Pressure-driven bubble dynamics is a major topic of current research in fluid dynamics, driven by innovative medical therapies, sonochemistry, material treatments, and geophysical exploration. First proposed in 1942, the Kirkwood–Bethe hypothesis provides a simple means to close the equations that govern pressure-driven bubble dynamics as well as the resulting flow field and acoustic emissions in spherical symmetry. The models derived from the Kirkwood–Bethe hypothesis can be solved using standard numerical integration methods at a fraction of the computational cost required for fully resolved simulations. Here, the theoretical foundation of the Kirkwood–Bethe hypothesis and contemporary models derived from it are gathered and reviewed, as well as generalized to account for spherically symmetric, cylindrically symmetric, and planar one-dimensional domains. In addition, the underpinning assumptions are clarified and new results that scrutinize the predictive capabilities of the Kirkwood–Bethe hypothesis with respect to the complex acoustic impedance experienced by curved acoustic waves and the formation of shock waves are presented. Although the Kirkwood–Bethe hypothesis is built upon simplifying assumptions and lacks some basic acoustic properties, models derived from it are able to provide accurate predictions under the specific conditions associated with pressure-driven bubble dynamics, cavitation, and underwater explosions.

1.
M. S.
Plesset
and
A.
Prosperetti
, “
Bubble dynamics and cavitation
,”
Annu. Rev. Fluid Mech.
9
,
145
185
(
1977
).
2.
C. E.
Brennen
,
Cavitation and Bubble Dynamics
, Oxford Engineering Science Series No. 44 (
Oxford University Press
,
New York
,
1995
).
3.
W.
Lauterborn
and
T.
Kurz
, “
Physics of bubble oscillations
,”
Rep. Prog. Phys.
73
,
106501
(
2010
).
4.
J. R.
Blake
and
D. C.
Gibson
, “
Cavitation bubbles near boundaries
,”
Annu. Rev. Fluid Mech.
19
,
99
123
(
1987
).
5.
F.
Reuter
,
C.
Deiter
, and
C.-D.
Ohl
, “
Cavitation erosion by shockwave self-focusing of a single bubble
,”
Ultrason. Sonochem.
90
,
106131
(
2022
).
6.
M.
Dular
and
C. D.
Ohl
, “
Bulk material influence on the aggressiveness of cavitation – Questioning the microjet impact influence and suggesting a possible way to erosion mitigation
,”
Wear
530–531
,
205061
(
2023
).
7.
K.
Johansen
,
J. H.
Song
,
K.
Johnston
, and
P.
Prentice
, “
Deconvolution of acoustically detected bubble-collapse shock waves
,”
Ultrasonics
73
,
144
153
(
2017
).
8.
L.
Gaisser
,
O.
Kirschner
, and
S.
Riedelbauch
, “
Cavitation detection in hydraulic machinery by analyzing acoustic emissions under strong domain shifts using neural networks
,”
Phys. Fluids
35
,
027128
(
2023
).
9.
S. C.
Haskell
,
N.
Lu
,
G. E.
Stocker
,
Z.
Xu
, and
J. R.
Sukovich
, “
Monitoring cavitation dynamics evolution in tissue mimicking hydrogels for repeated exposures via acoustic cavitation emissions
,”
J. Acoust. Soc. Am.
153
,
237
247
(
2023
).
10.
Cavitation in Biomedicine
, edited by
M.
Wan
and
Y.
Feng
, and
G.
ter Haar
(
Springer
,
Netherlands, Dordrecht
,
2015
).
11.
D.
Meroni
,
R.
Djellabi
,
M.
Ashokkumar
,
C. L.
Bianchi
, and
D. C.
Boffito
, “
Sonoprocessing: From concepts to large-scale reactors
,”
Chem. Rev.
122
,
3219
3258
(
2022
).
12.
K.
Maeda
,
A. D.
Maxwell
,
T.
Colonius
,
W.
Kreider
, and
M. R.
Bailey
, “
Energy shielding by cavitation bubble clouds in burst wave lithotripsy
,”
J. Acoust. Soc. Am.
144
,
2952
2961
(
2018
).
13.
O. A.
Sapozhnikov
,
A. D.
Maxwell
, and
M. R.
Bailey
, “
Maximizing mechanical stress in small urinary stones during burst wave lithotripsy
,”
J. Acoust. Soc. Am.
150
,
4203
4212
(
2021
).
14.
E.
Yeats
,
N.
Lu
,
J. R.
Sukovich
,
Z.
Xu
, and
T. L.
Hall
, “
Soft tissue aberration correction for histotripsy using acoustic emissions from cavitation cloud nucleation and collapse
,”
Ultrasound Med. Biol.
49
,
1182
1193
(
2023
).
15.
A.
Vogel
,
W.
Hentschel
,
J.
Holzfuss
, and
W.
Lauterborn
, “
Cavitation bubble dynamics and acoustic transient generation in ocular surgery with pulsed Neodymium:YAG lasers
,”
Ophthalmology
93
,
1259
1269
(
1986
).
16.
T.
Lee
,
W.
