Mechanism and characteristics of sound scattering modulation by underwater low frequency oscillating vortex flow field

Jing Chen-Xuan; Shi Sheng-Guo; Yang De-Sen; Zhang Jiang-Yi; Li Song

doi:10.7498/aps.72.20221748

Abstract

The scattering of sound waves by underwater vortex flow filed is the basic problem of sound waves propagating in complex flow fields, which has important significance in implementing underwater target detection and sound imaging of flow field. The theoretical analysis model and numerical calculation method are established for the problem of sound scattering modulation in underwater low frequency oscillating vortex flow fields, and the generation mechanism and time frequency and space characteristics of the scattering modulation sound field are explored. Firstly, based on the wave equation of the moving medium, in the first-order approximation the wave equation is decomposed into the flow-sound coupling term and the non flow-sound coupling term by introducing a potential function, and the flow-sound coupling term is analyzed in the frequency domain, revealing the underwater oscillating vortex flow field. Secondly, the discontinuous Galerkin numerical calculation method is used to solve the wave equation of the moving medium, and the sound propagation process in the underwater low frequency oscillating vortex flow field is numerically simulated. Under the condition of low Mach number, the effects of incident sound frequency, the oscillation frequency of the vortex flow field, and the scale of the vortex core on the time-frequency and space characteristics of the scattering modulating sound fields of vortex flow field are analyzed, and theoretical analysis model is used to explain the characteristics. The research results show that under the condition of low Mach number, the scattering of sound wave by oscillating vortex flow field can produce a scattering modulated sound field containing the harmonic of oscillating frequency side frequency modulation. The amplitude of the scattered sound pressure changes periodically with time, and the forward scattering is much stronger than the backward scattering. The fundamental frequency scattering modulation is much stronger than the frequency doubling scattering modulation. With the increase of the frequency of the incident sound wave and the scale of the vortex core, the intensity of the scattering modulating sound field increases, and the spatial distribution of the total scattering sound field has symmetry and an obvious main lobe, the main lobe is gradually sharpened, the azimuth angle of the main lobe is close to the propagation direction of the incident wave. When the frequency ratio is much greater than 1, the vortex flow field oscillation frequency has little effect on the spatial distribution of the sound field intensity of scattering modulating sound field.

Keywords:

Authors and contacts

1.
Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China
2.
Key Laboratory of Marine Information Acquisition and Security, Harbin Engineering University, Harbin 150001, China
3.
College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China

Corresponding author: Shi Sheng-Guo, shishengguo@hrbeu.edu.cn

Funds: Project supported by the National Defense Basic Scientific Research program of China (Grant No. JCKYS2022604SSJS006), the Fundamenta Research Funds for the Centra1 Universities (Grant No. 3072021CFT0501) and the Science and Technology on Sonar Laboratory(Grant No. 2021-JCJQ-LB-031/05).

