<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e345" altimg="si434.gif"><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> attractor bifurcation analysis for an electrically conducting fluid flow between two rotating cylinders

Liu, Ruikuan; Wang, Quan

doi:10.1016/j.physd.2019.03.001

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…Theorem 4.1. Let 𝐮(𝑥, 𝑡), 𝑇(𝑥, 𝑡) be the solution of equations ( 24), (26). If the functions Ψ, 𝑇 0 , 𝐹 0 satisfy Assumption 4.1, then the vector field 𝐮 has an interior separation near ( x, 𝑡 0 ).…”

Section: Interior Separation Theorem For 2d Incompressible Fluid Flow...mentioning

confidence: 99%

“…Remark 4.2. The conditions given in Assumption 4.1 are determined by the initial external force (25) and the initial conditions (26) It is clear that 𝐯 has an interior separation near ( x, 𝑡 0 ) is enough to judge the interior separation of 𝐮. Note that Theorem 4.1 provides an approach to predict the interior separation depending on the initial functions.…”

Section: 𝐮(𝑥 𝑡) = 𝐯(𝑥 𝑡) + 𝑜(|𝑡|)mentioning

confidence: 99%

“…More well‐posedness and numerical study related to patterns and stability of other fluid flows, we refer the readers to Refs. [23–32].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new fluid dynamical model coupling horizontal heat with an application to interior separations

Liu

Yang

2022

Z Angew Math Mech

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Based on the Newton's second law and Boussinesq equations, a new fluid dynamical model coupling horizontal heat is established. Moreover, the sufficient conditions of interior separation for this new model are obtained. It is shown that the sufficient conditions, determined by the initial value, may provide an approach to predict when and where the interior separations occur. In addition, an example is constructed to illustrate our main results.

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Section: Interior Separation Theorem For 2d Incompressible Fluid Flow...mentioning

confidence: 99%

Section: 𝐮(𝑥 𝑡) = 𝐯(𝑥 𝑡) + 𝑜(|𝑡|)mentioning

confidence: 99%

See 1 more Smart Citation

A new fluid dynamical model coupling horizontal heat with an application to interior separations

Liu

Yang

2022

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…This approach has been demonstrated to be a promising tool for studying nonlinear dynamical transition phenomena such as Rayleigh-Bénard problems, 25,26 Taylor problems, 30 boundary layer separation, [31][32][33] and more recent applications in fluid dynamics. 27,[34][35][36][37] In this study, we wish to present a simplified model to understand the formation of TCRs from the perspective of Ma and Wang's transition dynamics. By including the effects of latent heat release associated with roll cloud formation, we will show that the TCR formation experiences two dynamical processes consisting of (1) an attractor bifurcation when the Rayleigh number is larger than a critical value and (2) a boundary layer separation behavior for some specific threshold of the vertical wind shear, thus offering different insights into the formation of transverse rolls.…”

Section: Articlementioning

confidence: 99%

Dynamics of transverse cloud rolls in the boundary layer with the Poiseuille shear flow

Wang

Kieu

2019

Physics of Fluids

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This study examines the formation of transverse cloud rolls associated with the Poiseuille shear flows that are occasionally observed in the Earth's atmospheric boundary layer. It is shown that the mechanisms underlying the formation of this type of transverse roll clouds can be explained in the framework of the transition dynamics and structural bifurcation for the incompressible flows. Specifically, the formation of transverse roll clouds is attributed to a subtle interaction between the vertical wind shear and the vertical temperature gradient in the atmospheric well-mixed boundary layer, which results in an attractor bifurcation and subsequent boundary layer separations. The topological structure of the Poiseuille shear flow at the boundary layer separation can be identified as transverse roll cloud.

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“…Also, the global strong solutions for heat conducting 3-D classical magnetohydrodynamic flows with non-negative density were proved in [26]. For other various results related to the classical MHD model, we refer to [10], [13], [17], [22], and the references therein.…”

Section: Introductionmentioning

confidence: 98%

Global strong solutions of a 2-D new magnetohydrodynamic system

Liu

Yang

2020

Appl.Math.

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The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg's estimates for the stationary Stokes equation and Solonnikov's theorem on L p -L q -estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses a global strong solution. In addition, the uniqueness of the global strong solution is obtained.

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S1 attractor bifurcation analysis for an electrically conducting fluid flow between two rotating cylinders

Cited by 8 publications

References 19 publications

A new fluid dynamical model coupling horizontal heat with an application to interior separations

A new fluid dynamical model coupling horizontal heat with an application to interior separations

Dynamics of transverse cloud rolls in the boundary layer with the Poiseuille shear flow

Global strong solutions of a 2-D new magnetohydrodynamic system

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