Luo
,
Q.
Li
,
H.
Demirci
, and
L. J.
Guo
, “
Laser-induced focused ultrasound for cavitation treatment: toward high-precision invisible sonic scalpel
,”
Small
13
,
1701555
(
2017
).
17.
G.
Shakya
,
M.
Cattaneo
,
G.
Guerriero
,
A.
Prasanna
,
S.
Fiorini
, and
O.
Supponen
, “
Ultrasound-responsive microbubbles and nanodroplets: A pathway to targeted drug delivery
,”
Adv. Drug Deliv. Rev.
206
,
115178
(
2024
).
18.
M.
Habibi
,
S.
Foroughi
,
V.
Karamzadeh
, and
M.
Packirisamy
, “
Direct sound printing
,”
Nat. Commun.
13
,
1800
(
2022
).
19.
A. G.
Athanassiadis
,
Z.
Ma
,
N.
Moreno-Gomez
,
K.
Melde
,
E.
Choi
,
R.
Goyal
, and
P.
Fischer
, “
Ultrasound-responsive systems as components for smart materials
,”
Chem. Rev.
122
,
5165
5208
(
2022
).
20.
Z.
Ma
,
C.
Bourquard
,
Q.
Gao
,
S.
Jiang
,
T.
De Iure-Grimmel
,
R.
Huo
,
X.
Li
,
Z.
He
,
Z.
Yang
,
G.
Yang
,
Y.
Wang
,
E.
Lam
,
Z-h
Gao
,
O.
Supponen
, and
J.
Li
, “
Controlled tough bioadhesion mediated by ultrasound
,”
Science
377
,
751
755
(
2022
).
21.
C.-D.
Ohl
,
M.
Arora
,
R.
Ikink
,
N.
de Jong
,
M.
Versluis
,
M.
Delius
, and
D.
Lohse
, “
Sonoporation from jetting cavitation bubbles
,”
Biophys. J.
91
,
4285
4295
(
2006
).
22.
B.
Helfield
,
X.
Chen
,
S. C.
Watkins
, and
F. S.
Villanueva
, “
Biophysical insight into mechanisms of sonoporation
,”
Proc. Natl. Acad. Sci. U. S. A.
113
,
9983
9988
(
2016
).
23.
A.
Šarc
,
J.
Kosel
,
D.
Stopar
,
M.
Oder
, and
M.
Dular
, “
Removal of bacteria Legionella pneumophila, Escherichia coli, and Bacillus subtilis by (super)cavitation
,”
Ultrason. Sonochem.
42
,
228
236
(
2018
).
24.
G. L.
Chahine
,
A.
Kapahi
,
J.-K.
Choi
, and
C.-T.
Hsiao
, “
Modeling of surface cleaning by cavitation bubble dynamics and collapse
,”
Ultrason. Sonochem.
29
,
528
549
(
2016
).
25.
F.
Reuter
,
S.
Lauterborn
,
R.
Mettin
, and
W.
Lauterborn
, “
Membrane cleaning with ultrasonically driven bubbles
,”
Ultrason. Sonochem.
37
,
542
560
(
2017
).
26.
S.
Barcikowski
,
A.
Plech
,
K. S.
Suslick
, and
A.
Vogel
, “
Materials synthesis in a bubble
,”
MRS Bull.
44
,
382
391
(
2019
).
27.
H.
Soyama
and
A. M.
Korsunsky
, “
A critical comparative review of cavitation peening and other surface peening methods
,”
J. Mater. Process. Technol.
305
,
117586
(
2022
).
28.
U. J.
Gutiérrez-Hernández
,
H.
Reese
,
F.
Reuter
,
C.-D.
Ohl
, and
P. A.
Quinto-Su
, “
Nano-cracks and glass carving from non-symmetrically converging shocks
,”
Adv. Phys. Res.
2
,
2300030
(
2023
).
29.
C.
Llorens
,
M.
Argentina
,
N.
Rojas
,
J.
Westbrook
,
J.
Dumais
, and
X.
Noblin
, “
The fern cavitation catapult: Mechanism and design principles
,”
J. R Soc. Interface
13
,
20150930
(
2016
).
30.
P.
Koukouvinis
,
C.
Bruecker
, and
M.
Gavaises
, “
Unveiling the physical mechanism behind pistol shrimp cavitation
,”
Sci. Rep.
7
,
13994
(
2017
).
31.
R. H.
Cole
,
Underwater Explosions
(
Princeton University Press
,
Princeton, NJ
,
1948
).
32.
W.
Wu
,
A.-M.
Zhang
,
Y.-L.
Liu
, and
M.
Liu
, “
Interaction between shock wave and a movable sphere with cavitation effects in shallow water
,”
Phys. Fluids
32
,
016103
(
2020
).
33.
W.
Yu
,
S.
Song
, and
J.-I.
Choi
, “
Numerical simulations of underwater explosions using a compressible multi-fluid model
,”
Phys. Fluids
35
,
106102
(
2023
).
34.
K.
de Graaf
,
I.
Penesis
, and
P.
Brandner
, “
Modelling of seismic airgun bubble dynamics and pressure field using the Gilmore equation with additional damping factors
,”
Ocean Eng.
76
,
32
39
(
2014
).
35.
A. O.
MacGillivray
, “
An airgun array source model accounting for high-frequency sound emissions during firing—Solutions to the IAMW source test cases
,”
IEEE J. Oceanic Eng.
44
,
582
588
(
2019
).
36.
A. G.
Athanassiadis
, “
Optical breakdown acoustics: Transduction and sensing underwater
,” Ph.D. thesis (
Massachusetts Institute of Technology
,
2019
).
37.
M. A.
O'Reilly
and
K.
Hynynen
, “
Blood-brain barrier: real-time feedback-controlled focused ultrasound disruption by using an acoustic emissions–based controller
,”
Radiology
263
,
96
106
(
2012
).
38.
A.
Novell
,
H. A. S.
Kamimura
,
A.
Cafarelli
,
M.
Gerstenmayer
,
J.
Flament
,
J.
Valette
,
P.
Agou
,
A.
Conti
,
E.
Selingue
,
R.
Aron Badin
,
P.
Hantraye
, and
B.
Larrat
, “
A new safety index based on intrapulse monitoring of ultra-harmonic cavitation during ultrasound-induced blood-brain barrier opening procedures
,”
Sci. Rep.
10
,
10088
(
2020
).
39.
V.-S.
Doan
,
T.
Huynh-The
, and
D.-S.
Kim
, “
Underwater acoustic target classification based on dense convolutional neural network
,”
IEEE Geosci. Remote Sens. Lett.
19
,
1500905
(
2022
).
40.
M.
Rom
, “
Physics-informed neural networks for the Reynolds equation with cavitation modeling
,”
Tribol. Int.
179
,
108141
(
2023
).
41.
K.
Klapcsik
,
B.
Gyires-Tóth
,
J. M.
Rosselló
, and
F.
Hegedűs
, “
Position control of an acoustic cavitation bubble by reinforcement learning
,” arXiv:2312.05674 (
2023
).
42.
W.
Mallik
,
R.
Jaiman
, and
J.
Jelovica
, “
Deep neural network for learning wave scattering and interference of underwater acoustics
,”
Phys. Fluids
36
,
017137
(
2024
).
43.
J. G.
Kirkwood
and
H. A.
Bethe
, “
The pressure wave produced by an underwater explosion I
,”
Technical Report No. 588
(
Office of Scientific Research and Development
,
1942
).
44.
R.
Ivany
, “
Collapse of a cavitation bubble in viscous compressible liquid: Numerical and experimental analysis
,” Ph.D. thesis (
University of Michigan
,
1965
).
45.
R. R.
Lilliston
, “
Calculations on the collapse of a spherical gas-filled cavity in a compressible liquid
,” “
Technical Report No. 2223 (SP 6–0002)
(
David Taylor Model Basin, Washington, DC
,
1966
).
46.
F.
Denner
,
C.-N.
Xiao
, and
B.
van Wachem
, “
Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretisation
,”
J. Comput. Phys.
367
,
192
234
(
2018
).
47.
D.
Fuster
and
S.
Popinet
, “
An all-Mach method for the simulation of bubble dynamics problems in the presence of surface tension
,”
J. Comput. Phys.
374
,
752
768
(
2018
).
48.
K.
Schmidmayer
,
F.
Petitpas
,
S. L.
Martelot
, and
É.
Daniel
, “
ECOGEN: An open-source tool for multiphase, compressible, multiphysics flows
,”
Comput. Phys. Commun.
251
,
107093
(
2020
).
49.
S. H.
Bryngelson
,
K.
Schmidmayer
,
V.
Coralic
,
J. C.
Meng
,
K.
Maeda
, and
T.
Colonius
, “
MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver
,”
Comput. Phys. Commun.
266
,
107396
(
2021
).
50.
Y.
Saade
,
D.
Lohse
, and
D.
Fuster
, “
A multigrid solver for the coupled pressure-temperature equations in an all-Mach solver with VoF
,”
J. Comput. Phys.
476
,
111865
(
2023
).
51.
M.
Koch
,
C.
Lechner
,
F.
Reuter
,
K.
Köhler
,
R.
Mettin
, and
W.
Lauterborn
, “
Numerical modeling of laser generated cavitation bubbles with the finite volume and volume of fluid method, using OpenFOAM
,”
Comput. Fluids
126
,
71
90
(
2016
).
52.
F.
Denner
,
F.
Evrard
, and
B.
van Wachem
, “
Modeling acoustic cavitation using a pressure-based algorithm for polytropic fluids
,”
Fluids
5
,
69
(
2020
).
53.
S. R.
Gonzalez-Avila
,
F.
Denner
, and
C.-D.
Ohl
, “
The acoustic pressure generated by the cavitation bubble expansion and collapse near a rigid wall
,”
Phys. Fluids
33
,
032118
(
2021
).
54.
S.-P.
Wang
,
H.
Geng
,
S.
Zhang
, and
S.-W.
