Skip to main content
SpringerLink
Log in

Global nonlinear stability and “cold convection instability” of non-constant porous throughflows, 2D in vertical planes

  • Published:
Ricerche di Matematica Aims and scope Submit manuscript

Abstract

Porous horizontal layers are considered. A class of non-constant porous throughflows, 2D in vertical planes, is obtained. The global stability conditions and the “cold convection instability” conditions are investigated.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. The seepage (or filtration) velocity is the mean value of the effective fluid velocity in a pore. It is defined as \(\mathbf {v}=\varepsilon \bar{\mathbf {v}}\) where \(\varepsilon =\displaystyle \frac{\text{ empty } \text{ volume }}{\text{ total } \text{ volume }}\in [0,1]\) is the porosity and \(\bar{\mathbf {v}}\) is the effective fluid velocity.

References

  1. Rionero, S.: Global non-linear stability in double diffusive convection via hidden symmetries. Int. J. Non-Linear Mech. 47, 61–66 (2012)

    Google Scholar 

  2. Rionero, S.: Symmetries and skew-symmetries against onset of convection in porous layers salted from above and below. Int. J. Non-Linear Mech. 47, 61–67 (2012)

    Google Scholar 

  3. Capone, F., De Luca, R.: Onset of convection for ternary fluid mixtures saturating horizontal porous layers with large pores. Rendic. Accad. Lincei XXIII Ser. IX 4, 405–428 (2012)

  4. Capone, F., De Luca, R.: Ultimately boundedness and stability of triply diffusive mixtures in rotating porous layers under the action of Brinkman law. Int. J. Non-Linear Mech. 47(7), 799–805 (2012)

    Article  Google Scholar 

  5. Rionero, S.: Absence of subcritical instabilities and global nonlinear stability for porous ternary diffusive–convective fluid mixtures. Phys. Fluids 24, 104101 (2012)

    Article  MathSciNet  Google Scholar 

  6. Rionero, S.: Multicomponent diffusive–convective fluid motions in porous layers: ultimately boundedness, absence of subcritical instabilities and global nonlinear stability for any number of salts. Phys. Fluids 25, 054104 (2013)

    Article  Google Scholar 

  7. Capone, F., Rionero, S.: Inertia effect on the onset of convection in rotating porous layers via the “auxiliary system method”. Int. J. Non-linear Mech. 52, 192–200 (2013)

    Article  Google Scholar 

  8. Merkin, D.R.: Introduction to the theory of stability. In: Springer Texts in Applied Mathematics, Vol 24 (1997)

  9. Vargaftik, N.B., Filippov, L.P., Tarzimanov, A.A., Totskii, E.E.: Handbook of Thermal Conductivity of Liquids and Gases. CRC Press, Boca Raton (1994)

  10. Nield, D.A., Kuznetsov, A.V.: The effect of vertical throughflow on the onset of convection in a porous medium in a rectangular box. Transp. Porous Med. 90, 993–1000 (2011)

    Article  MathSciNet  Google Scholar 

  11. Murty, Y.N.: Effect of throughflow and magnetic field on Benard convection in micropolar fluids. Acta Mech. 150, 11–21 (2001)

    Article  MATH  Google Scholar 

  12. Nield, D.A.: Throughflow effects in the Rayleigh–Benard convective instability problem. J. Fluid Mech. 185, 353–360 (1987)

    Article  Google Scholar 

  13. Nield, D.A., Kuznetsov, A.V.: The onset of convection in a heterogeneous porous medium with vertical throughflow. Transp. Porous Med. 88, 347–355 (2011)

    Article  MathSciNet  Google Scholar 

  14. Hill, A.A.: Unconditional nonlinear stability for convection in a porous medium with vertical throughflow. Acta Mech. 193, 197–206 (2007)

    Article  MATH  Google Scholar 

  15. Hill, A.A., Rionero, S., Straughan, B.: Global stability for penetrative convection with throughflow in a porous material. IMA J. Appl. Math. 72, 635–643 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Capone, F., De Luca, R., Torcicollo, I.: Longtime behaviour of vertical throughflows for binary mixtures in porous layers. Int. J. Non-Linear Mech. 52, 1–7 (2013)

    Article  Google Scholar 

  17. Capone, F., De Cataldis, V., De Luca, R., Torcicollo, I.: On the stability of vertical constant throughflows for binary mixtures in porous layers. Int. J. Non-Linear Mech. 59, 1–8 (2014)

    Article  Google Scholar 

  18. Capone, F., De Luca, R.: On the stability–instability of vertical throughflows in double diffusive mixtures saturating rotating porous layers with large pores. Ric. Mat. 63(1), 119–148 (2014)

    MATH  MathSciNet  Google Scholar 

  19. Capone, F., De Luca, R.: Coincidence between linear and global nonlinear stability of non-constant throughflows via the Rionero “auxiliary system method”. Meccanica 49(9), 2025–2036 (2014)

    MATH  MathSciNet  Google Scholar 

  20. Rionero, S.: Soret effects on the onset of convection in rotating porous layers via the “auxiliary system method”. Ric. Mat. 62(2), 183–208 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  21. Rionero, S.: ”Cold convection“ in porous layers salted from above. Meccanica 49(9), 2061–2068 (2014)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This paper has been performed under the auspices of the G.N.F.M. of I.N.d.A.M.

Author information

Authors and Affiliations

  1. Department of Mathematics and Applications “Renato Caccioppoli”, University of Naples Federico II, Via Cinzia, 80126, Naples, Italy

    Roberta De Luca

Authors
  1. Roberta De Luca
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roberta De Luca.

Additional information

Communicated by Salvatore Rionero.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

De Luca, R. Global nonlinear stability and “cold convection instability” of non-constant porous throughflows, 2D in vertical planes. Ricerche mat. 64, 99–113 (2015). https://doi.org/10.1007/s11587-014-0219-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11587-014-0219-3

Keywords

Mathematics Subject Classification

Search

Navigation