial state of a system and form another spatiotemporal pattern when the system is driven far from equilibrium by temperature difference. For an annular channel, the axially symmetric flow becomes unstable beyond a given temperature difference threshold imposed in the system, leading to rotational oscillating waves. Many researchers have investigated this transition via linear stability analysis using the fundamental conservation equations and the generic model amplitude equation, i.e., the complex Ginzburg-Landau equation. Here, we present a quantitative study conducted of the thermal convection transition using thermodynamic analysis based on the maximum entropy production principle. Our analysis results reveal that the fluid system under nonequilibrium maximizes the entropy production induced by the thermodynamic flux in a direction perpendicular to the temperature difference. Further, we show that the thermodynamic flux as well as the entropy production can uniquely specify the thermodynamic states of the entire fluid system and propose an entropy production selection rule that can be used to specify the thermodynamic state of a nonequilibrium system.
Collapse
Affiliation(s)
- Takahiko Ban
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonaka City, Osaka, 560-8531, Japan.
| | - Keigo Shigeta
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonaka City, Osaka, 560-8531, Japan
| |
Collapse
|
4
|
Singh J, Bajaj R, Kaur P. Bicritical states in temperature-modulated Rayleigh-Bénard convection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:013005. [PMID: 26274268 DOI: 10.1103/physreve.92.013005] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2015] [Indexed: 06/04/2023]
Abstract
We investigate the Rayleigh-Bénard convection under sinusoidally varying temperatures of the horizontal rigid planes bounding a laterally infinite fluid layer for the bicritical states. The problem is analogous to the well studied Faraday instability and Rayleigh-Bénard convection under gravity modulation. Under modulation, the neutral instability curve is found to alternate between the conventional harmonic and subharmonic tongues in the space of the dimensionless wave number of disturbance and the control parameter. The transition between harmonic and subharmonic critical instability responses is found to occur via a bicritical state, where the two instability responses coexist with different wave numbers. These bicritical states are found to depend upon the modulation parameters and the Prandtl number.
Collapse
Affiliation(s)
- Jitender Singh
- Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, Punjab, India
| | - Renu Bajaj
- Department of Mathematics, Panjab University, Chandigarh 160014, India
| | - Puneet Kaur
- Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, Punjab, India
| |
Collapse
|
5
|
Rogers JL, Pesch W, Brausch O, Schatz MF. Complex-ordered patterns in shaken convection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:066214. [PMID: 16089856 DOI: 10.1103/physreve.71.066214] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2005] [Indexed: 05/03/2023]
Abstract
We report and analyze complex patterns observed in a combination of two standard pattern forming experiments. These exotic states are composed of two distinct spatial scales, each displaying a different temporal dependence. The system is a fluid layer experiencing forcing from both a vertical temperature difference and vertical time-periodic oscillations. Depending on the parameters these forcing mechanisms produce fluid motion with either a harmonic or a subharmonic temporal response. Over a parameter range where these mechanisms have comparable influence the spatial scales associated with both responses are found to coexist, resulting in complex, yet highly ordered patterns. Phase diagrams of this region are reported and criteria to define the patterns as quasiperiodic crystals or superlattices are presented. These complex patterns are found to satisfy four-mode (resonant tetrad) conditions. The qualitative difference between the present formation mechanism and the resonant triads ubiquitously used to explain complex-ordered patterns in other nonequilibrium systems is discussed. The only exception to quantitative agreement between our analysis based on Boussinesq equations and laboratory investigations is found to be the result of breaking spatial symmetry in a small parameter region near onset.
Collapse
|
6
|
Thompson KL, Bajaj KMS, Ahlers G. Traveling concentric-roll patterns in Rayleigh-Bénard convection with modulated rotation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:046218. [PMID: 12005987 DOI: 10.1103/physreve.65.046218] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2001] [Indexed: 05/23/2023]
Abstract
We present experimental results for pattern formation in Rayleigh-Bénard convection with modulated rotation about a vertical axis. The dimensionless rotation rate Omega was varied as Omega(m)=Omega[1+delta cos(phi Omega t)] (time is scaled by the vertical viscous diffusion time of the cell). We used a cylindrical cell of aspect ratio (radius/height) Gamma=11.8 and varied Omega, delta, phi, and epsilon identical with R/R(c)(Omega)-1 (R is the Rayleigh number). The fluid was water with a Prandtl number of 4.5. Sufficiently far above onset even a small delta greater than approximately 0.02 stabilized a concentric-roll (target) pattern. Multiarmed spirals were observed close to onset. The rolls of the target patterns traveled radially inward independent of the sense of rotation. The radial speed v was nearly independent of epsilon for fixed Omega, delta, and phi. However, v increased with any one of Omega, delta, and phi when all the other parameters were held fixed.
Collapse
Affiliation(s)
- Kim L Thompson
- Department of Physics and iQuest, University of California, Santa Barbara, California 93106, USA
| | | | | |
Collapse
|
7
|
Rogers JL, Schatz MF, Bougie JL, Swift JB. Rayleigh-Benard convection in a vertically oscillated fluid layer. PHYSICAL REVIEW LETTERS 2000; 84:87-90. [PMID: 11015841 DOI: 10.1103/physrevlett.84.87] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/1999] [Indexed: 05/23/2023]
Abstract
We report on the first quantitative observations of convection in a fluid layer driven by both heating from below and vertical sinusoidal oscillation. Just above onset, convection patterns are modulated either harmonically or subharmonically to the drive frequency. Single-frequency patterns exhibit nearly solid-body rotations with harmonic and subharmonic states always rotating in opposite directions. Flows with both harmonic and subharmonic responses are found near a codimension-two point, yielding novel coexisting patterns with symmetries not found in either single-frequency states. Predictions from linear stability analysis of the onset Rayleigh and wave numbers compare well with experiment, and phase boundaries for coexisting patterns track single-frequency marginal stability curves.
Collapse
Affiliation(s)
- JL Rogers
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA
| | | | | | | |
Collapse
|
8
|
Or AC, Kelly RE. Time-modulated convection with zero mean temperature gradient. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:1741-7. [PMID: 11969956 DOI: 10.1103/physreve.60.1741] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/1999] [Indexed: 11/07/2022]
Abstract
We study numerically the onset of temporally modulated Rayleigh-Bénard convection with zero mean gradient for cases of antisymmetric and asymmetric boundary temperatures over a continuous range of nondimensional frequencies omega, from omega approximately O(10(-1)) to omega approximately O(10(3)). For omega below 1, the neutral curves for Pr=7 in both cases alternate between synchronous and subharmonic responses, with increasingly shorter intervals as omega becomes small. At large omega, the critical wave number k(c) asymptotes to omega(1/2) and the critical Rayleigh number R(c) asymptotes to omega(3/2), via a subharmonic response in both cases. A comparison with the experimental results of Niemela and Donnelly [Phys. Rev. Lett. 57, 583 (1986)] shows fairly reasonable agreement.
Collapse
Affiliation(s)
- A C Or
- Department of Mechanical and Aerospace Engineering, University of California at Los Angeles, Los Angeles, California 90095-1597, USA
| | | |
Collapse
|
9
|
Moehlis J, Knobloch E. Eckhaus-Benjamin-Feir instability in systems with temporal modulation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:5161-5168. [PMID: 9965696 DOI: 10.1103/physreve.54.5161] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
10
|
Watanabe T, Kaburaki H, Machida M, Yokokawa M. Growth of long-range correlations in a transition between heat conduction and convection. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:1601-1605. [PMID: 9963580 DOI: 10.1103/physreve.52.1601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
11
|
Hu H, Kelly RE. Effect of a time-periodic axial shear flow upon the onset of Taylor vortices. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:3242-3251. [PMID: 9963002 DOI: 10.1103/physreve.51.3242] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
12
|
Watanabe T, Kaburaki H, Yokokawa M. Simulation of a two-dimensional Rayleigh-Bénard system using the direct simulation Monte Carlo method. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:4060-4064. [PMID: 9961694 DOI: 10.1103/physreve.49.4060] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|