Wang
, “
Pressure waves from air gun bubbles: A numerical analysis based on the finite volume method
,”
Phys. Fluids
36
,
013345
(
2024
).
55.
D. G.
Crighton
,
A. P.
Dowling
,
J. E.
Ffowcs Williams
,
M.
Heckl
, and
F. G.
Leppington
,
Modern Methods in Analytical Acoustics
(
Springer London
,
London
,
1992
).
56.
I. C.
Christov
and
C. I.
Christov
, “
On mechanical waves and Doppler shifts from moving boundaries
,”
Math. Methods Appl. Sci.
40
,
4481
4492
(
2017
).
57.
F.
Denner
, “
Acoustic pressure modulation driven by spatially non-uniform flow
,”
J. Acoust. Soc. Am.
155
,
984
989
(
2024
).
58.
G.
Lai
,
S.
Geng
,
H.
Zheng
,
Z.
Yao
,
Q.
Zhong
, and
F.
Wang
, “
Early dynamics of a laser-induced underwater shock wave
,”
J. Fluids Eng.
144
,
011501
(
2022
).
59.
X.-X.
Liang
,
N.
Linz
,
S.
Freidank
,
G.
Paltauf
, and
A.
Vogel
, “
Comprehensive analysis of spherical bubble oscillations and shock wave emission in laser-induced cavitation
,”
J. Fluid Mech.
940
,
A5
(
2022
).
60.
F.
Denner
and
S.
Schenke
, “
Modeling acoustic emissions and shock formation of cavitation bubbles
,”
Phys. Fluids
35
,
012114
(
2023
).
61.
H.
Wen
,
Z.
Yao
,
Q.
Zhong
,
Y.
Tian
,
Y.
Sun
, and
F.
Wang
, “
Energy partitioning in laser-induced millimeter-sized spherical cavitation up to the fourth oscillation
,”
Ultrason. Sonochem.
95
,
106391
(
2023
).
62.
F. R.
Gilmore
, “
The growth or collapse of a spherical bubble in a viscous compressible liquid
,”
Technical Report No. 26-4
(
California Institute of Technology
,
Pasadena, CA
,
1952
).
63.
H. G.
Flynn
, “
Collapse of a transient cavity in a compressible liquid
,”
Technical Memorandum
38
(
Acoustics Research Laboratory, Harvard University
,
Cambridge, MA
,
1957
).
64.
R.
Hickling
and
M. S.
Plesset
, “
The collapse of a spherical cavity in a compressible liquid
,”
Technical Report No. 85-24
(
California Institute of Technology
,
Pasadena, CA
,
1963
).
65.
R. T.
Beyer
, “
Nonlinear acoustics
,” Technical Report (
Brown University
,
Providence, RI
,
1974
).
66.
H. G.
Flynn
, “
Cavitation dynamics: IV. Collapse of transient cavities
,” Technical Report (
University of Rochester
,
Rochester, NY, USA
,
1978
).
67.
O. K.
Rice
and
R.
Ginell
, “
The pressure wave produced by an underwater explosion: Part VI: The case of cylindrical symmetry
,”
Technical Report 2023
(
Office of Scientific Research and Development
,
1943
).
68.
O. K.
Rice
and
R.
Ginell
, “
The pressure wave produced by an underwater explosion, part VIII. The case of cylindrical symmetry, II
,”
Technical Report 3950
(
Office of Scientific Research and Development
,
1944
).
69.
G. B.
Whitham
, “
Spherical waves and shocks
,”
Technical Report No. IMM-NYU 190
(
Courant Institute of Mathematical Sciences, New York University
,
New York, NY
,
1953
).
70.
H.
Snay
, “
Hydrodynamic concepts: Selected topics for underwater nuclear explosions
,”
Technical Report No. NOLTR 65-52
(
US Naval Ordnance Laboratory
,
White Oak, MD
,
1966
).
71.
K. A.
Naugol'nykh
and
N. A.
Roy
, “
Electrical discharges in water: A hydrodynamic description
,” Technical Report (
Academy of Sciences USSR, Acoustic Institute
,
Moscow
,
1971
).
72.
Second Symposium on Naval Hydrodynamics: Hydrodynamic Noise, Cavity Flow
, edited by
R.
Cooper
(
National Academy of Sciences–National Research Council
,
1958
).
73.
High-Intensity Ultrasonic Fields
, edited by
L. D.
Rozenberg
(
Springer US
,
Boston, MA
,
1971
).
74.
Cavitation and Inhomogeneities in Underwater Acoustics
,
W.
Lauterborn
(
Springer Berlin Heidelberg
,
Berlin, Heidelberg
,
1980
).
75.
A.
Schneider
, “
Some compressibility effects in cavitation bubble dynamics
,” Ph.D. thesis (
California Institute of Technology
,
Pasadena, CA
,
1949
).
76.
R.
Hickling
and
M. S.
Plesset
, “
Collapse and rebound of a spherical bubble in water
,”
Phys. Fluids
7
,
7
14
(
1964
).
77.
R. D.
Ivany
and
F. G.
Hammitt
, “
Cavitation bubble collapse in viscous, compressible liquids—Numerical analysis
,”
J. Basic Eng.
87
,
977
985
(
1965
).
78.
R. H.
Mellen
, “
An experimental study of the collapse of a spherical cavity in water
,”
J. Acoust. Soc. Am.
28
,
447
454
(
1956
).
79.
V. A.
Akulichev
,
Y. Y.
Boguslavskii
,
A. I.
Ioffe
, and
K. A.
Naugol'nykh
, “
Radiation of finite-amplitude spherical waves
,”
Sov. Phys. - Acoust.
13
,
281
285
(
1968
).
80.
V. K.
Kedrinskii
, “
Kirkwood-Bethe approximation for an underwater explosion with cylindrical symmetry
,”
Combust. Explos. Shock Waves
8
,
94
100
(
1972
).
81.
K. J.
Ebeling
, “
Zum Verhalten kugelförmiger, lasererzeugter Kavitationsblasen in Wasser
,”
Acustica
40
,
229
239
(
1978
).
82.
K.
Vokurka
, “
Comparison of Rayleigh's, Herring's, and Gilmore's models of gas bubbles
,”
Acta Acust. United Ac
59
,
214
219
(
1986
).
83.
C.
Herring
, “
Theory of the pulsations of the gas bubble produced by an underwater explosion
,”
Technical Report No. 236
(
Office of Scientific Research and Development
,
1941
).
84.
L.
Trilling
, “
The collapse and rebound of a gas bubble
,”
J. Appl. Phys.
23
,
14
17
(
1952
).
85.
V. K.
Kedrinskii
and
V. T.
Kuzavov
, “
Dynamics of a cylindrical cavity in a boundless compressible liquid
,” in
Cavitation and Inhomogeneities in Underwater Acoustics
, edited by
W.
Lauterborn
(
Springer
Berlin Heidelberg, Berlin, Heidelberg
,
1980
), pp.
119
124
.
86.
P. G.
Tait
, “
Report on some of the physical properties of fresh water and sea water
,” Technical Report (
1888
).
87.
L. D.
Landau
and
E. M.
Lifshitz
,
Fluid Mechanics
(
Pergamon Press Ltd
.,
1959
).
88.
O. L.
Métayer
and
R.
Saurel
, “
The Noble-Abel Stiffened-Gas equation of state
,”
Phys. Fluids
28
,
046102
(
2016
).
89.
M. I.
Radulescu
, “
Compressible flow in a Noble–Abel stiffened gas fluid
,”
Phys. Fluids
32
,
056101
(
2020
).
90.
F.
Denner
, “
The Gilmore-NASG model to predict single-bubble cavitation in compressible liquids
,”
Ultrason. Sonochem.
70
,
105307
(
2021
).
91.
M. H.
Rice
and
J. M.
Walsh
, “
Equation of state of water to 250 kilobars
,”
J. Chem. Phys.
26
,
824
830
(
1957
).
92.
A. B.
Arons
, “
Underwater explosion shock wave parameters at large distances from the charge
,”
J. Acoust. Soc. Am.
26
,
343
346
(
1954
).
93.
J. R.
McGrath
, “
Scaling underwater exploding wires
,”
J. Appl. Phys.
37
,
4439
4443
(
1966
).
94.
L. B.
Poché
, “
Underwater shock-wave pressures from small detonators
,”
J. Acoust. Soc. Am.
51
,
1733
1737
(
1972
).
95.
P. H.
Rogers
, “
Weak-shock solution for underwater explosive shock waves
,”
J. Acoust. Soc. Am.
62
,
1412
1419
(
1977
).
96.
J.
Best
, “
The dynamics of underwater explosions
,” Ph.D. thesis (
University of Wollongong
,
1991
).
97.
F.
Shan
,
Y.
He
,
J.-J.
Jiao
, and
H.-C.
Wang
, “
Experimental and theoretical analysis of detonation products state on bubble dynamics and energy distribution in underwater explosion
,”
J. Appl. Phys.
130
,
174701
(
2021
).
98.
J.
Zhang
,
S.
Wang
,
X.
Jia
,
Y.
Gao
, and
F.
Ma
, “
An improved Kirkwood–Bethe model for calculating near-field shockwave propagation of underwater explosions
,”
AIP Adv.
11
,
035123
(
2021
).
99.
L.
Likhterov
, “
High-frequency acoustic emission generated by underwater explosion with cylindrical symmetry
,”
J. Vib. Acoust.
122
,
140
142
(
2000
).
100.
H.-Y.
Kwak
,
K.-M.
Kang
,
I.
Ko
, and
J.-H.
Kang
, “
Fire-ball expansion and subsequent shock wave propagation from explosives detonation
,”
Int. J. Therm. Sci.
59
,
9
16
(
2012
).
101.
S.
Wang
,
Q.
Gui
,
J.
Zhang
,
Y.
Gao
,
J.
Xu
, and
X.
Jia
, “
Theoretical and experimental study of bubble dynamics in underwater explosions
,”
Phys. Fluids
33
,
126113
(
2021
).
