Skip to main content
Log in

Pattern Competition for the Sequential Bifurcations Approach (SBA) to Turbulence in the Co-Rotating Taylor–Couette System: Quinary States

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this study systematic numerical analyses are outlined searching for additional instabilities in the co-rotating Taylor–Couette system within the fully deterministic sequential approach of bifurcations (SBA) to turbulence. The main idea of the search strategy is the application of a forcing function, rotation, which has a direct physical interpretation, and that was realized in prior experimental work. The forcing induces disturbances that lead to bifurcations of new states. Thus, turbulence can be generated and observed in a rotating fluid without the imposing additional forcing sources. The imposition of thermoconvective forcing in the Taylor–Couette system will be discussed separately. Important findings include the discovery of the interplay of new and already known states, the transition of steady states to oscillatory ones and higher order states in the SBA via vortex merger/separation and re-allocation of symmetries for a more intensified mass transport. The results of the present work enhance the results of [1]. They will be revisited within an internal length gradient (ILG) framework accounting for weekly nonlocal effects as suggested in the concluding section of the paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

REFERENCES

  1. T. Akinaga, S. C. Generalis, and F. H. Busse, ‘‘Tertiary and quaternary states in the Taylor–Couette system,’’ Chaos Sol. Fr. 109, 107–117 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  2. P. J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows (Springer, New York, 2001).

    Book  MATH  Google Scholar 

  3. J. J. Hegseth, G. W. Baxter, and C. D. Andereck, ‘‘Bifurcations from Taylor vortices between corotating concentric cylinders,’’ Phys. Rev. E 53, 507–521 (1996).

    Article  Google Scholar 

  4. M. Nagata, ‘‘Bifurcations in Couette flow between almost corotating cylinders,’’ J. Fluid Mech. 169, 229–250 (1986).

    Article  MATH  Google Scholar 

  5. E. Weisshaar, F. H. Busse, and M. Nagata, ‘‘Twist vortices and their instabilities in the Taylor–Couette system,’’ J. Fluid Mech. 226, 549–564 (1991).

    Article  Google Scholar 

  6. T. Itano and S. C. Generalis, ‘‘Hairpin vortex solution in planar Couette flow: A tapestry of knotted vortices,’’ Phys. Rev. Lett. 102, 114501 (2009).

    Article  Google Scholar 

  7. E. C. Aifantis, ‘‘Internal Length Gradient (ILG) material mechanics across scales and disciplines,’’ Adv. Appl. Mech. 49, 1–110 (2016).

    Article  Google Scholar 

  8. E. C. Aifantis, ‘‘Gradient extension of classical material models: From nuclear to condensed matter scales to earth and cosmological states,’’ in Size-Dependent Continuum Mechanics Approaches, Ed. by E. Ghavanloo et al., Vol. 2 of Springer Tracts in Mechanical Engineering (Springer Nature, Switzerland, AG, 2021), pp. 417–452.

  9. G. Silber, R. Trostel, M. Alizadeh, and G. Benderoth, ‘‘A continuum mechanical gradient theory with applications to fluid mechanics,’’ J. Phys. IV (France) 8, 365–376 (1998).

    Article  Google Scholar 

  10. E. Fried and M. E. Gurtin, ‘‘Tractions, balances and boundary conditions for nonsimple materials with application to liquid flow at small-length scales,’’ Arch. Rat Mech. Anal. 182, 513–554 (2006).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

This work was funded by the RISE-Grant 824022—ATM2BT of the European H2020-MSCA programme.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to T. Akinaga, S. C. Generalis or E. C. Aifantis.

Additional information

(Submitted by A. M. Elizarov)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akinaga, T., Generalis, S.C. & Aifantis, E.C. Pattern Competition for the Sequential Bifurcations Approach (SBA) to Turbulence in the Co-Rotating Taylor–Couette System: Quinary States. Lobachevskii J Math 44, 2202–2212 (2023). https://doi.org/10.1134/S1995080223060045

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080223060045

Keywords:

Navigation