FullText HTML : translate this paragraph

References

[1]	Ostashev V E, Wilson D K 2015 Acoustics in Moving Inhomogeneous Media (New York: CRC Press) pp1–23
[2]	Aurégan Y, Maurel A, Pagneux V 2008 Sound-Flow Interactions (Berlin: Springer) pp112–158
[3]	Chakraborty P, Balachandar S, Adrian R J 2005 J. Fluid Mech. 535 189 Google Scholar
[4]	Clair V, Gabard G 2018 J. Fluid Mech. 841 50 Google Scholar
[5]	Colonius T, Lele S K, Moin P 1994 J. Fluid Mech. 260 271 Google Scholar
[6]	Karabasov S, Kopiev V, Goloviznin V 2009 Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference) Miami, USA, May 10–12, 2009
[7]	马瑞轩, 王益民, 张树海, 武从海, 王勋年 2021 物理学报 70 104301 Google Scholar Ma R X, Wang Y M, Zhang S H, Wu C H, Wang X N 2021 Acta Phys. Sin. 70 104301 Google Scholar
[8]	王益民, 马瑞轩, 武从海, 罗勇, 张树海 2021 物理学报 79 194302 Google Scholar Wang Y M, Ma R X, Wu C H, Luo Y, Zhang S H 2021 Acta Phys. Sin. 79 194302 Google Scholar
[9]	Semenov A G. 2017 Ultra Low Frequency Fields of Moving Bodies (New York: Nova Science Publishers) pp118–141
[10]	Catalano P, Wang M, Iaccarino G 2003 Int. J. Heat Fluid Fl. 24 463 Google Scholar
[11]	Zdravkovich M M 1997 Flow Around Circular Cylinders: Volume 2: Applications (Oxford: Oxford University Press) pp163–201
[12]	Lighthill M J 1953 Proc. Cambridge Philos. Soc. 49 531 Google Scholar
[13]	Kraichnan R H 1953 J. Acoust. Soc. Am. 25 1096 Google Scholar
[14]	Bogey C, Bailly C, Juve D 2002 AIAA J. 40 235 Google Scholar
[15]	Bailly C, Juve D 2000 AIAA J. 38 22 Google Scholar
[16]	Pierce A D. 2019 Acoustics: An Introduction to Its Physical Principles and Applications (East Sandwich: Springer) pp427– 480
[17]	Pierce A D 1990 J. Acoust. Soc. Am. 87 2292 Google Scholar
[18]	Cheinet S, Ehrhardt L, Juve D, Benon B P 2012 J. Acoust. Soc. Am. 132 2198 Google Scholar
[19]	Cockburn B, Shu C W 2001 J. Sci. Comput. 16 173 Google Scholar
[20]	Cockburn B, Shu C W 1989 Math. Comp. 52 411 Google Scholar
[21]	Lee H D, Kwon O J 2013 J. Mech. Sci. Technol. 27 3331 Google Scholar
[22]	Williamschen M, Gabard G J 2020 AIAA J. 58 1079 Google Scholar
[23]	程建春 2019 声学原理(第二版下卷) (北京: 科学出版社) 第969页 Cheng J C 2012 Acoustic principles (Volume II of the Second Edition) (Beijing: Science Press) p969 (in Chinese)
[24]	冯士筰, 李凤岐, 李少菁 1999 海洋科学导论 (北京: 高等教育出版社) 第181页 Feng S Z, Li F Q, Li S J 1999 Introduction to Marine Science (Beijing: Higher Education Press) p181 (in Chinese)
[25]	杜浩, 熊鳌魁, 张咏鸥 2020 声学学报 45 55 Google Scholar Du H, Xiong A K, Zhang Y O 2020 Acta Acoust. 45 55 Google Scholar
[26]	Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (New York: Springer) pp531– 610
[27]	Headrick R H, Lynch J F, Kemp J N, Newhall A E, Heydt K 2000 J. Acoust. Soc. Am. 107 201 Google Scholar
[28]	Ford R, Smith S G L 1999 J. Fluid Mech. 386 305 Google Scholar
[29]	Fetter A L 1964 Phys. Rev. A 136 1488 Google Scholar

Cited By

图 1 计算域示意图

Figure 1. Schematic diagram of computation configuration.

DownLoad: Full-Size Img PowerPoint

图 2 不同时刻$ x = 0 $轴线涡流场速度分布

Figure 2. Velocity distribution of vortex flow field on $ x = 0 $ axis at different time.

DownLoad: Full-Size Img PowerPoint

图 3 模型验证

Figure 3. Comparison with previous literature.

DownLoad: Full-Size Img PowerPoint

图 4 网格无关性和时间步长无关性验证　(a) 网格无关性验证; (b)时间步长无关性验证

Figure 4. Verification of grid independence and time step independence: (a) Grid independence verification; (b) time step independence verification.

DownLoad: Full-Size Img PowerPoint

图 5 定常涡流场与振荡涡流场散射指向性图

Figure 5. Scattering directivity of steady vortex flow field and oscillating vortex flow field.

DownLoad: Full-Size Img PowerPoint

图 7 $ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.000625 $时不同时刻散射声压云图　(a) $ t = {T_{{\text{osc}}}} $; (b) $ t = 1.25{T_{{\text{osc}}}} $; (c) $ t = 1.5{T_{{\text{osc}}}} $

Figure 7. Scattering sound contours of $ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.000625 $ at different time: (a)$ t = {T_{{\text{osc}}}} $; (b) $ t = 1.25{T_{{\text{osc}}}} $; (c) $ t = 1.5{T_{{\text{osc}}}} $.

DownLoad: Full-Size Img PowerPoint

图 6 $ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0 $时, 不同时刻散射声压云图　(a)$ t = {T_{{\text{osc}}}} $; (b) $ t = 1.25{T_{{\text{osc}}}} $; (c) $ t = 1.5{T_{{\text{osc}}}} $

Figure 6. Scattering sound contours of $ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0 $ at different times: (a) $ t = {T_{{\text{osc}}}} $; (b) $ t = 1.25{T_{{\text{osc}}}} $; (c) $ t = 1.5{T_{{\text{osc}}}} $.

DownLoad: Full-Size Img PowerPoint

图 8 $ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.0025 $不同时刻散射声压云图　(a) $ t = {T_{{\text{osc}}}} $; (b) $ t = 1.25{T_{{\text{osc}}}} $; (c) $ t = 1.5{T_{{\text{osc}}}} $

Figure 8. Scattering sound contours of $ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.0025 $ at different times: (a) $ t = {T_{{\text{osc}}}} $; (b) $ t = 1.25{T_{{\text{osc}}}} $; (c) $ t = 1.5{T_{{\text{osc}}}} $.

DownLoad: Full-Size Img PowerPoint

图 9 定常涡流场与振荡涡流场散射声压时域图　(a)$ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0 $; (b)$ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.000625 $; (c)$ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.0025 $

Figure 9. Time domain diagram of scattering sound of steady vortex flow field and oscillating vortex flow field: (a)$ M{a_{{\text{ste}}}} = $$ 0.005{\text{ }}M{a_{{\text{osc}}}} = 0 $; (b)$ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.000625 $; (c)$ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.0025 $.

DownLoad: Full-Size Img PowerPoint

图 10 定常涡流场与振荡涡流场散射声压频域图

Figure 10. Frequency domain diagram of scattering sound of steady vortex flow field and oscillating vortex flow field.

DownLoad: Full-Size Img PowerPoint

图 11 不同入射声波频率散射指向性图

Figure 11. Scattering directivity of different incident sound frequencies.

DownLoad: Full-Size Img PowerPoint

图 12 不同入射声波频率$ t = {T_{{\text{osc}}}} $时刻散射声压云图　(a) f/F = 50; (b) f/F = 100; (c) f/F = 200

Figure 12. Scattering sound contours of different incident sound frequencies at $ t = {T_{{\text{osc}}}} $: (a) f/F = 50; (b) f/F = 100; (c) f/F = 200.

DownLoad: Full-Size Img PowerPoint

图 13 不同入射声波频率散射声压时域图　(a) f/F = 50; (b) f/F = 100; (c) f/F = 200

Figure 13. Time domain diagram of scattering sound of different incident sound frequencies: (a) f/F = 50; (b) f/F = 100; (c) f/F = 200.

DownLoad: Full-Size Img PowerPoint

图 14 不同入射声波频率散射声压频域图　(a) f/F = 50; (b) f/F = 100; (c) f/F = 200

Figure 14. Frequency domain diagram of scattering sound of different incident sound frequencies: (a) f/F = 50; (b) f/F = 100; (c) f/F = 200

DownLoad: Full-Size Img PowerPoint

图 15 散射强度和散射调制强度随入射声波频率变化规律

Figure 15. The variation of scattering filed intensity and scattering modulating filed intensity of different incident sound frequencies.

DownLoad: Full-Size Img PowerPoint

图 16 不同涡流场振荡频率散射指向性图

Figure 16. Scattering directivity of different vortex flow field oscillation frequencies.

DownLoad: Full-Size Img PowerPoint

图 17 不同涡流场振荡频率$ t = {T_{{\text{osc}}}} $时刻散射声压云图　(a) f/F = 50; (b) f/F = 100; (c) f/F = 200

Figure 17. Scattering sound contours of different vortex flow field oscillation frequencies at $ t = {T_{{\text{osc}}}} $: (a) f/F = 50; (b) f/F = 100; (c) f/F = 200.

DownLoad: Full-Size Img PowerPoint

图 18 不同涡流场振荡频率散射声压时域图　(a) f/F = 50; (b) f/F = 100; (c) f/F = 200

Figure 18. Time domain diagram of scattering sound of different vortex flow field oscillation frequencies: (a) f/F = 50; (b) f/F = 100; (c) f/F = 200.

DownLoad: Full-Size Img PowerPoint

图 19 不同涡流场振荡频率散射声压频域图　(a) f/F = 50; (b) f/F = 100; (c) f/F = 200

Figure 19. Frequency domain diagram of scattering sound of different vortex flow field oscillation frequencies: (a) f/F = 50; (b) f/F = 100; (c) f/F = 200.

DownLoad: Full-Size Img PowerPoint

图 20 不同马赫数散射指向性图　(a) $ M{a_{{\text{ste}}}} = 0.005—0.04, M{a_{{\text{osc}}}} = 0.0025 $; (b) $M{a_{{\text{ste}}}} = 0.005, $$ M{a_{{\text{osc}}}} = 0.0003125—0.0025$

Figure 20. Scattering directivity of different Mach numbers: (a) $M{a_{{\text{ste}}}} = 0.005-0.04, M{a_{{\text{osc}}}} = 0.0025$; (b) $M{a_{{\text{ste}}}} = 0.005, $$ M{a_{{\text{osc}}}} = 0.0003125-0.0025$.

DownLoad: Full-Size Img PowerPoint

图 21 不同马赫数振荡涡流场$ t = {T_{{\text{osc}}}} $时刻散射声压云图　(a) $ M{a_{{\text{ste}}}} = 0.01 M{a_{{\text{osc}}}} = 0.0025 $; (b) $ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.0025 $; (c) $ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.00125 $

Figure 21. Scattering sound contours of different Mach number at $ t = {T_{{\text{osc}}}} $: (a) $ M{a_{{\text{ste}}}} = 0.01 M{a_{{\text{osc}}}} = 0.0025 $; (b) $M{a_{{\text{ste}}}} = $$ 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.0025$; (c) $ M{a_{{\text{ste}}}} = 0.005{\text{ }}M{a_{{\text{osc}}}} = 0.00125 $.

DownLoad: Full-Size Img PowerPoint

图 22 $ M{a_{{\text{osc}}}} = 0.0025 $, 不同$ M{a_{{\text{ste}}}} $散射声压时域图　(a)$ M{a_{{\text{ste}}}} = 0.01 $; (b)$ M{a_{{\text{ste}}}} = 0.02 $; (c)$ M{a_{{\text{ste}}}} = 0.04 $

Figure 22. $ M{a_{{\text{osc}}}} = 0.0025 $, time domain diagram of scattering sound of different $ M{a_{{\text{ste}}}} $: (a)$ M{a_{{\text{ste}}}} = 0.01 $; (b)$ M{a_{{\text{ste}}}} = 0.02 $; (c)$ M{a_{{\text{ste}}}} = 0.04 $.

DownLoad: Full-Size Img PowerPoint

图 23 $ M{a_{{\text{osc}}}} = 0.0025 $, 不同$ M{a_{{\text{ste}}}} $散射声压频域图　(a)$ M{a_{{\text{ste}}}} = 0.01 $; (b)$ M{a_{{\text{ste}}}} = 0.02 $; (c)$ M{a_{{\text{ste}}}} = 0.04 $

Figure 23. $ M{a_{{\text{osc}}}} = 0.0025 $, frequency domain diagram of scattering sound of different $ M{a_{{\text{ste}}}} $: (a)$ M{a_{{\text{ste}}}} = 0.01 $; (b)$ M{a_{{\text{ste}}}} = 0.02 $; (c)$ M{a_{{\text{ste}}}} = 0.04 $.

DownLoad: Full-Size Img PowerPoint

图 24 $ M{a_{{\text{ste}}}} = 0.005 $, 不同$ M{a_{{\text{osc}}}} $散射声压时域图　(a)$ M{a_{{\text{osc}}}} = 0.0003125 $; (b)$ M{a_{{\text{osc}}}} = 0.000625 $; (c)$ M{a_{{\text{osc}}}} = 0.00125 $

Figure 24. $ M{a_{{\text{ste}}}} = 0.005 $, time domain diagram of scattering sound of different $ M{a_{{\text{osc}}}} $: (a)$ M{a_{{\text{osc}}}} = 0.0003125 $; (b)$M{a_{{\text{osc}}}} = $$ 0.000625$; (c)$ M{a_{{\text{osc}}}} = 0.00125 $.

DownLoad: Full-Size Img PowerPoint

图 25 $ M{a_{{\text{ste}}}} = 0.005 $, 不同$ M{a_{{\text{osc}}}} $散射声压频域图　(a)$ M{a_{{\text{osc}}}} = 0.0003125 $; (b)$ M{a_{{\text{osc}}}} = 0.000625 $; (c)$ M{a_{{\text{osc}}}} = 0.00125 $

Figure 25. $ M{a_{{\text{ste}}}} = 0.005 $, frequency domain diagram of scattering sound of different $ M{a_{{\text{osc}}}} $: (a)$ M{a_{{\text{osc}}}} = 0.0003125 $; (b)$M{a_{{\text{osc}}}} = $$ 0.000625$; (c) $ M{a_{{\text{osc}}}} = 0.00125 $.

DownLoad: Full-Size Img PowerPoint

图 26 散射声场强度和散射调制声场强度随$ M{a_{{\text{ste}}}} $(a)和$ M{a_{{\text{osc}}}} $(b)变化规律

Figure 26. The variation of scattering filed intensity and scattering modulating filed intensity of different $ M{a_{{\text{ste}}}} $(a)and $ M{a_{{\text{osc}}}} $(b).

DownLoad: Full-Size Img PowerPoint

图 27 不同涡核尺度散射声压指向性图

Figure 27. Scattering directivity of different vortex core scales.

DownLoad: Full-Size Img PowerPoint

图 28 不同涡核尺度$ t = {T_{{\text{osc}}}} $时刻散射声压云图　(a) L = 0.5 m; (b) L = 1 m; (c) L = 2 m

Figure 28. Scattering sound pressure contours of different vortex core scales at $t = {T_{{\text{osc}}}}$:(a) L = 0.5 m; (b) L = 1 m; (c) L = 2 m.

DownLoad: Full-Size Img PowerPoint

图 29 不同涡核尺度散射声压时域图　(a) L = 0.5 m; (b) L = 1 m; (c) L = 2 m

Figure 29. Time domain diagram of scattering sound pressure of different vortex core scales: (a) L = 0.5 m; (b) L = 1 m; (c) L = 2 m.

DownLoad: Full-Size Img PowerPoint

图 30 不同涡核尺度散射声压频域图　(a) L = 0.5 m; (b) L = 1 m; (c) L = 2 m

Figure 30. Frequency domain diagram of scattering sound pressure of different vortex core scales: (a) L = 0.5 m; (b) L = 1 m; (c) L = 2 m.

DownLoad: Full-Size Img PowerPoint

图 31 散射声场强度和散射调制声场强度随涡核尺度变化规律

Figure 31. The variation of scattering field intensity and scattering modulating field intensity of different vortex core scales.

DownLoad: Full-Size Img PowerPoint

[1]	Ostashev V E, Wilson D K 2015 Acoustics in Moving Inhomogeneous Media (New York: CRC Press) pp1–23
[2]	Aurégan Y, Maurel A, Pagneux V 2008 Sound-Flow Interactions (Berlin: Springer) pp112–158
[3]	Chakraborty P, Balachandar S, Adrian R J 2005 J. Fluid Mech. 535 189 Google Scholar
[4]	Clair V, Gabard G 2018 J. Fluid Mech. 841 50 Google Scholar
[5]	Colonius T, Lele S K, Moin P 1994 J. Fluid Mech. 260 271 Google Scholar
[6]	Karabasov S, Kopiev V, Goloviznin V 2009 Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference) Miami, USA, May 10–12, 2009
[7]	马瑞轩, 王益民, 张树海, 武从海, 王勋年 2021 物理学报 70 104301 Google Scholar Ma R X, Wang Y M, Zhang S H, Wu C H, Wang X N 2021 Acta Phys. Sin. 70 104301 Google Scholar
[8]	王益民, 马瑞轩, 武从海, 罗勇, 张树海 2021 物理学报 79 194302 Google Scholar Wang Y M, Ma R X, Wu C H, Luo Y, Zhang S H 2021 Acta Phys. Sin. 79 194302 Google Scholar
[9]	Semenov A G. 2017 Ultra Low Frequency Fields of Moving Bodies (New York: Nova Science Publishers) pp118–141
[10]	Catalano P, Wang M, Iaccarino G 2003 Int. J. Heat Fluid Fl. 24 463 Google Scholar
[11]	Zdravkovich M M 1997 Flow Around Circular Cylinders: Volume 2: Applications (Oxford: Oxford University Press) pp163–201
[12]	Lighthill M J 1953 Proc. Cambridge Philos. Soc. 49 531 Google Scholar
[13]	Kraichnan R H 1953 J. Acoust. Soc. Am. 25 1096 Google Scholar
[14]	Bogey C, Bailly C, Juve D 2002 AIAA J. 40 235 Google Scholar
[15]	Bailly C, Juve D 2000 AIAA J. 38 22 Google Scholar
[16]	Pierce A D. 2019 Acoustics: An Introduction to Its Physical Principles and Applications (East Sandwich: Springer) pp427– 480
[17]	Pierce A D 1990 J. Acoust. Soc. Am. 87 2292 Google Scholar
[18]	Cheinet S, Ehrhardt L, Juve D, Benon B P 2012 J. Acoust. Soc. Am. 132 2198 Google Scholar
[19]	Cockburn B, Shu C W 2001 J. Sci. Comput. 16 173 Google Scholar
[20]	Cockburn B, Shu C W 1989 Math. Comp. 52 411 Google Scholar
[21]	Lee H D, Kwon O J 2013 J. Mech. Sci. Technol. 27 3331 Google Scholar
[22]	Williamschen M, Gabard G J 2020 AIAA J. 58 1079 Google Scholar
[23]	程建春 2019 声学原理(第二版下卷) (北京: 科学出版社) 第969页 Cheng J C 2012 Acoustic principles (Volume II of the Second Edition) (Beijing: Science Press) p969 (in Chinese)
[24]	冯士筰, 李凤岐, 李少菁 1999 海洋科学导论 (北京: 高等教育出版社) 第181页 Feng S Z, Li F Q, Li S J 1999 Introduction to Marine Science (Beijing: Higher Education Press) p181 (in Chinese)
[25]	杜浩, 熊鳌魁, 张咏鸥 2020 声学学报 45 55 Google Scholar Du H, Xiong A K, Zhang Y O 2020 Acta Acoust. 45 55 Google Scholar
[26]	Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (New York: Springer) pp531– 610
[27]	Headrick R H, Lynch J F, Kemp J N, Newhall A E, Heydt K 2000 J. Acoust. Soc. Am. 107 201 Google Scholar
[28]	Ford R, Smith S G L 1999 J. Fluid Mech. 386 305 Google Scholar
[29]	Fetter A L 1964 Phys. Rev. A 136 1488 Google Scholar

[1]	Chen Chong, Ma Ming-Yuan, Pan Feng, Song Cheng. Magneto-acoustic coupling: Physics, materials, and devices. Acta Physica Sinica, 2024, 73(5): 058502. doi: 10.7498/aps.73.20231908
[2]	Zhong Guo-Hua, Lin Hai-Qing. Aromatic superconductors: Electron-phonon coupling and electronic correlations. Acta Physica Sinica, 2023, 72(23): 237403. doi: 10.7498/aps.72.20231751
[3]	Man Liang, Deng Hao-Chuan, Wu Yang, Yu Xi-Long, Xiao Zhi-He. Echo spectrum modulation characteristics of plasma flow field simulated by wind tunnel. Acta Physica Sinica, 2022, 71(3): 035203. doi: 10.7498/aps.71.20211471
[4]	Shi Hui-Min, Mo Run-Yang, Wang Cheng-Hui. Oscillation behavior of bubble pair in magnetic fluid tube under magneto-acoustic complex field. Acta Physica Sinica, 2022, 71(8): 084302. doi: 10.7498/aps.71.20212150
[5]	. Experimental study on echo spectrum modulation characteristics of plasma flow field simulated by wind tunnel. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20211471
[6]	Yu Ming-Hao. Numerical investigation on interaction mechanisms between flow field and electromagnetic field for nonequilibrium inductively coupled plasma. Acta Physica Sinica, 2019, 68(18): 185202. doi: 10.7498/aps.68.20190865
[7]	Zhang Bu-Qiang, Xu Zhen-Yu, Liu Jian-Guo, Yao Lu, Ruan Jun, Hu Jia-Yi, Xia Hui-Hui, Nie Wei, Yuan Feng, Kan Rui-Feng. Temperature measurement method of high temperature and high pressure flow field based on wavelength modulation spectroscopy technology. Acta Physica Sinica, 2019, 68(23): 233301. doi: 10.7498/aps.68.20190515
[8]	Li Yang, Su Ting, Liang Hong, Xu Jiang-Rong. Phase field lattice Boltzmann model for two-phase flow coupled with additional interfacial force. Acta Physica Sinica, 2018, 67(22): 224701. doi: 10.7498/aps.67.20181230
[9]	Ma Ping, Shi An-Hua, Yang Yi-Jian, Yu Zhe-Feng, Liang Shi-Chang, Huang Jie. Experiment on similarity between wake flow field and electromagnetic scattering characteristic of the hypersonic model. Acta Physica Sinica, 2017, 66(10): 102401. doi: 10.7498/aps.66.102401
[10]	Wang Tuo, Wu Feng, Li Duan-Yong, Chen Hao, Lin Jie. Self-excited oscillation mechanism of a standing-wave thermoacoustic system. Acta Physica Sinica, 2015, 64(4): 044301. doi: 10.7498/aps.64.044301
[11]	Gao Miao, Kong Xin, Lu Zhong-Yi, Xiang Tao. First-principles study of electron-phonon coupling and superconductivity in compound Li2C2. Acta Physica Sinica, 2015, 64(21): 214701. doi: 10.7498/aps.64.214701
[12]	Chen Xing-Le, Lei Yin-Zhao. Analytical solutions to pulsed eddy current field excited by a differently oriented probe coil outside a conducting ferromagnetic pipe. Acta Physica Sinica, 2014, 63(24): 240301. doi: 10.7498/aps.63.240301
[13]	Ye Xi, Yao Xiong-Liang, Zhang A-Man, Pang Fu-Zhen. The motion and acoustic radiation characteristics for cavitation in the compressible vortex fluid. Acta Physica Sinica, 2013, 62(11): 114702. doi: 10.7498/aps.62.114702
[14]	Su Jin, Ouyang Jie, Wang Xiao-Dong. Lattice Boltzmann method for an advective transport equation coupled with incompressible flow field. Acta Physica Sinica, 2012, 61(10): 104702. doi: 10.7498/aps.61.104702
[15]	Wei Wei, Lu Lu-Yi, Gu Zhao-Lin. Modeling and simulation of electrification of wind-blown-sand two-phase flow. Acta Physica Sinica, 2012, 61(15): 158301. doi: 10.7498/aps.61.158301
[16]	Cao Bing-Hua, Yang Xue-Feng, Fan Meng-Bao. Analytical time-domain model of transient eddy current field in pulsed eddy current testing. Acta Physica Sinica, 2010, 59(11): 7570-7574. doi: 10.7498/aps.59.7570
[17]	QI MING, LUO JIN-SHENG, J. SHIRAKASHI, S. NOZAKI, K. TAKAHASHI, E. TOKUMITSU, M. KONAGAI. RAMAN SCATTERING STUDY OF LO PHONON-PLASMON COUPLED MODE IN HEAVILY CARBON DOPED p-TYPE GaAs. Acta Physica Sinica, 1993, 42(6): 963-968. doi: 10.7498/aps.42.963
[18]	QIAN ZU-WEN. ON THE SCATTERING OF SOUND BY SOUND. Acta Physica Sinica, 1976, 25(6): 472-480. doi: 10.7498/aps.25.472
[19]	LI YIN-YUAN, LENG ZHONG-AHG, PAN SHOU-FU. THEORY OF THE PARAMETRIC OSCILLATION OF MAGNETOACOUSTIC MODES. Acta Physica Sinica, 1960, 16(8): 448-461. doi: 10.7498/aps.16.448
[20]	. . Acta Physica Sinica, 1956, 12(6): 511-527. doi: 10.7498/aps.12.511

Catalog

Vol. 72, Issue 1 - 2023-01-05

Metrics

Abstract views: 4647
PDF Downloads: 124
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板