102.
J.
Zhang
,
S.
Wang
,
X.
Jia
,
Y.
Gao
, and
F.
Ma
, “
An engineering application of Prosperetti and Lezzi equation to solve underwater explosion bubbles
,”
Phys. Fluids
33
,
017118
(
2021
).
103.
M.-K.
Li
,
S.-P.
Wang
,
S.
Zhang
, and
H.
Sagar
, “
Experimental study of underwater explosions below a free surface: Bubble dynamics and pressure wave emission
,”
Phys. Fluids
35
,
083313
(
2023
).
104.
Z.
Sheng
,
Y.
Hao
,
J.
Liu
,
H.
Wang
,
Y.
Gao
, and
F.
Ma
, “
A shockwave calculation method for aluminized explosive of deep water explosion based on the Kirkwood-Bethe model
,”
Propellants. Explo. Pyrotec.
48
,
e202200247
(
2023
).
105.
D.
Mavaleix-Marchessoux
, “
Modelling the fluid-structure coupling caused by a far-field underwater explosion
,” Ph.D. thesis (
Institut Polytechnique de Paris
,
2020
).
106.
A.
Ziolkowski
, “
A method for calculating the output pressure waveform from an air gun
,”
Geophys. J. Int.
21
,
137
161
(
1970
).
107.
A.
Ziolkowski
, “
Measurement of air-gun bubble oscillations
,”
Geophysics
63
,
2009
2024
(
1998
).
108.
H.
Bing-Shou
,
G.
Hao
, and
H.
Nan
, “
Simplified traditional bubble-motion equation and air-gun wavelet simulation based on a Van der Waals gas model
,”
Appl. Geophys.
18
,
537
544
(
2021
).
109.
M.
Landrø
and
R.
Sollie
, “
Source signature determination by inversion
,”
Geophysics
57
,
1633
1640
(
1992
).
110.
R.
Laws
,
M.
Landrø
, and
L.
Amundsen
, “
An experimental comparison of three direct methods of marine source signature estimation
,”
Geophys. Prospect.
46
,
353
389
(
1998
).
111.
H. O.
Sertlek
and
G.
Blacquiere
, “
Effects of the rough sea surface on the signature of a single air gun
,”
IEEE J. Oceanic Eng.
44
,
575
581
(
2019
).
112.
D.
Wehner
,
U. P.
Svensson
, and
M.
Landrø
, “
Acoustic signals in air and water generated by very shallow marine seismic sources: An experimental study
,”
J. Acoust. Soc. Am.
147
,
1092
1103
(
2020
).
113.
I.
Akhatov
,
O.
Lindau
,
A.
Topolnikov
,
R.
Mettin
,
N.
Vakhitova
, and
W.
Lauterborn
, “
Collapse and rebound of a laser-induced cavitation bubble
,”
Phys. Fluids
13
,
2805
2819
(
2001
).
114.
A.
Vogel
,
N.
Linz
,
S.
Freidank
, and
G.
Paltauf
, “
Femtosecond-laser-induced nanocavitation in water: Implications for optical breakdown threshold and cell surgery
,”
Phys. Rev. Lett.
100
,
038102
(
2008
).
115.
O.
Supponen
,
D.
Obreschkow
,
M.
Tinguely
,
P.
Kobel
,
N.
Dorsaz
, and
M.
Farhat
, “
Scaling laws for jets of single cavitation bubbles
,”
J. Fluid Mech.
802
,
263
293
(
2016
).
116.
G. T.
Bokman
,
L.
Biasiori-Poulanges
,
B.
Lukić
,
C.
Bourquard
,
D. W.
Meyer
,
A.
Rack
, and
O.
Supponen
, “
High-speed x-ray phase-contrast imaging of single cavitation bubbles near a solid boundary
,”
Phys. Fluids
35
,
013322
(
2023
).
117.
F.
Reuter
,
T.
Sato
,
V.
Bellucci
,
S.
Birnsteinova
,
C.
Deiter
,
J. C. P.
Koliyadu
,
R.
Letrun
,
P.
Villanueva-Perez
,
R.
Bean
,
A. P.
Mancuso
,
A.
Meents
,
P.
Vagovic
, and
C.-D.
Ohl
, “
Laser-induced, single droplet fragmentation dynamics revealed through megahertz x-ray microscopy
,”
Phys. Fluids
35
,
113323
(
2023
).
118.
B.
Zhao
and
O.
Coutier-Delgosha
, “
The impacts of material acoustic impedance and thickness on single laser-induced bubble dynamics and determining factors in resulting pressure
,”
Phys. Fluids
35
,
103303
(
2023
).
119.
J.
Mur
,
V.
Agrež
,
J.
Zevnik
,
R.
Petkovšek
, and
M.
Dular
, “
Microbubble collapse near a fiber: Broken symmetry conditions and a planar jet formation
,”
Phys. Fluids
35
,
023305
(
2023
).
120.
X.
Wang
,
G.
Wu
,
J.
Shen
,
Z.
Sun
,
Y.
Zhang
,
L.
Zhang
, and
Y.
