# Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability

## Abstract

Weakly nonlinear (WN) Rayleigh-Taylor instability (RTI) initiated by single-mode cosinusoidal interface and velocity perturbations is investigated analytically up to the third order. Expressions of the temporal evolutions of the amplitudes of the first three harmonics are derived. It is shown that there are coupling between interface and velocity perturbations, which plays a prominent role in the WN growth. When the 'equivalent amplitude' of the initial velocity perturbation, which is normalized by its linear growth rate, is compared to the amplitude of the initial interface perturbation, the coupling between them dominates the WN growth of the RTI. Furthermore, the RTI would be mitigated by initiating a velocity perturbation with a relative phase shift against the interface perturbation. More specifically, when the phase shift between the interface perturbation and the velocity perturbation is {pi} and their equivalent amplitudes are equal, the RTI could be completely quenched. If the equivalent amplitude of the initial velocity perturbation is equal to the initial interface perturbation, the difference between the WN growth of the RTI initiated by only an interface perturbation and by only a velocity perturbation is found to be asymptotically negligible. The dependence of the WN growth on the Atwood numbers and the initialmore »

- Authors:

- HEDPS and CAPT, Peking University, Beijing 100871 (China)
- (China)
- Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China)

- Publication Date:

- OSTI Identifier:
- 22068899

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 19; Journal Issue: 11; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AMPLITUDES; DISTURBANCES; EXPLOSIONS; HARMONICS; IMPLOSIONS; INERTIAL CONFINEMENT; NONLINEAR PROBLEMS; PHASE SHIFT; RAYLEIGH-TAYLOR INSTABILITY; SUPERNOVAE; TIME DEPENDENCE; VELOCITY

### Citation Formats

```
Wang, L. F., Ye, W. H., He, X. T., Institute of Applied Physics and Computational Mathematics, Beijing 100088, Wu, J. F., Fan, Z. F., Zhang, W. Y., Dai, Z. S., Gu, J. F., and Xue, C.
```*Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability*. United States: N. p., 2012.
Web. doi:10.1063/1.4766165.

```
Wang, L. F., Ye, W. H., He, X. T., Institute of Applied Physics and Computational Mathematics, Beijing 100088, Wu, J. F., Fan, Z. F., Zhang, W. Y., Dai, Z. S., Gu, J. F., & Xue, C.
```*Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability*. United States. doi:10.1063/1.4766165.

```
Wang, L. F., Ye, W. H., He, X. T., Institute of Applied Physics and Computational Mathematics, Beijing 100088, Wu, J. F., Fan, Z. F., Zhang, W. Y., Dai, Z. S., Gu, J. F., and Xue, C. Thu .
"Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability". United States. doi:10.1063/1.4766165.
```

```
@article{osti_22068899,
```

title = {Coupling between interface and velocity perturbations in the weakly nonlinear Rayleigh-Taylor instability},

author = {Wang, L. F. and Ye, W. H. and He, X. T. and Institute of Applied Physics and Computational Mathematics, Beijing 100088 and Wu, J. F. and Fan, Z. F. and Zhang, W. Y. and Dai, Z. S. and Gu, J. F. and Xue, C.},

abstractNote = {Weakly nonlinear (WN) Rayleigh-Taylor instability (RTI) initiated by single-mode cosinusoidal interface and velocity perturbations is investigated analytically up to the third order. Expressions of the temporal evolutions of the amplitudes of the first three harmonics are derived. It is shown that there are coupling between interface and velocity perturbations, which plays a prominent role in the WN growth. When the 'equivalent amplitude' of the initial velocity perturbation, which is normalized by its linear growth rate, is compared to the amplitude of the initial interface perturbation, the coupling between them dominates the WN growth of the RTI. Furthermore, the RTI would be mitigated by initiating a velocity perturbation with a relative phase shift against the interface perturbation. More specifically, when the phase shift between the interface perturbation and the velocity perturbation is {pi} and their equivalent amplitudes are equal, the RTI could be completely quenched. If the equivalent amplitude of the initial velocity perturbation is equal to the initial interface perturbation, the difference between the WN growth of the RTI initiated by only an interface perturbation and by only a velocity perturbation is found to be asymptotically negligible. The dependence of the WN growth on the Atwood numbers and the initial perturbation amplitudes is discussed. In particular, we investigate the dependence of the saturation amplitude (time) of the fundamental mode on the Atwood numbers and the initial perturbation amplitudes. It is found that the Atwood numbers and the initial perturbation amplitudes play a crucial role in the WN growth of the RTI. Thus, it should be included in applications where the seeds of the RTI have velocity perturbations, such as inertial confinement fusion implosions and supernova explosions.},

doi = {10.1063/1.4766165},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 11,

volume = 19,

place = {United States},

year = {2012},

month = {11}

}