Reduction of a Tri-Modal Lorenz Model of Ferrofluid Convection to a Cubic–Quintic Ginzburg–Landau Equation Using the Center Manifold Theorem

Siddheshwar, P. G.; Sushma, T. S.

doi:10.1007/s12591-021-00565-9

Cited by 2 publications

(2 citation statements)

References 35 publications

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“…In their investigation, it is observed that, heat transfer is greatest in shallow and least in tall enclosure. Siddheshwar and Sushma [24] performed non-linear analysis of Rayleigh-Bénard convection for rigid isothermal boundaries. While comparing heat transfer, they discovered that the rigid isothermal boundary has less heat transfer rate than the free isothermal case.…”

Section: Introductionmentioning

confidence: 99%

Linear and Non-Linear Analysis of Rayleigh-Bénard Convection in a Micropolar Fluid Occupying Enclosures With Realistic Boundaries

Jestine,

Pranesh

2023

Comm. Math. Appl.

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The linear and non-linear analysis of Rayleigh-Bénard convection (RBC) in a micropolar fluid (MPF) occupying enclosures are analyzed for realistic boundaries. The different enclosures considered are shallow enclosure (h < b), square enclosure (h = b) and tall enclosure (h > b). Linear analysis is conducted to study the on-set-of-convection, using the Fourier series representation. The different boundaries taken into consideration are Free-Free (F-F), Rigid-Free (R-F) and Rigid-Rigid (R-R). Using the Fourier-series representation, the fourth order Lorenz model is derived to quantify the heat transport. The effect of various MPF parameters has been analyzed. The rate of heat transfer is calculated from average Nusselt number, (Nu(t)).

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Section: Introductionmentioning

confidence: 99%

Linear and Non-Linear Analysis of Rayleigh-Bénard Convection in a Micropolar Fluid Occupying Enclosures With Realistic Boundaries

Jestine,

Pranesh

2023

Comm. Math. Appl.

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“…This landmark result changed how researchers view the role of numerical simulations and reduced-order modelling in science, and it established the modern field of chaos theory. Similar approaches have been applied to rotating convection or Ferrofluid convection resulting in a three-mode second-order nonlinear model known as the Glukhovsky-Dolzhansky system [13][14][15][16]. However, this type of simplified dynamical system model has not yet been demonstrated for convective systems with more complex coupling mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Sparse nonlinear models of chaotic electroconvection

2021

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Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modelling convection has given rise to the development of chaos theory and the reduced-order modelling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh–Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.

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Reduction of a Tri-Modal Lorenz Model of Ferrofluid Convection to a Cubic–Quintic Ginzburg–Landau Equation Using the Center Manifold Theorem

Cited by 2 publications

References 35 publications

Linear and Non-Linear Analysis of Rayleigh-Bénard Convection in a Micropolar Fluid Occupying Enclosures With Realistic Boundaries

Linear and Non-Linear Analysis of Rayleigh-Bénard Convection in a Micropolar Fluid Occupying Enclosures With Realistic Boundaries

Sparse nonlinear models of chaotic electroconvection

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