Zhang
, “
Research on the collapse dynamics of a restricted cavitation bubble near a right-angle wall based on Kelvin impulse theory
,”
Phys. Fluids
35
,
073335
(
2023
).
121.
D.
Mnich
,
F.
Reuter
,
F.
Denner
, and
C.-D.
Ohl
, “
Single cavitation bubble dynamics in a stagnation flow
,”
J. Fluid Mech.
979
,
A18
(
2024
).
122.
L.
Fu
,
J.
Wang
,
S.
Wang
,
Z.
Zhang
,
A.
Vogel
,
X-x
Liang
, and
C.
Yao
, “
Secondary cavitation bubble dynamics during laser-induced bubble formation in a small container
,”
Opt. Express
32
,
9747
(
2024
).
123.
A.
Vogel
,
S.
Busch
, and
U.
Parlitz
, “
Shock wave emission and cavitation bubble generation by picosecond and nanosecond optical breakdown in water
,”
J. Acoust. Soc. Am.
100
,
148
165
(
1996
).
124.
K.-T.
Byun
and
H.-Y.
Kwak
, “
A model of laser-induced cavitation
,”
Jpn. J. Appl. Phys.
43
,
621
630
(
2004
).
125.
J.
Oh
,
Y.
Yoo
,
S.
Seung
, and
H.-Y.
Kwak
, “
Laser-induced bubble formation on a micro gold particle levitated in water under ultrasonic field
,”
Exp. Therm. Fluid Sci.
93
,
285
291
(
2018
).
126.
S.
Geng
,
Z.
Yao
,
Q.
Zhong
,
Y.
Du
,
R.
Xiao
, and
F.
Wang
, “
Propagation of shock wave at the cavitation bubble expansion stage induced by a nanosecond laser pulse
,”
J. Fluids Eng.
143
,
051209
(
2021
).
127.
V.
Agrež
,
J.
Mur
,
J.
Petelin
, and
R.
Petkovšek
, “
Near threshold nucleation and growth of cavitation bubbles generated with a picosecond laser
,”
Ultrason. Sonochem.
92
,
106243
(
2023
).
128.
Z.
Yang
,
H.
Bao
,
L.
Dai
,
H.
Zhang
, and
J.
Lu
, “
Experimental investigation of nanosecond laser-induced shock waves in water using multiple excitation beams
,”
Opt. Express
31
,
21845
(
2023
).
129.
M.
Vassholz
,
H. P.
Hoeppe
,
J.
Hagemann
,
J. M.
Rosselló
,
M.
Osterhoff
,
R.
Mettin
,
T.
Kurz
,
A.
Schropp
,
F.
Seiboth
,
C. G.
Schroer
,
M.
Scholz
,
J.
Möller
,
J.
Hallmann
,
U.
Boesenberg
,
C.
Kim
,
A.
Zozulya
,
W.
Lu
,
R.
Shayduk
,
R.
Schaffer
,
A.
Madsen
, and
T.
Salditt
, “
Pump-probe X-ray holographic imaging of laser-induced cavitation bubbles with femtosecond FEL pulses
,”
Nat. Commun.
12
,
3468
(
2021
).
130.
M.
Vacher
,
G.
Gimenez
, and
R.
Goutte
, “
Nonlinear behaviour microbubbles: Application to their ultrasonic detection
,”
Acta Acust. United Ac
54
,
274
283
(
1984
).
131.
M.
Versluis
,
E.
Stride
,
G.
Lajoinie
,
B.
Dollet
, and
T.
Segers
, “
Ultrasound contrast agent modeling: A review
,”
Ultrasound Med. Biol.
46
,
2117
2144
(
2020
).
132.
F.
Chavrier
,
J. Y.
Chapelon
,
A.
Gelet
, and
D.
Cathignol
, “
Modeling of high-intensity focused ultrasound-induced lesions in the presence of cavitation bubbles
,”
J. Acoust. Soc. Am.
108
,
432
440
(
2000
).
133.
S. K.
Berlinda Law
and
Y.
Zhou
, “
High-intensity focused ultrasound ablation by the dual-frequency excitation
,”
IEEE Trans. Ultrason, Ferroelect, Freq. Control
66
,
18
25
(
2019
).
134.
M.
Wang
,
Y.
Lei
, and
Y.
Zhou
, “
High-intensity focused ultrasound (HIFU) ablation by the frequency chirps: Enhanced thermal field and cavitation at the focus
,”
Ultrasonics
91
,
134
149
(
2019
).
135.
K. J.
Pahk
,
D. K.
Dhar
,
M.
Malago
, and
N.
Saffari
, “
Ultrasonic histotripsy for tissue therapy
,”
J. Phys.: Conf. Ser.
581
,
012001
(
2015
).
136.
K. J.
Pahk
,
P.
Gélat
,
H.
Kim
, and
N.
Saffari
, “
Bubble dynamics in boiling histotripsy
,”
Ultrasound Med. Biol.
44
,
2673
2696
(
2018
).
137.
K. J.
Pahk
,
M. O.
De Andrade
,
P.
