skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES

Abstract

This paper is the second in 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 where 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 second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicitiesmore » found in polar and lower latitudes of Venus's atmosphere.« less

Authors:
;  [1];  [2];  [3];  [4];  [5]
  1. Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain)
  2. Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan)
  3. Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford (United Kingdom)
  4. Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal)
  5. LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)
Publication Date:
OSTI Identifier:
22340197
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal, Supplement Series; Journal Volume: 213; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; CLASSIFICATION; DISPERSION RELATIONS; LAMB SHIFT; PLANETARY ATMOSPHERES; SOLAR WIND; VENUS PLANET; WAVE PROPAGATION

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. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES. United States: N. p., 2014. Web. doi:10.1088/0067-0049/213/1/18.
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. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES. United States. doi:10.1088/0067-0049/213/1/18.
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. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES". United States. doi:10.1088/0067-0049/213/1/18.
@article{osti_22340197,
title = {ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. II. LAMB, SURFACE, AND CENTRIFUGAL 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 second in 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 where 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 second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.},
doi = {10.1088/0067-0049/213/1/18},
journal = {Astrophysical Journal, Supplement Series},
number = 1,
volume = 213,
place = {United States},
year = {Tue Jul 01 00:00:00 EDT 2014},
month = {Tue Jul 01 00:00:00 EDT 2014}
}
  • 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 backgroundmore » 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.« less
  • The Green's function for the problem of excitation of acoustic-gravity waves by an impulsive linear mass source, lying in an isothermal atmosphere at an altitude of z/sub 0/ above the earth's surface, is found. In this system, together with volume low-frequency waves, there exist Lamb surface waves. The solution obtained enables clarifying all characteristic features of the reflected pulse and establishing the limits of applicability of the well-known approximate solutions. The Green's function found was employed to determine the field of a monochromatic source and to analyze the conditions for excitation of a Lamb surface wave.
  • We analyzed the Kepler light curves of four transiting hot Jupiter systems—KOI-13, HAT-P-7, TrES-2, and Kepler-76, which show BEaming, Ellipsoidal, and Reflection (BEER) phase modulations. The mass of the four planets can be estimated from either the beaming or the ellipsoidal amplitude, given the mass and radius of their parent stars. For KOI-13, HAT-P-7, and Kepler-76 we find that the beaming-based planetary mass estimate is larger than the mass estimated from the ellipsoidal amplitude, consistent with previous studies. This apparent discrepancy may be explained by equatorial superrotation of the planet atmosphere, which induces an angle shift of the planet reflection/emissionmore » phase modulation, as was suggested for Kepler-76 in the first paper of this series. We propose a modified BEER model that supports superrotation, assuming either a Lambertian or geometric reflection/emission phase function, and provides a photometry-consistent estimate of the planetary mass. Our analysis shows that for Kepler-76 and HAT-P-7, the Lambertian superrotation BEER model is highly preferable over an unshifted null model, while for KOI-13 it is preferable only at a 1.4σ level. For TrES-2 we do not find such preference. For all four systems the Lambertian superrotation model mass estimates are in excellent agreement with the planetary masses derived from, or constrained by, radial velocity measurements. This makes the Lambertian superrotation BEER model a viable tool for estimating the masses of hot Jupiters from photometry alone. We conclude that hot Jupiter superrotation may be a common phenomenon that can be detected in the visual light curves of Kepler.« less
  • We investigate numerically the propagation of density waves excited by a low-mass planet in a protoplanetary disk in the nonlinear regime, using two-dimensional local shearing box simulations with the grid-based code Athena at high spatial resolution (256 grid points per scale height h). The nonlinear evolution results in the wave steepening into a shock, causing damping and angular momentum transfer to the disk. On long timescales this leads to spatial redistribution of the disk density, causing migration feedback and potentially resulting in gap opening. Previous numerical studies concentrated on exploring these secondary phenomena as probes of the nonlinear wave evolution.more » Here we focus on exploring the evolution of the basic wave properties, such as its density profile evolution, shock formation, and post-shock wave behavior, and provide comparison with analytical theory. The generation of potential vorticity at the shock is computed analytically and is subsequently verified by simulations and used to pinpoint the shock location. We confirm the theoretical relation between the shocking length and the planet mass (including the effect of the equation of state), and the post-shock decay of the angular momentum flux carried by the wave. The post-shock evolution of the wave profile is explored, and we quantitatively confirm its convergence to the theoretically expected N-wave shape. The accuracy of various numerical algorithms used to compute the nonlinear wave evolution is also investigated: we find that higher order spatial reconstruction and high resolution are crucial for capturing the shock formation correctly.« less