# Gravity Waves in Planetary Atmospheres: Their Effects and Parameterization in Global Circulation Models

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## Abstract

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## 1. Introduction

## 2. Atmospheric Gravity Waves

#### 2.1. Physics of Gravity Waves

#### 2.2. Linear Theory of Gravity Waves

#### 2.3. Wave Generation and Sources of Gravity Waves

#### 2.4. Observations of Gravity Waves

## 3. Methods of Parameterizing Gravity Waves in General Circulation Models

#### 3.1. Principles of Parameterization

#### 3.2. Instability Threshold

#### 3.3. Spectral Schemes

#### 3.4. Nonlinear Spectral Schemes

#### 3.5. Whole Atmosphere Gravity Wave Scheme

#### 3.6. Stochastic Modifications of Parameterizations

## 4. Modeling Gravity Wave Effects in Planetary Atmospheres

#### 4.1. Dynamical Effects

#### 4.2. Thermal Effects

## 5. Phenomena Associated with Gravity Waves in Planetary Atmospheres

#### 5.1. Sudden Stratospheric Warmings

#### 5.2. Martian Polar Warmings

#### 5.3. Gravity Waves and Ice Clouds

#### 5.4. Ionospheric Effects

## 6. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

GWs | Gravity waves |

GCM | General (or global) circulation models |

MAVEN | Mars Atmosphere and Volatile Evolution |

WKB | Wentzel–Kramer–Brilloin |

SSW | Sudden stratospheric warming |

TIDs | Traveling ionospheric disturbances |

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**Figure 1.**Zonal mean zonal GW drag and ion drag simulated by the CMAT2-GCM for solstice conditions: (

**a**) GW drag for cut-off case; (

**b**) GW drag for extended simulation; (

**c**) ion drag for cut-off run; and (

**d**) ion drag for extended run. Adapted from [73].

**Figure 2.**Zonally and diurnally averaged temperatures in the Martian atmosphere (solid lines) at p = 0.0002 Pa (≈120 km) from the runs without GWs (black), with only dynamical effects of GWs (“drag”) included (gray), and with both dynamical and thermal effects accounted for (red). The blue dotted line presents the night-time temperature inferred from ODY aerobraking measurements [102]. The red dashed line corresponds to the night-time (near 02:00 h) temperature from the run including both dynamical and thermal GW effects. Adapted from [101].

**Figure 3.**Results of the simulation with the Martian GCM for the aphelion season (${L}_{s}={90}^{\circ}$): (

**a**) zonal mean temperature (shaded), and the residual circulation (white streamlines); (

**b**) Eliassen–Palm fluxes (red arrows) and their divergence (thin blue lines). Adapted from [119].

**Figure 4.**Simulated around ${L}_{s}={0}^{\circ}$, quantities averaged over 40 sols: (

**left**) zonal mean temperature T (contour lines) and GW-induced temperature perturbation $|{T}^{\prime}|$ (color shaded) in Kelvin degrees; (

**right**) probability P of CO${}_{2}$ ice cloud formation in percentage (blue shaded), and the planetary potential height of the corresponding pressure levels in km (contours). Adapted from [127].

**Table 1.**Characteristics of planetary atmospheres and expected maximal horizontal phase speeds of gravity waves. Jovian and Saturnian parameters are given for the stratospheric heights.

Earth | Mars | Venus | Jupiter | Saturn | |
---|---|---|---|---|---|

Rotational frequency $\Omega $, s${}^{-1}$ | 7.29 × 10${}^{-5}$ | 7.09 × 10${}^{-5}$ | 2.99 × 10${}^{-7}$ | 1.76 × 10${}^{-4}$ | 1.64 × 10${}^{-4}$ |

Acceleration of gravity g, m s${}^{-2}$ | 9.81 | 3.72 | 8.87 | 24.79 | 10.44 |

Scale height H, km | 5.5–9 | 7.5–11.5 | 5–16 | 27 | 60 |

Buoyancy frequency N, s${}^{-1}$ | ∼2 × 10${}^{-2}$ | ∼2 × 10${}^{-2}$ | ∼2 × 10${}^{-2}$ | ∼2 × 10${}^{-2}$ | ∼2 × 10${}^{-2}$ |

Max horizontal phase velocity, ${c}_{max}$, m s${}^{-1}$ | 220–360 | 300–460 | 200–640 | 1080 | 2400 |

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Medvedev, A.S.; Yiğit, E.
Gravity Waves in Planetary Atmospheres: Their Effects and Parameterization in Global Circulation Models. *Atmosphere* **2019**, *10*, 531.
https://doi.org/10.3390/atmos10090531

**AMA Style**

Medvedev AS, Yiğit E.
Gravity Waves in Planetary Atmospheres: Their Effects and Parameterization in Global Circulation Models. *Atmosphere*. 2019; 10(9):531.
https://doi.org/10.3390/atmos10090531

**Chicago/Turabian Style**

Medvedev, Alexander S., and Erdal Yiğit.
2019. "Gravity Waves in Planetary Atmospheres: Their Effects and Parameterization in Global Circulation Models" *Atmosphere* 10, no. 9: 531.
https://doi.org/10.3390/atmos10090531