### Abstract

This is the final part of a three-part study of the stability of vertically oriented double-diffusive interfaces having an imposed vertical stable temperature gradient. In this study flow is forced within a fluid of infinite extent by a prescribed excess of compositionally buoyant material within a circular cylindrical interface. Compositional diffusivity is ignored while thermal diffusivity and viscosity are finite. The instability of the interface is determined by quantifying the exponential growth rate of a harmonic deflection of infinitesimal amplitude. Attention is focused on the zonal wavenumber of the fastest growing mode. The interface is found to be unstable for some wavenumber tor all values of the Prandtl number and interface radius. The zonal wavenumber of the fastest growing mode increases roughly linearly with interface radius, except for small values of the Prandtl number (<0.065). For small and moderate values of the radius, the preferred mode is either axisymmetric or has zonal wavenumber of 1, representing a helical instability. The growth rate of the fastest-growing mode is largest for interfaces having radii of from 2 to 3 salt-finger lengths.

Original language | English |
---|---|

Pages (from-to) | 45-66 |

Number of pages | 22 |

Journal | Journal of Fluid Mechanics |

Volume | 353 |

Publication status | Published - Dec 25 1997 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*353*, 45-66.

**On the stability of vertical double-diffusive interfaces. Part 3. Cylindrical interface.** / Eltayeb, I. A.; Loper, D. E.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 353, pp. 45-66.

}

TY - JOUR

T1 - On the stability of vertical double-diffusive interfaces. Part 3. Cylindrical interface

AU - Eltayeb, I. A.

AU - Loper, D. E.

PY - 1997/12/25

Y1 - 1997/12/25

N2 - This is the final part of a three-part study of the stability of vertically oriented double-diffusive interfaces having an imposed vertical stable temperature gradient. In this study flow is forced within a fluid of infinite extent by a prescribed excess of compositionally buoyant material within a circular cylindrical interface. Compositional diffusivity is ignored while thermal diffusivity and viscosity are finite. The instability of the interface is determined by quantifying the exponential growth rate of a harmonic deflection of infinitesimal amplitude. Attention is focused on the zonal wavenumber of the fastest growing mode. The interface is found to be unstable for some wavenumber tor all values of the Prandtl number and interface radius. The zonal wavenumber of the fastest growing mode increases roughly linearly with interface radius, except for small values of the Prandtl number (<0.065). For small and moderate values of the radius, the preferred mode is either axisymmetric or has zonal wavenumber of 1, representing a helical instability. The growth rate of the fastest-growing mode is largest for interfaces having radii of from 2 to 3 salt-finger lengths.

AB - This is the final part of a three-part study of the stability of vertically oriented double-diffusive interfaces having an imposed vertical stable temperature gradient. In this study flow is forced within a fluid of infinite extent by a prescribed excess of compositionally buoyant material within a circular cylindrical interface. Compositional diffusivity is ignored while thermal diffusivity and viscosity are finite. The instability of the interface is determined by quantifying the exponential growth rate of a harmonic deflection of infinitesimal amplitude. Attention is focused on the zonal wavenumber of the fastest growing mode. The interface is found to be unstable for some wavenumber tor all values of the Prandtl number and interface radius. The zonal wavenumber of the fastest growing mode increases roughly linearly with interface radius, except for small values of the Prandtl number (<0.065). For small and moderate values of the radius, the preferred mode is either axisymmetric or has zonal wavenumber of 1, representing a helical instability. The growth rate of the fastest-growing mode is largest for interfaces having radii of from 2 to 3 salt-finger lengths.

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UR - http://www.scopus.com/inward/citedby.url?scp=0031384191&partnerID=8YFLogxK

M3 - Article

VL - 353

SP - 45

EP - 66

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -