Influence of higher-order modes on ferroconvection

Title

Influence of higher-order modes on ferroconvection

Creator

Kanchana C.; Vez J.A.; Pez L.M.; Laroze D.; Siddheshwar P.G.

Description

Using Fourier representations, an elaborate study of regular cellular-convective and chaotic motions in a ferrofluid is made. Investigation is made on the adequacy or otherwise of the minimal mode in studying such motions. Higher-order modes are also considered by adding modes (vertical/horizontal/combined extension). For higher modes, the extensions yield a dynamical system of order greater than three. The characteristic features of extended ferromagnetic-Lorenz models are analyzed using the largest Lyapunov exponent(LE), second largest LE, bifurcation diagram, and phase-space plots. The effect of additional modes on critical modal-Rayleigh (infinitesimal and finite-amplitude ones) numbers and the Rayleigh number at which transition to chaos occurs are examined to report features of ferroconvection hitherto unseen in previous studies. As both horizontal and vertical modes are increased, our findings infer that the dynamical system displays advanced onset of regular convection and delayed chaotic motion. Vigorous-chaotic motion is seen on adding vertical modes, whereas on adding horizontal modes, intense chaos appears with decreased intensity for large values of the scaled Rayleigh number. Most important finding from the study is that as modes are increased (vertical/horizontal), the transition from regular to chaotic motion is greatly modified and leads the system to a hyper-chaotic state. Conventionally, the chaotic or hyper-chaotic state is intermittent with a periodic/quasi-periodic state but it can be retained in the chaotic or hyper-chaotic state by considering moderate values of the Prandtl number and/or by bringing in the ferromagnetic effect. 2022 Author(s).

Source

Chaos, Vol-32, No. 8

Date

2022-01-01

Publisher

American Institute of Physics Inc.

Coverage

Kanchana C., Instituto de Alta Investigaci, Sede Esmeralda Universidad de Tarapac Av. Luis Emilio Recabarren 2477, Iquique, Chile; Vez J.A., Instituto de Alta Investigaci, CEDENNA, Universidad de Tarapac Casilla 7 D, Arica, 1000000, Chile; Pez L.M., Departamento de Fica, FACI, Universidad de Tarapac Casilla 7 D, Arica, 1000000, Chile; Laroze D., Instituto de Alta Investigaci, CEDENNA, Universidad de Tarapac Casilla 7 D, Arica, 1000000, Chile; Siddheshwar P.G., Center for Mathematical Needs, Department of Mathematics, CHRIST(Deemed to Be University), Bengaluru, 560029, India

Rights

Restricted Access

Relation

ISSN: 10541500; PubMed ID: 36049924

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1063/5.0097398

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85137102996&doi=10.1063%2f5.0097398&partnerID=40&md5=2c06a9fefed4f0bd53b40e937886423f