# A self-consistent three-wave coupling model with complex linear frequencies

## Abstract

A three-wave coupling model with complex linear frequencies is investigated for the nonlinear interaction in a triad that has linearly unstable and stable modes. Time scales associated with linear and nonlinear physics are identified and compared with features of the frequency spectrum. From appropriate time scales, the frequency spectra are well characterized even in the transition to the steady state. The nonlinear time scales that best match spectral features are the nonlinear frequency of the fixed point and a frequency that depends on the amplitude displacement from the fixed point through the large-amplitude Jacobian elliptic solution. Two limited efforts to model the effect of other triads suggest robustness in the single triad results.

- Authors:

- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)

- Publication Date:

- OSTI Identifier:
- 22043492

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 9; Other Information: (c) 2011 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:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; COUPLING; INTERACTIONS; JACOBIAN FUNCTION; PLASMA; SPECTRA; STEADY-STATE CONDITIONS; TURBULENCE

### Citation Formats

```
Kim, J.-H., and Terry, P. W.
```*A self-consistent three-wave coupling model with complex linear frequencies*. United States: N. p., 2011.
Web. doi:10.1063/1.3640807.

```
Kim, J.-H., & Terry, P. W.
```*A self-consistent three-wave coupling model with complex linear frequencies*. United States. doi:10.1063/1.3640807.

```
Kim, J.-H., and Terry, P. W. Thu .
"A self-consistent three-wave coupling model with complex linear frequencies". United States. doi:10.1063/1.3640807.
```

```
@article{osti_22043492,
```

title = {A self-consistent three-wave coupling model with complex linear frequencies},

author = {Kim, J.-H. and Terry, P. W.},

abstractNote = {A three-wave coupling model with complex linear frequencies is investigated for the nonlinear interaction in a triad that has linearly unstable and stable modes. Time scales associated with linear and nonlinear physics are identified and compared with features of the frequency spectrum. From appropriate time scales, the frequency spectra are well characterized even in the transition to the steady state. The nonlinear time scales that best match spectral features are the nonlinear frequency of the fixed point and a frequency that depends on the amplitude displacement from the fixed point through the large-amplitude Jacobian elliptic solution. Two limited efforts to model the effect of other triads suggest robustness in the single triad results.},

doi = {10.1063/1.3640807},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 9,

volume = 18,

place = {United States},

year = {2011},

month = {9}

}