Skip to main content
SpringerLink
Log in

The stability chart of double-diffusive processes with parallel flows — construction by the Galerkin and continuation methods

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

Summary

The stability of an infinite fluid layer subject to arbitrary horizontal flow and to arbitrary vertical temperature and salinity distributions is considered. Linear stability analysis is used to investigate the stability under general three-dimensional perturbations.

A general discussion of the properties of the stability chart, using only the governing equations, but not their solution for any particular case, is presented in [1]. This paper contributes a numerical scheme, based on a combination of the Galerkin and the continuation methods, to obtain the stability chart from the characteristic equation. The method is applied to an example with a parabolic velocity distribution and linear temperature and salinity fields. The stability chart in the plane of the Rayleigh numbers is obtained for the region corresponding to solar ponds.

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

References

  1. M. Magen, D. Pnueli and Y. Zvirin, Tge stability chart of parallel shear flows with double diffusive processes — general properties,J. Eng. Math. 19 (1985) 175–187.

    Google Scholar 

  2. M. Magen, Thermohaline stability with general horizontal flows. D.Sc. thesis, Technion, Haifa, Israel (1983).

  3. E. Wasserstrom, Numerical solution by the continuation method,SIAM Review 15 (1973) 89–119.

    Google Scholar 

  4. S.A. Orszag, Accurate solution of the Orr-Sommerfeld stability equation,J. Fluid Mech. 50 (1971) 689–703.

    Google Scholar 

  5. C.E. Grosch and H. Salwen, The stability of steady and time-dependent plane Poiseuille flow,J. Fluid Mech. 34 (1968) 177–205.

    Google Scholar 

  6. H. Weinberger, The physics of the solar pond,Solar Energy 8 (1964) 45–56.

    Google Scholar 

  7. A. Rabl and C.E. Nielsen, Solar ponds for space heating,Solar Energy 17 (1975) 1–12.

    Google Scholar 

  8. F. Zangrando and H.C. Bryant, A salt gradient solar pond,Solar Age 3 (1978) 21–36.

    Google Scholar 

  9. D.L. Harris and W.H. Reid, On orthogonal functions which satisfy four boundary conditions.Astrophys. J. Suppl. Ser. 3 (1958) 429–452.

    Google Scholar 

  10. D.A. Nield, The thermohaline Rayleigh-Jeffreys problem,J. Fluid Mech. 29 (1967) 545–558.

    Google Scholar 

  11. J.H. Wilkinson,The Algebraic Eigenvalue Problem, Oxford Univ. Press (1965).

  12. S.G. Mikhlin,Direct Methods in Mathematical Physics (in Russian), Gos. Izd. Technico-Teor. Lit., Moskwa-Leningrad (1950).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, Technion, Israel Institute of Technology, 32 000, Haifa, Israel

    M. Magen, D. Pnueli & Y. Zvirin

Authors
  1. M. Magen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Pnueli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Zvirin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Magen, M., Pnueli, D. & Zvirin, Y. The stability chart of double-diffusive processes with parallel flows — construction by the Galerkin and continuation methods. J Eng Math 20, 127–144 (1986). https://doi.org/10.1007/BF00042772

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00042772

Keywords

Search

Navigation