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Atmospheric Acoustics of Titan, Mars, Venus, and Earth

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Atmospheric Acoustics of Titan, Mars, Venus, and Earth Icarus 186 (2007) 413–419 www.elsevier.com/locate/icarus Atmospheric acoustics of Titan, Mars, Venus, and Earth Andi Petculescu ∗, Richard M. Lueptow Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA Received 5 May 2006; revised 5 September 2006 Available online 22 November 2006 Abstract Planetary atmospheres are complex dynamical systems whose structure, composition, and dynamics intimately affect the propagation of sound. Thus, acoustic waves, being coupled directly to the medium, can effectively probe planetary environments. Here we show how the acoustic absorption and speed of sound in the atmospheres of Venus, Mars, Titan, and Earth (as predicted by a recent molecular acoustics model) mirror the different environments. Starting at the surface, where the sound speed ranges from ∼200 m/s for Titan to ∼410 m/s for Venus, the vertical sound speed profiles reveal differences in the atmospheres’ thermal layering and composition. The absorption profiles are relatively smooth for Mars, Titan, and Earth while Venus stands out with a noticeable attenuation dip occurring between 40 and 100 km. We also simulate a descent module sampling the sound field produced by a low-frequency “event” near the surface noting the occurrence of acoustic quiet zones. © 2006 Elsevier Inc. All rights reserved. Keywords: Atmospheres, composition; Atmospheres, structure; Mars, atmosphere; Titan; Venus, atmosphere 1. Introduction ing the descent of the Huygens Titan probe (Fulchignoni et al., 1997, 2005; Zarnecki et al., 1997). Recent work (Bass On January 14, 2005, the Huygens lander made planetfall and Chambers, 2001; Williams, 2001) on extraterrestrial at- on Titan. The probe carried not only a microphone for record- mospheric acoustics has been focused on Mars and then only ing ambient noise and potential lightning events (Fulchignoni on sound propagation close to the planet’s surface. We present et al., 1997), but also active acoustic sensors for measuring a comparative theoretical study of acoustic propagation through surface topography, average molecular weight, altitude, wind the entire extent of the atmospheres of Titan, Venus, Mars, and speed, and surface acoustic impedance (Zarnecki et al., 1997). Earth, as well as at the planets’ surfaces using a sophisticated Huygens’ acoustic devices signal a successful resurgence in us- molecular acoustics model. ing acoustic instrumentation for planetary science after the late Titan—the only moon with a significant atmosphere—with 90s’ ill-fated Mars Polar Lander’s microphone (http://sprg.ssl. its cold (90 K) and thick (1.6 atm) nitrogen–methane at- berkeley.edu/marsmic), which followed a lull of almost two mosphere, interests scientists since it may hold clues to the decades since two Russian Venera spacecraft carried micro- prebiotic Earth. It is a relatively young body, which may have phones in an attempt to detect thunder signatures on Venus weather cycles similar to Earth’s. As described, Titan’s surface (Lorenz, 1999). may contain liquid hydrocarbon lakes and “cryovolcanoes”— The structure of planetary atmospheres is imposed by the phenomena that can be probed directly by sound waves—while atmospheric composition, pressure, density, and temperature its atmosphere may sustain strong lightning activity (Sotin et profiles. The propagation of acoustic waves is very sensitive al., 2005). The data obtained so far is still being analyzed, and to these quantities, a property that was recently exploited dur- more work is needed to understand Titan’s environment. With a surface pressure of 90 atm and a temperature of 730 K, Venus is veiled in mystery despite decades of studies. Observations * Corresponding author. Corresponding address: Department of Physics, Uni- have revealed electromagnetic radiation in the visible and radio versity of Louisiana at Lafayette, P.O. Box 44210, Lafayette, LA 70504, USA. E-mail addresses: [email protected], [email protected] ranges from localized sources, raising the potential for light- (A. Petculescu). ning. On Mars, a heavy dust presence conveys heat from the 0019-1035/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2006.09.014 414 A. Petculescu, R.M. Lueptow / Icarus 186 (2007) 413–419 surface into the thin atmosphere thus preventing cloud forma- of state. The second, third, and fourth equations express the tion. Strong tornado-like dust devils are a common occurrence. conservation of mass, momentum, and energy, respectively. The Electrically charged dust present in the martian atmosphere energy fluctuation depends not only on the acoustic tempera- may generate wide diffuse electrical discharges (Kolecki and ture T but also on the fluctuations of the internal temperatures vib = Hillard, 1992). Sensing packages incorporating microphones of the relaxing vibrational modes, Tj (j 1, 2,...), of the tailored specifically for each environment can be used to ana- molecular species forming the gas mixture, lyze acoustic arrivals and, by comparing these with electromag- = + vib vib netic signatures, determine the occurrence of lightning. cV T ξj cj Tj , (2) Very little work has been done to quantify sound propagation j in planetary atmospheres based on non-empirical models, even where c is the translational isochoric specific heat of the mix- though several planetary probes have implemented acoustic V ture, and cvib and ξ are, respectively, the internal specific heat sensors. Notable contributions were a study of sound propaga- j j and the molar fraction of the jth vibrational mode. The inter- tion at the martian surface based on a quasi-empirical approach ν (Bass and Chambers, 2001) and a more general survey of the nal temperatures of the vibrational modes j participating in the acoustic environment of Mars (Williams, 2001). However, both relaxation process are of the form: studies only address sound propagation in the vicinity of the dT vib T − T vib planet’s surface and neither uses a first-principles model to cal- j = j tran culate the acoustic properties of the martian atmosphere. Stud- dt τj ies of the atmospheric acoustic properties on Venus and Titan − (−hν /k T ) + 1 1 exp j B 0 appear to be even sparser. vib τ 1 − exp(−hνk/kB T0) k=1,k=j j,k The focus in this paper is the prediction of acoustic proper- ties over a range of altitudes based on the local atmospheric × − vib − νk − vib conditions (temperature, pressure, and gas composition) us- T Tj T Tk , (3) νj ing a relatively recent quantitative, first-principles physical model that has been successful in predicting sound absorption based on single-quantum collisions, where h = 6.626 × 10−34 33 in multi-component gas mixtures (Dain and Lueptow, 2001; J s is Planck’s constant, and kB = 1.38 × 10 J/K is Boltz- Petculescu et al., 2006). Using molecular acoustics and at- mann’s constant. The relaxation times τ are dependent upon mospheric data, we calculate the vertical profiles of attenuation the molecular collision rates and the transition probabilities for and sound speed for the four planets. (Although Titan is tech- molecular excitation/relaxation processes. The kinetic theory nically a moon, we use the term “planet” cavalierly.) For high- of gases provides the collision rates while quantum mechan- frequency active sensing (e.g. sound and wind speed measure- ics provides the transition probabilities. The above equations ment), we show quantitatively how the different atmospheres form an eigenvalue problem that can be solved to determine the would affect the acoustic signal over a 1-m sensing path. Then acoustic attenuation and sound speed as a function of frequency we consider passive acoustic sensing that can be used to detect (Dain and Lueptow, 2001 ), via an effective wave-number low-frequency signatures of natural phenomena (e.g. thunder, − − given by keff(f ) = 2πf ρ p 1ceff(f )c (f ) 1 (Petculescu turbulence, etc.), with particular attention to the “ground-effect” 0 0 V P and Lueptow, 2004, 2005), where f is the acoustic frequency acoustic interference patterns that would be sampled by a de- and ceff and ceff are the complex-valued isochoric and isobaric scending atmospheric probe. V P effective specific heats, respectively—fundamental footprints of 2. Theoretical model of sound propagation in polyatomic thermal relaxation phenomena (Herzfeld and Litovitz, 1959). eff = gases The effective wave-number can also be expressed as k (2πf )/c − iαrelax, thus providing the frequency-dependent In a gas, the classical acoustic attenuation due to viscosity, acoustic phase velocity c and relaxational attenuation αrelax. heat conduction, and diffusion is supplemented by the non- Adding the classical attenuation αclass, sound propagation in classical absorption associated with molecular relaxation. We a relaxing gas is described by the full acoustic wave-number, = − [ + ] model the acoustic wave-number (including the sound speed kac (2πf )/c i αrelax αclass . The classical attenuation co- and attenuation) using the linear acoustics equations involving efficient is calculated based on the gas viscosity η and thermal small fluctuations of pressure p, density ρ, temperature T , par- conductivity κ: ticle velocity u, and energy , written as in Eq. (1). (We assume 2π 2f 2 4 κ that diffusion effects are negligible.) α = η + (γ − ) , class 3 1 (4) ρ0c 3 cP p T ρ ∂ρ ∂u = + , + ρ = 0, 0 where cP is the isobaric specific heat and γ = cP /cV .Forasin- p0 T0 ρ0 ∂t ∂x η ∂u 1 ∂p ∂ p ∂ρ gle gas component, the coefficients of viscosity and thermal + = 0, − 0 = 0. (1) conductivity κ are available from tables. For a mixture of gases, ∂t ρ ∂x ∂t 2 ∂t 0 ρ0 however, one needs to calculate the composition-dependent val- Here, p0, T0, ρ0 are, respectively, the ambient pressure, tem- ues of the two coefficients. We used generalizations of Wilke’s perature, and density. The first equation in (1) is the equation expressions for the viscosity and thermal conductivity of mix- Acoustics on Titan, Mars, Venus, and Earth 415 tures (Wilke, 1950), namely: N x A = a a Amixture N , (5) a=1 b=1 xbφab where √ 1/4 2 [1 + ηa/ηb(Mb/Ma) ] φab ≡ √ .
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