### Abstract

The three-dimensional (3D) Richtmyer-Meshkov instability of incompressible, miscible liquids with a 3D single-mode initial perturbation is investigated. This study uses the apparatus of the earlier experiments of Niederhaus and Jacobs [J. Fluid Mech. 485, 243 (2003)] in which the instability is generated by impulsively accelerating a tank containing the two liquids. However, the present investigation uses a tank with square cross section allowing the generation of a square-mode 3D initial perturbation by lateral oscillation along the tank's diagonal. Amplitude measurements of the 3D instability are found to be effectively collapsed by the dimensionless scaling used in the two-dimensional (2D) study and to be in good agreement with linear stability theory up until a dimensionless time kv_{0}t ≈ 1, later than is found for the 2D flow. Late-time 3D amplitude measurements show faster growth than 2D as is predicted by popular bubble models. However, late-time growth rate measurements are found to deviate from model predictions at the latest times showing a constant growth rate instead of the 1/t dependence given by the models. The constant late-time growth rate is the result of the observed vorticity distribution which takes the form of an array of upward and downward traveling vortex rings. This fundamental difference between existing models and observation indicates that bubble models may not be suitable for predicting the behavior of the low Atwood number instability which is vortex dominated.

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

Article number | 074101 |

Journal | Physics of Fluids |

Volume | 18 |

Issue number | 7 |

DOIs | |

State | Published - Jul 2006 |

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### ASJC Scopus subject areas

- Mechanics of Materials
- Computational Mechanics
- Physics and Astronomy(all)
- Fluid Flow and Transfer Processes
- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*18*(7), [074101]. https://doi.org/10.1063/1.2214647

**Experiments on the three-dimensional incompressible Richtmyer-Meshkov instability.** / Chapman, P. R.; Jacobs, Jeffrey W.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 18, no. 7, 074101. https://doi.org/10.1063/1.2214647

}

TY - JOUR

T1 - Experiments on the three-dimensional incompressible Richtmyer-Meshkov instability

AU - Chapman, P. R.

AU - Jacobs, Jeffrey W

PY - 2006/7

Y1 - 2006/7

N2 - The three-dimensional (3D) Richtmyer-Meshkov instability of incompressible, miscible liquids with a 3D single-mode initial perturbation is investigated. This study uses the apparatus of the earlier experiments of Niederhaus and Jacobs [J. Fluid Mech. 485, 243 (2003)] in which the instability is generated by impulsively accelerating a tank containing the two liquids. However, the present investigation uses a tank with square cross section allowing the generation of a square-mode 3D initial perturbation by lateral oscillation along the tank's diagonal. Amplitude measurements of the 3D instability are found to be effectively collapsed by the dimensionless scaling used in the two-dimensional (2D) study and to be in good agreement with linear stability theory up until a dimensionless time kv0t ≈ 1, later than is found for the 2D flow. Late-time 3D amplitude measurements show faster growth than 2D as is predicted by popular bubble models. However, late-time growth rate measurements are found to deviate from model predictions at the latest times showing a constant growth rate instead of the 1/t dependence given by the models. The constant late-time growth rate is the result of the observed vorticity distribution which takes the form of an array of upward and downward traveling vortex rings. This fundamental difference between existing models and observation indicates that bubble models may not be suitable for predicting the behavior of the low Atwood number instability which is vortex dominated.

AB - The three-dimensional (3D) Richtmyer-Meshkov instability of incompressible, miscible liquids with a 3D single-mode initial perturbation is investigated. This study uses the apparatus of the earlier experiments of Niederhaus and Jacobs [J. Fluid Mech. 485, 243 (2003)] in which the instability is generated by impulsively accelerating a tank containing the two liquids. However, the present investigation uses a tank with square cross section allowing the generation of a square-mode 3D initial perturbation by lateral oscillation along the tank's diagonal. Amplitude measurements of the 3D instability are found to be effectively collapsed by the dimensionless scaling used in the two-dimensional (2D) study and to be in good agreement with linear stability theory up until a dimensionless time kv0t ≈ 1, later than is found for the 2D flow. Late-time 3D amplitude measurements show faster growth than 2D as is predicted by popular bubble models. However, late-time growth rate measurements are found to deviate from model predictions at the latest times showing a constant growth rate instead of the 1/t dependence given by the models. The constant late-time growth rate is the result of the observed vorticity distribution which takes the form of an array of upward and downward traveling vortex rings. This fundamental difference between existing models and observation indicates that bubble models may not be suitable for predicting the behavior of the low Atwood number instability which is vortex dominated.

UR - http://www.scopus.com/inward/record.url?scp=33746714333&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746714333&partnerID=8YFLogxK

U2 - 10.1063/1.2214647

DO - 10.1063/1.2214647

M3 - Article

AN - SCOPUS:33746714333

VL - 18

JO - Physics of Fluids

JF - Physics of Fluids

SN - 0031-9171

IS - 7

M1 - 074101

ER -