### Abstract

Theory and experiments are reported that explore the behaviour of the Rayleigh-Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order of , where is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duff et al. (Phys. Fluids, vol. 5, 1962, pp. 417-425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh-Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162-178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duff et al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a decay in growth rates as for large-wavenumber perturbations.

Original language | English (US) |
---|---|

Pages (from-to) | 34-60 |

Number of pages | 27 |

Journal | Journal of Fluid Mechanics |

Volume | 791 |

DOIs | |

State | Published - Feb 15 2016 |

### Fingerprint

### Keywords

- buoyancy-driven instability
- gas dynamics
- turbulent mixing

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*791*, 34-60. https://doi.org/10.1017/jfm.2016.46

**Rarefaction-driven Rayleigh-Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory.** / Morgan, R. V.; Likhachev, O. A.; Jacobs, Jeffrey W.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 791, pp. 34-60. https://doi.org/10.1017/jfm.2016.46

}

TY - JOUR

T1 - Rarefaction-driven Rayleigh-Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

AU - Morgan, R. V.

AU - Likhachev, O. A.

AU - Jacobs, Jeffrey W

PY - 2016/2/15

Y1 - 2016/2/15

N2 - Theory and experiments are reported that explore the behaviour of the Rayleigh-Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order of , where is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duff et al. (Phys. Fluids, vol. 5, 1962, pp. 417-425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh-Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162-178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duff et al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a decay in growth rates as for large-wavenumber perturbations.

AB - Theory and experiments are reported that explore the behaviour of the Rayleigh-Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order of , where is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duff et al. (Phys. Fluids, vol. 5, 1962, pp. 417-425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh-Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162-178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duff et al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a decay in growth rates as for large-wavenumber perturbations.

KW - buoyancy-driven instability

KW - gas dynamics

KW - turbulent mixing

UR - http://www.scopus.com/inward/record.url?scp=84958260506&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958260506&partnerID=8YFLogxK

U2 - 10.1017/jfm.2016.46

DO - 10.1017/jfm.2016.46

M3 - Article

AN - SCOPUS:84958260506

VL - 791

SP - 34

EP - 60

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -