# Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability

## Abstract

We report nonlinear solutions for a system of conservation laws describing the dynamics of the large-scale coherent structure of bubbles and spikes in the Rayleigh-Taylor instability (RTI) for fluids with a finite density ratio. Three-dimensional flows are considered with general type of symmetry in the plane normal to the direction of gravity. The nonlocal properties of the interface evolution are accounted for on the basis of group theory. It is shown that isotropic coherent structures are stable. For anisotropic structures, secondary instabilities develop with the growth rate determined by the density ratio. For stable structures, the curvature and velocity of the nonlinear bubble have nontrivial dependencies on the density ratio, yet their mutual dependence on one another has an invariant form independent of the density ratio. The process of bubble merge is not considered. Based on the obtained results we argue that the large-scale coherent dynamics in RTI has a multiscale character and is governed by two length scales: the period of the coherent structure and the bubble (spike) position.

- Authors:

- FLASH, University of Chicago, Chicago, Illinois (United States)
- (United States)
- Institute for Laser Engineering, Osaka University, Osaka (Japan)

- Publication Date:

- OSTI Identifier:
- 20778872

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevE.73.036310; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; BUBBLES; CONSERVATION LAWS; EVOLUTION; GRAVITATION; GROUP THEORY; INTERFACES; MATHEMATICAL SOLUTIONS; MULTIPHASE FLOW; NONLINEAR PROBLEMS; RAYLEIGH-TAYLOR INSTABILITY; SYMMETRY; THREE-DIMENSIONAL CALCULATIONS; VELOCITY

### Citation Formats

```
Abarzhi, S.I., Center for Turbulence Research, Stanford University, Stanford, California, Nishihara, K., and Rosner, R.
```*Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVE.73.0.

```
Abarzhi, S.I., Center for Turbulence Research, Stanford University, Stanford, California, Nishihara, K., & Rosner, R.
```*Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability*. United States. doi:10.1103/PHYSREVE.73.0.

```
Abarzhi, S.I., Center for Turbulence Research, Stanford University, Stanford, California, Nishihara, K., and Rosner, R. Wed .
"Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability". United States.
doi:10.1103/PHYSREVE.73.0.
```

```
@article{osti_20778872,
```

title = {Multiscale character of the nonlinear coherent dynamics in the Rayleigh-Taylor instability},

author = {Abarzhi, S.I. and Center for Turbulence Research, Stanford University, Stanford, California and Nishihara, K. and Rosner, R.},

abstractNote = {We report nonlinear solutions for a system of conservation laws describing the dynamics of the large-scale coherent structure of bubbles and spikes in the Rayleigh-Taylor instability (RTI) for fluids with a finite density ratio. Three-dimensional flows are considered with general type of symmetry in the plane normal to the direction of gravity. The nonlocal properties of the interface evolution are accounted for on the basis of group theory. It is shown that isotropic coherent structures are stable. For anisotropic structures, secondary instabilities develop with the growth rate determined by the density ratio. For stable structures, the curvature and velocity of the nonlinear bubble have nontrivial dependencies on the density ratio, yet their mutual dependence on one another has an invariant form independent of the density ratio. The process of bubble merge is not considered. Based on the obtained results we argue that the large-scale coherent dynamics in RTI has a multiscale character and is governed by two length scales: the period of the coherent structure and the bubble (spike) position.},

doi = {10.1103/PHYSREVE.73.0},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 3,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}