# ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. I. ACOUSTIC AND INERTIA-GRAVITY WAVES

## Abstract

This paper is the first of a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases when the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this first part, only waves that are direct solutions of the generic dispersion relation are studied—acoustic and inertia-gravity waves. Concerning inertia-gravity waves, we found that in the cases of short horizontal wavelengths, null background wind, or propagation in the equatorial region, only pure gravity waves are possible, while for the limit of large horizontal wavelengths and/or null static stability, the waves are inertial. The correspondence between classical atmospheric approximations and wavemore »

- Authors:

- Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain)
- Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan)
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford (United Kingdom)
- Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal)
- LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)

- Publication Date:

- OSTI Identifier:
- 22340196

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal, Supplement Series

- Additional Journal Information:
- Journal Volume: 213; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0067-0049

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CLASSIFICATION; CLOUDS; GRAVITATION; GRAVITY WAVES; MATHEMATICAL SOLUTIONS; METRICS; MOMENT OF INERTIA; PLANETS; SHEAR; WAVE FUNCTIONS

### Citation Formats

```
Peralta, J., López-Valverde, M. A., Imamura, T., Read, P. L., Luz, D., and Piccialli, A., E-mail: peralta@iaa.es.
```*ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. I. ACOUSTIC AND INERTIA-GRAVITY WAVES*. United States: N. p., 2014.
Web. doi:10.1088/0067-0049/213/1/17.

```
Peralta, J., López-Valverde, M. A., Imamura, T., Read, P. L., Luz, D., & Piccialli, A., E-mail: peralta@iaa.es.
```*ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. I. ACOUSTIC AND INERTIA-GRAVITY WAVES*. United States. doi:10.1088/0067-0049/213/1/17.

```
Peralta, J., López-Valverde, M. A., Imamura, T., Read, P. L., Luz, D., and Piccialli, A., E-mail: peralta@iaa.es. Tue .
"ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. I. ACOUSTIC AND INERTIA-GRAVITY WAVES". United States. doi:10.1088/0067-0049/213/1/17.
```

```
@article{osti_22340196,
```

title = {ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. I. ACOUSTIC AND INERTIA-GRAVITY WAVES},

author = {Peralta, J. and López-Valverde, M. A. and Imamura, T. and Read, P. L. and Luz, D. and Piccialli, A., E-mail: peralta@iaa.es},

abstractNote = {This paper is the first of a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases when the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this first part, only waves that are direct solutions of the generic dispersion relation are studied—acoustic and inertia-gravity waves. Concerning inertia-gravity waves, we found that in the cases of short horizontal wavelengths, null background wind, or propagation in the equatorial region, only pure gravity waves are possible, while for the limit of large horizontal wavelengths and/or null static stability, the waves are inertial. The correspondence between classical atmospheric approximations and wave filtering has been examined too, and we carried out a classification of the mesoscale waves found in the clouds of Venus at different vertical levels of its atmosphere. Finally, the classification of waves in exoplanets is discussed and we provide a list of possible candidates with cyclostrophic regimes.},

doi = {10.1088/0067-0049/213/1/17},

journal = {Astrophysical Journal, Supplement Series},

issn = {0067-0049},

number = 1,

volume = 213,

place = {United States},

year = {2014},

month = {7}

}