### Abstract

The stability of a compositionally buoyant plume, of circular cross-section, rising in a rotating infinite fluid is investigated. Both plume and fluid have the same non-zero kinematic viscosity, v, and thermal diffusivity, κ. The growth rate of the instability depends on the Taylor number, Ta (which is a dimensionless number measuring the effect of the Coriolis force relative to the viscous force) and on the thickness, s_{0}, of the plume in addition to the Prandtl number, σ(= ν/κ) and the Reynolds number, R (which measures the strength of the forcing). The analysis is restricted to the case of small R. It is found that the presence of rotation enhances instability. A simple model of a single interface separating the two parts of an infinite fluid is investigated first in order to isolate the mechanism responsible for the increase in the growth rate with rotation. It is shown that the Coriolis force interacts with the zonal velocity component to produce a velocity component normal to the interface. For the right choice of wave vector components, this normal velocity component is in phase with the displacement of the interface and this leads to instability. The maximum growth rate is identified in the whole space of the parameters σ, Ta, s_{0} when R ≪ 1. While the maximum growth rate is of order R^{2} in the absence of rotation, it is increased to order R in the presence of rotation. It is also found that the Prandtl number, σ, which has a strong influence on the growth rate in the absence of rotation, plays a subservient role when rotation is present.

Original language | English |
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Pages (from-to) | 277-299 |

Number of pages | 23 |

Journal | Journal of Fluid Mechanics |

Volume | 354 |

Publication status | Published - Jan 10 1998 |

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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*,

*354*, 277-299.

**Compositional convection in the presence of rotation.** / Eltayeb, I. A.; Hamza, E. A.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 354, pp. 277-299.

}

TY - JOUR

T1 - Compositional convection in the presence of rotation

AU - Eltayeb, I. A.

AU - Hamza, E. A.

PY - 1998/1/10

Y1 - 1998/1/10

N2 - The stability of a compositionally buoyant plume, of circular cross-section, rising in a rotating infinite fluid is investigated. Both plume and fluid have the same non-zero kinematic viscosity, v, and thermal diffusivity, κ. The growth rate of the instability depends on the Taylor number, Ta (which is a dimensionless number measuring the effect of the Coriolis force relative to the viscous force) and on the thickness, s0, of the plume in addition to the Prandtl number, σ(= ν/κ) and the Reynolds number, R (which measures the strength of the forcing). The analysis is restricted to the case of small R. It is found that the presence of rotation enhances instability. A simple model of a single interface separating the two parts of an infinite fluid is investigated first in order to isolate the mechanism responsible for the increase in the growth rate with rotation. It is shown that the Coriolis force interacts with the zonal velocity component to produce a velocity component normal to the interface. For the right choice of wave vector components, this normal velocity component is in phase with the displacement of the interface and this leads to instability. The maximum growth rate is identified in the whole space of the parameters σ, Ta, s0 when R ≪ 1. While the maximum growth rate is of order R2 in the absence of rotation, it is increased to order R in the presence of rotation. It is also found that the Prandtl number, σ, which has a strong influence on the growth rate in the absence of rotation, plays a subservient role when rotation is present.

AB - The stability of a compositionally buoyant plume, of circular cross-section, rising in a rotating infinite fluid is investigated. Both plume and fluid have the same non-zero kinematic viscosity, v, and thermal diffusivity, κ. The growth rate of the instability depends on the Taylor number, Ta (which is a dimensionless number measuring the effect of the Coriolis force relative to the viscous force) and on the thickness, s0, of the plume in addition to the Prandtl number, σ(= ν/κ) and the Reynolds number, R (which measures the strength of the forcing). The analysis is restricted to the case of small R. It is found that the presence of rotation enhances instability. A simple model of a single interface separating the two parts of an infinite fluid is investigated first in order to isolate the mechanism responsible for the increase in the growth rate with rotation. It is shown that the Coriolis force interacts with the zonal velocity component to produce a velocity component normal to the interface. For the right choice of wave vector components, this normal velocity component is in phase with the displacement of the interface and this leads to instability. The maximum growth rate is identified in the whole space of the parameters σ, Ta, s0 when R ≪ 1. While the maximum growth rate is of order R2 in the absence of rotation, it is increased to order R in the presence of rotation. It is also found that the Prandtl number, σ, which has a strong influence on the growth rate in the absence of rotation, plays a subservient role when rotation is present.

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M3 - Article

VL - 354

SP - 277

EP - 299

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -