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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Transition to chaos in a reduced-order model of a shear layer

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Author(s):
Cavalieri, Andre V. G. [1] ; Rempel, Erico L. [2] ; Nogueira, Petronio A. S. [3]
Total Authors: 3
Affiliation:
[1] Inst Tecnol Aeronaut, Div Engn Aerosp, Sao Jose Dos Campos, SP - Brazil
[2] Inst Tecnol Aeronaut, Div Ciencias Fundamentais, Sao Jose Dos Campos, SP - Brazil
[3] Monash Univ, Dept Mech & Aerosp Engn, Lab Turbulence Res Aerosp & Combust, Clayton, Vic - Australia
Total Affiliations: 3
Document type: Journal article
Source: JOURNAL OF FLUID MECHANICS; v. 932, DEC 14 2021.
Web of Science Citations: 0
Abstract

The present work studies the nonlinear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira \& Cavalieri (J. Fluid Mech., vol. 907, 2021, A32), and is here studied using a reduced-order model based on a Galerkin projection of the Navier-Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin-Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number Re leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the direct numerical simulations by Nogueira \& Cavalieri. Further increase of Re leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher Re, leading to a chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents a dynamics consistent with features of shear layers and jets. (AU)

FAPESP's process: 19/27655-3 - Control-oriented reduced-order modelling for aerodynamics and aeroacoustics
Grantee:André Valdetaro Gomes Cavalieri
Support Opportunities: Regular Research Grants