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2. Excitation of atmospheric waves by volcanic eruptions

The thermal energy emitted by a volcanic eruption excites atmospheric waves and oscillations(Fig. 1). A comprehensive review on this subject is found in Blanc (1985). The most notable isthe air wave excited by the 1883 Krakatoa eruption in Indonesia (Harkrider and Press, 1967), andthe most recent is that excited by the 1991 Pinatubo eruption in the Philippines. In general, threetypes of waves can be excited as illustrated by Fig. 1b which shows the dispersion relation foracoustic-gravity waves for an isothermal atmosphere on the frequency-wave number space (e.g.,Gill, 1982; Hines, 1960). We summarize the basic concept in the following, taken mainly fromHoughton (1986).

2.1. Basic equations and dispersion relation

We take a Cartesian co-ordinate system (x; y; z), with the z-axis taken upward vertical in anisothermal atmosphere, and write the x, y, and z components of the velocity !eld measured fromthe stationary state by u, v, and w, respectively. The pressure and density are written as p+p0, and!+ !0 where p0 and !0 represent the background states and p and !, the perturbations from them.Then the equations of state and hydrostatic equilibrium are given by

p0 = !0RT0;@p0@z

=−g!0; (1)

Fig. 1. (a) An eruption of Mount Pinatubo (Courtesy of Dr. J. Mori). (b) Dispersion relation of acoustic-gravity wavesin an isothermal atmosphere (modi!ed from Gill (1982)). The vertical axis is the angular frequency, !, and k and m arethe horizontal and vertical wave numbers, respectively, and H is the vertical scale height. (c) Schematic diagram showingthe excitation mechanism of atmospheric oscillations by a volcanic eruption. The eruption can be modeled as injectionof mass, "!, injection of energy, "e, and perturbation of pressure "p. The thermal energy emitted by an eruption excitesacoustic and gravity modes of atmospheric oscillations. The energy of the atmospheric acoustic mode is coupled to theground and excites seismic Rayleigh waves.

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H. Kanamori / Fluid Dynamics Research 34 (2004) 1 { 19 9

Fig. 5. Left: Hubble Space Telescope image of the impact site of the G fragment of the Shoemaker-Levy 9 comet. Theimage was taken at 109 min after the impact. The radius of the prominent dark ring is 3700 km (from the cover pageof Nature, 374, No. 6524, 1995). Right: Synthetic ring pattern computed for the 10 × solar case. Note the approximateagreement of the positions of the outer and inner rings between the observed and synthetic patterns.

Fig. 6. Time{di stance curve for the circular rings shown in Fig. 5. The shape of the symbols identi!es the fragments A,E, G, Q1, and R. \ Acoustic" refers to the speed of sound at the temperature minimum in Jupiter' s atmosphere. \ solar"and \ 10×solar" refer to the speed of a gravity wave in the water cloud with solar and 10×solar abundance of water. Thedata points around the line with v= 210 m=s are for the inner rings. Redrawn from Hammel et al. (1995), and Ingersolland Kanamori (1995b).

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Fig. 7. Left: Temperature pro!les for the no-water (adiabatic), solar, 5 × solar (not labeled), and 10 × solar cases usedby Ingersoll and Kanamori (1995a). Right: The pro!les of the Brunt-V"ais"al"a frequency corresponding to the temperaturepro!les shown on the left.

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74 CHAPITRE 3. ONDES ET COUPLAGES

3.2.3 Variabilité du couplage

En analysant le bruit sismique enregistré par un réseau global de sismomètres Nishidaet al. (2000) ont observé la variation annuelle de l’énergie des modes propres de la Terreet démontré l’excitation continue des modes 0S29 et 0S37. Ces auteurs soulignent aussi quela variation observée peut atteindre 40% pour les modes 0S29 et 0S37 tandis que pour lesautres modes, elle est de 10% maximum.

Rappelons que les modes solides sont e�cacement couplés avec l’atmosphère lorsqueleurs fréquences propres sont proches des modes atmosphériques. Les modes atmosphé-riques les plus énergétiques sont piégés dans le guide d’onde de la basse atmosphère à3.7 mHz et 4.3 mHz (Lognonné et al., 1998). En fonction des conditions atmosphériques,les modes solides 0S28 ou 0S29 sont alternativement résonants à environ 3.7 mHz. Le mode

0S37 est résonant à 4.4 mHz. Lognonné (2009) a ainsi montré que la proportion d’énergieinjectée par couplage dans l’atmosphère est dépendante de l’heure solaire locale2. La fi-gure 3.10 illustre cette variation au niveau de l’amplitude des modes 0S28 ou 0S29 pour unprofil d’atmosphère modélisée pour le cas du séisme de Tokachi-Oki survenu à 19 : 50 GMTà une longitude de 144�, soit 5 : 25 heure solaire locale.

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Practically: • Rayleigh and Acoustic waves are modelled with Radiative BL at low altitude

or FS at high altitude (600-400 km e.g. where waves are damped by attenuation) • Tsunami and gravity waves are modelled with FS at high altitude (600-400

km range e.g. where waves are damped by attenuation)

JOVIAL Kick-Off meeting– April 19, 2016

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JOVIAL Kick-Off meeting– April 19, 2016