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Methods of modelling dispersive sound speed profiles of Martian atmosphere and their effects on sound propagation paths

Sun Guan-Wen Cui Han-Yin Li Chao Lin Wei-Jun

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Methods of modelling dispersive sound speed profiles of Martian atmosphere and their effects on sound propagation paths

Sun Guan-Wen, Cui Han-Yin, Li Chao, Lin Wei-Jun
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  • At present, Mars acoustic detection is gradually becoming an important new tool for understanding and exploring Mars. To explore the sources of Mars sound, it is necessary to study the sound speed and the sound attenuation in the thin and low-temperature Martian atmosphere, and to model the sound propagation in the stratified atmosphere. According to the extremely low pressure of Mars and the large variation of gas composition with altitude, we propose a simulation method based on the Navier-Stokes (NS) equation and the mixed-gas model to calculate the vertical profiles of sound speed and attenuation in the Martian atmosphere at 0–250 km altitude in this work. A comparison among sound-speed profiles at different frequencies shows that there is a notable sound dispersion in the Martian atmosphere, especially at high altitudes and in the high frequency range. It is also verified through sound speed measurement experiments that significant sound dispersion does exist in low-pressure carbon dioxide, implying the need to consider sound dispersion in the modelling of Martian sound speed profiles. The scope of application of the NS equation in modelling the sound speed of the Martian atmosphere is also discussed, as the NS equation may fail in a too rarefied gas. Next, the non-dispersive ideal-gas sound speed profiles and the dispersive NS sound speed at different frequencies (0.01, 0.1, 1 Hz) are used to simulate the sound propagation paths in the multilayered Martian atmosphere. And both cases of the Martian ground-based and high-altitude sources are compared with each other. It is found that the dispersive sound speed has a significant effect on the sound propagation path on Mars. The main influence is that the first fold back height and the first return distance of the sound ray to the surface are both shortened, which directly changes the area and location of the acoustic quiet zone. The effect of dispersion on the sound propagation path becomes more notable with both the frequency and the elevation of the acoustic source increasing, confirming that consideration of dispersion has a significant effect on the calculation of the sound propagation path.
      Corresponding author: Cui Han-Yin, cuihanyin@mail.ioa.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874385) and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA17040505)
    [1]

    Maurice S, Chide B, Murdoch N, Lorenz R D, Mimoun D, Wiens R C, Stott A, Jacob X, Bertrand T, Montmessin F, Lanza N L, Alvarez-Llamas C, Angel S M, Aung M, Balaram J, Beyssac O, Cousin A, Delory G, Forni O, Fouchet T, Gasnault O, Grip H, Hecht M, Hoffman J, Laserna J, Lasue J, Maki J, McClean J, Meslin P Y, Le Mouélic S, Munguira A, Newman C E, Rodríguez Manfredi J A, Moros J, Ollila A, Pilleri P, Schröder S, de la Torre Juárez M, Tzanetos T, Stack K M, Farley K, Williford K, the SuperCam team 2022 Nature 605 653Google Scholar

    [2]

    Peng Y, Zhang L, Cai Z, Wang Z, Jiao H, Wang D, Li Y 2020 Earth Planet. Phys. 4 371Google Scholar

    [3]

    Christie R, Campus P 2010 Infrasound Monitoring for Atmospheric Studies (Dordrecht: Springer Science and Business Media) pp541–574

    [4]

    Lamb D, Lees J M, Bowman D C 2018 Geophys. Res. Lett. 45 7176Google Scholar

    [5]

    毕思昭, 彭朝晖 2021 物理学报 70 114303Google Scholar

    Bi S Z, Peng Z H 2021 Acta Phys. Sin. 70 114303Google Scholar

    [6]

    程巍, 滕鹏晓, 吕君, 姬培锋, 戴翊靖 2021 物理学报 70 244203Google Scholar

    Cheng W, Teng P X, Lü J, Ji P F, Dai Y J 2021 Acta Phys. Sin. 70 244203Google Scholar

    [7]

    苏林, 马力, 宋文华, 郭圣明, 鹿力成 2015 物理学报 64 024302Google Scholar

    Su L, Ma L, Song W H, Guo S M, Lu L C 2015 Acta Phys. Sin. 64 024302Google Scholar

    [8]

    Williams J P 2001 J. Geophys. Res. Planets 106 5033Google Scholar

    [9]

    Kalempa D, Sharipov F 2009 Phys. Fluids 21 103601Google Scholar

    [10]

    Rayleigh J W S B 1896 The Theory of Sound (Vol. 2) (London: Macmillan) pp344–352

    [11]

    Chang W, Uhlenbeck G E 1948 Studies Statistical Mech. 5 1

    [12]

    Chang W, Uhlenbeck G E 1948 Studies Statistical Mech. 5 17

    [13]

    Sirovich L, Thurber J K 1965 J. Acoust. Soc. Am. 37 329Google Scholar

    [14]

    Greenspan M 1950 J. Acoust. Soc. Am. 22 568Google Scholar

    [15]

    Greenspan M 1954 J. Acoust. Soc. Am. 26 70Google Scholar

    [16]

    Greenspan M 1956 J. Acoust. Soc. Am. 28 644Google Scholar

    [17]

    Greenspan M 1959 J. Acoust. Soc. Am. 31 155Google Scholar

    [18]

    Bird G A 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows (USA: Oxford University Press) pp1–29

    [19]

    Cercignani C 1988 The Boltzmann Equation and its Application (New York: SpringerVerlag) pp351–385

    [20]

    Sharipov F 2016 Rarefied Gas Dynamics. Fundamentals for Research and Practice (Berlin: Wiley-VCH) pp73–81

    [21]

    Hadjiconstantinou N G, Garcia A L 2001 Phys. Fluids 13 1040Google Scholar

    [22]

    Hanford A D 2008 Ph. D. Dissertation (Pennsylvania: The Pennsylvania State University)

    [23]

    Kalempa D, Sharipov F 2016 Eur. J. Mech. B-Fluid 57 50Google Scholar

    [24]

    Kalempa D, Sharipov F, Silva J C 2019 Vacuum 159 82Google Scholar

    [25]

    Meyer E, Sessler G 1957 Z. Phys. 149 15Google Scholar

    [26]

    Maidanik G, Heckl M 1965 Phys. Fluids 8 266Google Scholar

    [27]

    Hirschfelder J O, Curtiss C F, Bird R B 1964 Molecular Theory of Gases and Liquids (New York: John Wiley & Sons, Inc) pp533–543

    [28]

    Mason W P 1984 Physical Acoustics : Principles and Methods (Vol. 17) (New York: Academic Press) pp145–228

    [29]

    Sutherland L C, Bass H E 2004 J. Acoust. Soc. Am. 115 1012Google Scholar

    [30]

    Bass H E, Chambers J P 2001 J. Acoust. Soc. Am. 109 3069Google Scholar

    [31]

    Petculescu A, Achi P 2012 J. Acoust. Soc. Am. 131 3671Google Scholar

    [32]

    Petculescu A 2016 J. Acoust. Soc. Am. 140 1439Google Scholar

    [33]

    Trahan A J, Petculescu A 2020 J. Acoust. Soc. Am. 148 141Google Scholar

    [34]

    Forget F, Hourdin F, Fournier R, Hourdin C, Talagrand O, Collins M, Huot J P 1999 J. Geophys. Res. Planets 104 24155Google Scholar

    [35]

    Millour E, Forget F, Spiga A, Vals M, Zakharov V, Montabone L 2018 Icarus From Mars Express to ExoMars 150 27

    [36]

    Chase M W, National Information Standards Organization (US) 1998 NIST-JANAF Thermochemical Tables (Vol. 9) (Washington, DC: American Chemical Society) pp1–1951

    [37]

    Greenspan M 1987 J. Acoust. Soc. Am. 82 370Google Scholar

    [38]

    Greenspan M 1965 Physical Acoustics, 2 (Part A) (New York: Academic Press) pp1–43

    [39]

    Bird R B 2002 Appl. Mech. Rev. 55 R1Google Scholar

    [40]

    Hirschfelder J O, Bird R B, Spotz E L 1948 J. Chem. Phys. 16 968Google Scholar

    [41]

    杨训仁, 陈宇 2007 大气声学 (北京: 科学出版社) 第52—59页

    Yang X R, Chen Y 2007 Atmospheric Acoustic (Beijing: Science Press) pp52–59 (in Chinese)

    [42]

    White R D, Neeson I, Schmid E S, Merrison J, Iversen J J, Banfield D 2020 AIAA Scitech 2020 Forum Orlando, Florida, USA, January 6–10, 2020 p0712

  • 图 1  不同海拔下火星的大气参数 (a)气体成分; (b)温度; (c)气压; (d)水平风速

    Figure 1.  Atmospheric parameters of Mars at different altitudes: (a) Gas composition; (b) temperature; (c) pressure; (d) horizontal wind speed

    图 2  火星大气(a)分子摩尔质量、(b)比热比和(c)理想气体声速的垂直剖面图

    Figure 2.  Vertical profiles of (a) the molecular molar mass, (b) specific heat ratio, and (c) ideal gas sound speed of the Martian atmosphere

    图 3  火星大气中6种主要气体成分的定压热容随温度的变化

    Figure 3.  Variation of the constant pressure heat capacity of the six main gas components of the Martian atmosphere with temperature

    图 4  时差法测量声速实验装置图 (a)示意图; (b)实物图

    Figure 4.  Diagram of the experimental setup for measuring sound speed by the time difference method: (a) Schematic diagram; (b) physical diagram

    图 5  二氧化碳中21 kHz 声波速度随气压的变化 (a) 0 ℃左右; (b) –20 ℃左右

    Figure 5.  Variation of sound speed of 21 kHz sound wave with pressure in carbon dioxide: (a) Around 0 ℃; (b) around –20 ℃

    图 6  火星大气6种主要气体成分在100—300 K温度范围内的黏温曲线

    Figure 6.  Viscosity-temperature curves of the six main gas components of the Martian atmosphere in the temperature range of 100–300 K

    图 7  不同海拔下火星多组分混合大气中的(a)黏度、(b)热导率和(c)无量纲数P的垂直剖面图

    Figure 7.  Vertical profiles of (a) viscosity, (b) thermal conductivity, and (c) dimensionless number P in the multi-component mixed atmosphere of Mars at different altitudes

    图 8  不同海拔下、不同频率的声波在火星大气中的NS方程声速剖面, 其中虚线代表NS声速不适用的海拔范围

    Figure 8.  NS equation sound speed profiles in the Martian atmosphere for sound waves at different altitudes and frequencies, where the dashed line represents the altitude range where the NS sound velocity does not apply

    图 9  火星大气中0.01 Hz声波的声吸收系数随海拔的变化

    Figure 9.  Variation of the acoustic absorption coefficient with altitude for 0.01 Hz sound waves in the Martian atmosphere

    图 10  火星不同声速剖面模型下声传播路径预测 (a)理想气体声速; (b) 0.01 Hz, (c) 0.1 Hz和(d) 1 Hz的声波NS声速, 其中不同曲线表示声线向不同角度发射, 射线发射角度范围15°—60°, 角度间隔3°, 水平范围0—700 km

    Figure 10.  Predicted sound propagation paths for different sound speed profile models of Mars: (a) Ideal gas sound speed; (b) 0.01 Hz, (c) 0.1 Hz and (d) 1 Hz NS sound speed, where different curves indicate sound lines emitted at different angles, with ray emission angles range from 15° to 60°, angular interval 3°, horizontal range 0–700 km

    图 11  声源高度对声传播路径的影响. 基于理想气体声速剖面的 (a) 50 km, (c) 110 km, (e) 150 km高度声源的传播路径; 基于0.01 Hz声波的NS声速剖面模拟的(b) 50 km, (d) 110 km, (f) 150 km高度声源的传播路径; 其中不同曲线表示声线向不同角度发射, 射线的发射角度–45°—45°, 角度间隔3°, 水平范围0—700 km

    Figure 11.  Effect of sound source height on sound propagation paths. Propagation paths of sources at (a) 50 km, (c) 110 km, and (e) 150 km based on ideal gas sound speed profiles; propagation paths of sources at (b) 50 km, (d) 110 km, and (f) 150 km based on simulated NS sound speed profiles of 0.01 Hz sound waves; where different curves indicate sound lines emitted at different angles, with ray emission angles range from –45° to 45°, angular interval 3°, horizontal range 0–700 km

    表 1  不同气体的分子摩尔质量

    Table 1.  Molar masses of molecules of different gases

    气体种类分子摩尔质量Mi /(g·mol–1)
    CO244.0095
    N228.0134
    Ar39.9480
    CO28.0101
    O15.9994
    H22.01588
    DownLoad: CSV

    表 2  火星主要气体成分Shomate公式系数

    Table 2.  Shomate formula coefficients for the major gas constituents of Mars

    气体ABCDE
    CO224.997455.1870–33.69147.94839–0.136638
    Ar20.78602.82591 × 10–7–1.46419 × 10–71.09213 × 10–8–3.66137 × 10–8
    N228.98641.85398–9.6474616.63540.000117
    CO25.56766.096134.05466–2.671300.131021
    O
    H233.0662–11.363411.4328–2.7728–0.15856
    DownLoad: CSV

    表 3  火星大气中不同频率声波NS声速适用失效海拔范围

    Table 3.  Applicable failure altitude range of the NS sound speed for different frequencies of acoustic waves in the Martian atmosphere

    频率/Hz
    0.010.11
    NS声速适用高度/km< 250.0< 188.0< 149.9
    DownLoad: CSV

    表 4  不同声速剖面下的声线对比

    Table 4.  Comparison of sound lines at different sound velocity profiles

    理想气体声速0.01 Hz NS声速0.1 Hz NS声速1 Hz NS声速
    折回高度/km237.3190.5163.2141.3
    声影区/km554.3231.2194.9167.3
    DownLoad: CSV
  • [1]

    Maurice S, Chide B, Murdoch N, Lorenz R D, Mimoun D, Wiens R C, Stott A, Jacob X, Bertrand T, Montmessin F, Lanza N L, Alvarez-Llamas C, Angel S M, Aung M, Balaram J, Beyssac O, Cousin A, Delory G, Forni O, Fouchet T, Gasnault O, Grip H, Hecht M, Hoffman J, Laserna J, Lasue J, Maki J, McClean J, Meslin P Y, Le Mouélic S, Munguira A, Newman C E, Rodríguez Manfredi J A, Moros J, Ollila A, Pilleri P, Schröder S, de la Torre Juárez M, Tzanetos T, Stack K M, Farley K, Williford K, the SuperCam team 2022 Nature 605 653Google Scholar

    [2]

    Peng Y, Zhang L, Cai Z, Wang Z, Jiao H, Wang D, Li Y 2020 Earth Planet. Phys. 4 371Google Scholar

    [3]

    Christie R, Campus P 2010 Infrasound Monitoring for Atmospheric Studies (Dordrecht: Springer Science and Business Media) pp541–574

    [4]

    Lamb D, Lees J M, Bowman D C 2018 Geophys. Res. Lett. 45 7176Google Scholar

    [5]

    毕思昭, 彭朝晖 2021 物理学报 70 114303Google Scholar

    Bi S Z, Peng Z H 2021 Acta Phys. Sin. 70 114303Google Scholar

    [6]

    程巍, 滕鹏晓, 吕君, 姬培锋, 戴翊靖 2021 物理学报 70 244203Google Scholar

    Cheng W, Teng P X, Lü J, Ji P F, Dai Y J 2021 Acta Phys. Sin. 70 244203Google Scholar

    [7]

    苏林, 马力, 宋文华, 郭圣明, 鹿力成 2015 物理学报 64 024302Google Scholar

    Su L, Ma L, Song W H, Guo S M, Lu L C 2015 Acta Phys. Sin. 64 024302Google Scholar

    [8]

    Williams J P 2001 J. Geophys. Res. Planets 106 5033Google Scholar

    [9]

    Kalempa D, Sharipov F 2009 Phys. Fluids 21 103601Google Scholar

    [10]

    Rayleigh J W S B 1896 The Theory of Sound (Vol. 2) (London: Macmillan) pp344–352

    [11]

    Chang W, Uhlenbeck G E 1948 Studies Statistical Mech. 5 1

    [12]

    Chang W, Uhlenbeck G E 1948 Studies Statistical Mech. 5 17

    [13]

    Sirovich L, Thurber J K 1965 J. Acoust. Soc. Am. 37 329Google Scholar

    [14]

    Greenspan M 1950 J. Acoust. Soc. Am. 22 568Google Scholar

    [15]

    Greenspan M 1954 J. Acoust. Soc. Am. 26 70Google Scholar

    [16]

    Greenspan M 1956 J. Acoust. Soc. Am. 28 644Google Scholar

    [17]

    Greenspan M 1959 J. Acoust. Soc. Am. 31 155Google Scholar

    [18]

    Bird G A 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows (USA: Oxford University Press) pp1–29

    [19]

    Cercignani C 1988 The Boltzmann Equation and its Application (New York: SpringerVerlag) pp351–385

    [20]

    Sharipov F 2016 Rarefied Gas Dynamics. Fundamentals for Research and Practice (Berlin: Wiley-VCH) pp73–81

    [21]

    Hadjiconstantinou N G, Garcia A L 2001 Phys. Fluids 13 1040Google Scholar

    [22]

    Hanford A D 2008 Ph. D. Dissertation (Pennsylvania: The Pennsylvania State University)

    [23]

    Kalempa D, Sharipov F 2016 Eur. J. Mech. B-Fluid 57 50Google Scholar

    [24]

    Kalempa D, Sharipov F, Silva J C 2019 Vacuum 159 82Google Scholar

    [25]

    Meyer E, Sessler G 1957 Z. Phys. 149 15Google Scholar

    [26]

    Maidanik G, Heckl M 1965 Phys. Fluids 8 266Google Scholar

    [27]

    Hirschfelder J O, Curtiss C F, Bird R B 1964 Molecular Theory of Gases and Liquids (New York: John Wiley & Sons, Inc) pp533–543

    [28]

    Mason W P 1984 Physical Acoustics : Principles and Methods (Vol. 17) (New York: Academic Press) pp145–228

    [29]

    Sutherland L C, Bass H E 2004 J. Acoust. Soc. Am. 115 1012Google Scholar

    [30]

    Bass H E, Chambers J P 2001 J. Acoust. Soc. Am. 109 3069Google Scholar

    [31]

    Petculescu A, Achi P 2012 J. Acoust. Soc. Am. 131 3671Google Scholar

    [32]

    Petculescu A 2016 J. Acoust. Soc. Am. 140 1439Google Scholar

    [33]

    Trahan A J, Petculescu A 2020 J. Acoust. Soc. Am. 148 141Google Scholar

    [34]

    Forget F, Hourdin F, Fournier R, Hourdin C, Talagrand O, Collins M, Huot J P 1999 J. Geophys. Res. Planets 104 24155Google Scholar

    [35]

    Millour E, Forget F, Spiga A, Vals M, Zakharov V, Montabone L 2018 Icarus From Mars Express to ExoMars 150 27

    [36]

    Chase M W, National Information Standards Organization (US) 1998 NIST-JANAF Thermochemical Tables (Vol. 9) (Washington, DC: American Chemical Society) pp1–1951

    [37]

    Greenspan M 1987 J. Acoust. Soc. Am. 82 370Google Scholar

    [38]

    Greenspan M 1965 Physical Acoustics, 2 (Part A) (New York: Academic Press) pp1–43

    [39]

    Bird R B 2002 Appl. Mech. Rev. 55 R1Google Scholar

    [40]

    Hirschfelder J O, Bird R B, Spotz E L 1948 J. Chem. Phys. 16 968Google Scholar

    [41]

    杨训仁, 陈宇 2007 大气声学 (北京: 科学出版社) 第52—59页

    Yang X R, Chen Y 2007 Atmospheric Acoustic (Beijing: Science Press) pp52–59 (in Chinese)

    [42]

    White R D, Neeson I, Schmid E S, Merrison J, Iversen J J, Banfield D 2020 AIAA Scitech 2020 Forum Orlando, Florida, USA, January 6–10, 2020 p0712

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Publishing process
  • Received Date:  28 July 2022
  • Accepted Date:  05 September 2022
  • Available Online:  06 December 2022
  • Published Online:  24 December 2022

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