### Abstract

We consider the long-standing problem of Rayleigh-Taylor instability with variable acceleration, and focus on the early-time scale-dependent dynamics of an interface separating incompressible ideal fluids of different densities subject to an acceleration being a power-law function of time for a spatially extended three-dimensional flow periodic in the plane normal to the acceleration with symmetry group p6mm. By employing group theory and scaling analysis, we discover two distinct subregimes of the early-time dynamics depending on the exponent of the acceleration power-law. The time scale and the early-time dynamics are set by the acceleration for exponents greater than (-2), and by the initial growth-rate (due to, e.g., initial conditions) for exponents smaller than (-2). At the exponent value (-2) a transition occurs from one subregime to the other with varying acceleration strength. For a broad range of the acceleration parameters, the instability growth rate is explicitly found, the dependence of the dynamics on the initial conditions is investigated, and theory benchmarks are elaborated.

Original language | English |
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Article number | 063905 |

Number of pages | 18 |

Journal | Physical Review Fluids |

Volume | 4 |

Issue number | 6 |

DOIs | |

Publication status | Published - 21 Jun 2019 |

### Cite this

*Physical Review Fluids*,

*4*(6), [063905]. https://doi.org/10.1103/PhysRevFluids.4.063905

}

*Physical Review Fluids*, vol. 4, no. 6, 063905. https://doi.org/10.1103/PhysRevFluids.4.063905

**Group theory analysis of early-time scale-dependent dynamics of the Rayleigh-Taylor instability with time varying acceleration.** / Hill, Desmond L.; Bhowmick, Aklant K.; Ilyin, Dan; Abarzhi, Snezhana.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Group theory analysis of early-time scale-dependent dynamics of the Rayleigh-Taylor instability with time varying acceleration

AU - Hill, Desmond L.

AU - Bhowmick, Aklant K.

AU - Ilyin, Dan

AU - Abarzhi, Snezhana

PY - 2019/6/21

Y1 - 2019/6/21

N2 - We consider the long-standing problem of Rayleigh-Taylor instability with variable acceleration, and focus on the early-time scale-dependent dynamics of an interface separating incompressible ideal fluids of different densities subject to an acceleration being a power-law function of time for a spatially extended three-dimensional flow periodic in the plane normal to the acceleration with symmetry group p6mm. By employing group theory and scaling analysis, we discover two distinct subregimes of the early-time dynamics depending on the exponent of the acceleration power-law. The time scale and the early-time dynamics are set by the acceleration for exponents greater than (-2), and by the initial growth-rate (due to, e.g., initial conditions) for exponents smaller than (-2). At the exponent value (-2) a transition occurs from one subregime to the other with varying acceleration strength. For a broad range of the acceleration parameters, the instability growth rate is explicitly found, the dependence of the dynamics on the initial conditions is investigated, and theory benchmarks are elaborated.

AB - We consider the long-standing problem of Rayleigh-Taylor instability with variable acceleration, and focus on the early-time scale-dependent dynamics of an interface separating incompressible ideal fluids of different densities subject to an acceleration being a power-law function of time for a spatially extended three-dimensional flow periodic in the plane normal to the acceleration with symmetry group p6mm. By employing group theory and scaling analysis, we discover two distinct subregimes of the early-time dynamics depending on the exponent of the acceleration power-law. The time scale and the early-time dynamics are set by the acceleration for exponents greater than (-2), and by the initial growth-rate (due to, e.g., initial conditions) for exponents smaller than (-2). At the exponent value (-2) a transition occurs from one subregime to the other with varying acceleration strength. For a broad range of the acceleration parameters, the instability growth rate is explicitly found, the dependence of the dynamics on the initial conditions is investigated, and theory benchmarks are elaborated.

KW - FLUID

KW - FLOWS

U2 - 10.1103/PhysRevFluids.4.063905

DO - 10.1103/PhysRevFluids.4.063905

M3 - Article

VL - 4

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 6

M1 - 063905

ER -