Page 20 - January 2007

ronment can be used to analyze acoustic arrivals and, togeth- er with the electromagnetic signatures, determine the occur- rence of lightning. Of interest is also low-frequency sound, which can propagate over large distances, even in thin atmos- pheres. Low-frequency sound can be generated aero-acousti- cally by gas flow around vehicles, meteorological phenomena such as dust devils and lightning, booming sand dunes, bolide impacts, and maybe even as nonlinear interactions at the interface between the atmosphere and liquid bodies such as Titan’s hydrocarbon “lakes.” Furthermore, long-wave- length ducted acoustic propagation in a planet’s atmosphere can be inverted to yield quantitative information on the
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shows much promise is acoustic anemometry enabling direct measurements of local velocity fields. Due to the direct cou- pling of acoustic waves and the medium of propagation, acoustics may provide a very good tool to investigate and
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quantify three-dimensional turbulence. In broad terms, tur-
bulence creates an effective medium with a complex com- pressibility that affects the acoustic wave number while tur- bulent eddies can efficiently scatter acoustic wavelengths
9 commensurate with the turbulence length scales. Therefore,
sound waves can effectively be “tuned” to investigate specific turbulent regimes in the atmosphere.
Attenuation and speed of sound on Venus, Mars, Titan, and Earth
A quantitative analysis of a fluid environment can be achieved acoustically if both the sound speed and attenuation are measured. Besides the classical attenuation due to viscos- ity, heat conduction, and diffusion, non-classical losses arise from molecular relaxation. The non-classical, or molecular, acoustic attenuation provides a direct way to measure the relaxation times, characteristic of the molecular species and atmospheric composition. The frequency dependence of the sound speed can yield the specific heat ratio of the medium under study.
Physical models10,11 of acoustic wave propagation in the mixtures of gases forming a planetary atmosphere combine the equations of linear acoustics, namely conservation of mass, momentum, and energy, and the equation of state. When the system is solved, the outcome is a complex-valued effective wave number that is a function of the effective spe-
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where f is the acoustic frequency.
To understand the dependence of acoustics on a planet’s
environment better, we compare the acoustic attenuation and sound speed in the atmospheres of Earth and three solar sys- tem bodies whose environments are compositionally similar to
atmospheric boundary layer.
An application of atmospheric acoustic sensing that
The real and imaginary parts of the effective wave number contain, respectively, the frequency-dependent acoustic phase veloci- ty (speed of sound) c and relaxational attenuation αrelax. By adding the classical absorption component αclass to the relax- ational component, sound propagation in a relaxing medium
(1)
cific heats—footprints of molecular relaxation.
is described by the full acoustic wave-number, 2π f
kac = c -i(αrelax+αclass),
Earth’s—Venus, Mars, and Titan. The average surface condi- tions (temperature in degrees Kelvin, pressure in Earth atmos- pheres) and approximate compositions are given below:
Table 1. Surface temperature, pressure, and composition of the atmospheres of Venus, Mars, Titan, and Earth.
Predictions based on a physical model11,13 for the frequency- dependent attenuation coefficient α and sound speed c in the surface atmospheres of Venus, Mars, Titan, and Earth are shown in Fig. 1. At acoustic frequencies corresponding to periods comparable to molecular relaxation times, both sound speed and attenuation go through inflection points. This effect on the two acoustic quantities is different depend- ing on the relaxation characteristics of the particular gas environments. The acoustic attenuation coefficient α is shown in Fig. 1(a), along with the normalized attenuation αλ, where λ is the acoustic wavelength. Representing αλ as a function of frequency has the advantage of emphasizing the molecular relaxation times, which are proportional to the inverses of the frequencies where the αλ maxima occur. Mars and Earth have maxima at about 80 Hz due largely to the relaxation of the vibrational degrees of freedom of CO2 and N2 molecules, respectively. Venus’ two maxima (~ 1 kHz and 320 kHz) also arise from the vibrational relaxation of CO2. In the 1–10 kHz window, the attenuation on Mars is compara- ble to that on Venus. The high values of pressure and tem- perature of Venus’ atmosphere lead to increased molecular collision rates that shift the relaxational effects to higher fre- quencies.14 Titan’s very cold nitrogen-rich environment inhibits the collisional exchange of translational energy with internal energy among molecules. This makes classical effects dominant on the attenuation, imposing virtually quadratic frequency dependence. Over the entire frequency range considered, Titan’s atmosphere absorbs the least amount of acoustic energy.
When signal loss is a major concern (as is the case on Mars), acoustic modeling can identify frequency windows of relatively low attenuation that can be explored for measure- ments. For example, in the Martian atmosphere the approxi- mate range between 1 kHz and 50 kHz would be a good choice for applications that require higher frequencies such as Doppler wind speed measurements or analysis of small- to medium-scale turbulence. Propagation in the low-frequency and infrasonic ranges (<10 Hz) occurs with small losses in all four atmospheres, so these frequencies can be monitored over long distances.
Figure 1(b) shows the frequency dependence of the sound speeds. Due to the scale of the graph, chosen to show the sound speed values in all four environments, the inflec- tion points associated with molecular relaxation are only apparent for Venus and Mars, where relaxational effects are several orders of magnitude stronger than on Earth and Titan, as can be seen from the αλ peaks. Owing to its high
18 Acoustics Today, January 2007