Stability and dynamical transition of a electrically conducting rotating fluid

by   Liang Li, et al.

In this article, we aim to study the stability and dynamic transition of an electrically conducting fluid in the presence of an external uniform horizontal magnetic field and a rotation based on a Boussinesq approximation model. We take a hybrid approach combining theoretical analysis with numerical computation to study the transition from a simple real eigenvalue, a pair of complex conjugate eigenvalues and a pair of real eigenvalues. The center manifold reduction theory is applied to reduce the infinite dimensional system to the corresponding finite dimensional one together with several non-dimensional transition numbers that determine the dynamic transition types. Careful numerical computations are performed to determine these transition numbers as well as related temporal and flow patterns etc. Our results indicate that both transition of continuous type and transition of jump type can occur at certain parameter region. For the continuous transition from a simple real eigenvalue, the Boussinesq approximation model bifurcates to two nontrivial stable steady-state solutions. For the continuous transition from a pair of complex conjugate eigenvalues, the model bifurcates to a stable periodic solutions. For the continuous transition from a pair of real eigenvalues, the model bifurcates to a local attractor at the critical Rayleigh number. The local attractor contains two (four) stable nodes and two (four) saddle points.



There are no comments yet.


page 30

page 32


Eigenvector distribution in the critical regime of BBP transition

In this paper, we study the random matrix model of Gaussian Unitary Ense...

Spectrum-based stability analysis and stabilization of a class of time-periodic time delay systems

We develop an eigenvalue-based approach for the stability assessment and...

Bifurcation analysis of two-dimensional Rayleigh–Bénard convection using deflation

We perform a bifurcation analysis of the steady state solutions of Rayle...

A numerical approach for transient magnetohydrodynamic flows

In the article the authors present a numerical method for modelling a la...

Stable Dynamic Mode Decomposition Algorithm for Noisy Pressure-Sensitive Paint Measurement Data

In this study, we proposed the truncated total least squares dynamic mod...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.