Gélat
,
H.
Kim
, and
N.
Saffari
, “
Mechanical damage induced by the appearance of rectified bubble growth in a viscoelastic medium during boiling histotripsy exposure
,”
Ultrason. Sonochem.
53
,
164
177
(
2019
).
138.
D. L.
Sokolov
, “
Dual pulses for cavitation control in lithotripsy: Shock wave-bubble interactions and bioeffects
,” Ph.D. thesis (
University of Washington
,
2002
).
139.
E.
Ayme
and
E.
Carstensen
, “
Cavitation induced by asymmetric distorted pulses of ultrasound: Theoretical predictions
,”
IEEE Trans. Ultrason, Ferroelect, Freq. Control
36
,
32
40
(
1989
).
140.
E. J.
Aymé-Bellegarda
, “
Collapse and rebound of a gas-filled spherical bubble immersed in a diagnostic ultrasonic field
,”
J. Acoust. Soc. Am.
88
,
1054
1060
(
1990
).
141.
W.
Kreider
,
L. A.
Crum
,
M. R.
Bailey
, and
O. A.
Sapozhnikov
, “
A reduced-order, single-bubble cavitation model with applications to therapeutic ultrasound
,”
J. Acoust. Soc. Am.
130
,
3511
3530
(
2011
).
142.
J.
Gümmer
,
S.
Schenke
, and
F.
Denner
, “
Modelling lipid-coated microbubbles in focused ultrasound applications at subresonance frequencies
,”
Ultrasound Med. Biol.
47
,
2958
2979
(
2021
).
143.
Z.
Li
,
Q.
Zou
, and
D.
Qin
, “
Enhancing cavitation dynamics and its mechanical effects with dual-frequency ultrasound
,”
Phys. Med. Biol.
67
,
085017
(
2022
).
144.
D.
Qin
,
S.
Lei
,
X.
Wang
,
X.
Zhong
,
X.
Ji
, and
Z.
Li
, “
Resonance behaviors of encapsulated microbubbles oscillating nonlinearly with ultrasonic excitation
,”
Ultrason. Sonochem.
94
,
106334
(
2023
).
145.
J. H.
Song
,
A.
Moldovan
, and
P.
Prentice
, “
Non-linear acoustic emissions from therapeutically driven contrast agent microbubbles
,”
Ultrasound Med. Biol.
45
,
2188
2204
(
2019
).
146.
E.
Zilonova
,
M.
Solovchuk
, and
T.
Sheu
, “
Bubble dynamics in viscoelastic soft tissue in high-intensity focal ultrasound thermal therapy
,”
Ultrason. Sonochem.
40
,
900
911
(
2018
).
147.
E.
Zilonova
,
M.
Solovchuk
, and
T.
Sheu
, “
Simulation of cavitation enhanced temperature elevation in a soft tissue during high-intensity focused ultrasound thermal therapy
,”
Ultrason. Sonochem.
53
,
11
24
(
2019
).
148.
S.
Bredihin
,
V.
Andreev
,
A.
Martekha
,
M.
Schenzle
, and
I.
Korotkiy
, “
Erosion potential of ultrasonic food processing
,”
Foods Raw Mater.
9
,
335
344
(
2021
).
149.
B.
Glam
,
M.
Strauss
,
S.
Eliezer
, and
D.
Moreno
, “
Shock compression and spall formation in aluminum containing helium bubbles at room temperature and near the melting temperature: Experiments and simulations
,”
Int. J. Impact Eng.
65
,
1
12
(
2014
).
150.
E.
Sonde
,
T.
Chaise
,
N.
Boisson
, and
D.
Nelias
, “
Modeling of cavitation peening: Jet, bubble growth and collapse, micro-jet and residual stresses
,”
J. Mater. Process. Technol.
262
,
479
491
(
2018
).
151.
Z.
Zhang
,
S.
Wei
,
P.
Wang
,
W.
Qiu
, and
G.
Zhang
, “
Progress in applications of laser induced cavitation on surface processing
,”
Opt. Laser Technol.
170
,
110212
(
2024
).
152.
H.
Huang
,
L.
Qin
,
H.
Tang
,
D.
Shu
,
W.
Yan
,
B.
Sun
, and
J.
Mi
, “
Ultrasound cavitation induced nucleation in metal solidification: An analytical model and validation by real-time experiments
,”
Ultrason. Sonochem.
80
,
105832
(
2021
).
153.
H.
Huang
,
H.
Tu
,
H.
Xu
,
P.
Shi
, and
D.
Wang
, “
Insight of external ultrasound on energy-production acceleration from renewable Al-water reaction in Al-based metallic materials
,”
Int. J. Hydrogen Energy
48
,
20253
20263
(
2023
).
154.
M.
Rakita
and
Q.
Han
, “
Influence of pressure field in melts on the primary nucleation in solidification processing
,”
Metall. Mater. Trans. B
48
,
2232
2244
(
2017
).
155.
V.
Minsier
and
J.
Proost
, “
Shock wave emission upon spherical bubble collapse during cavitation-induced megasonic surface cleaning
,”
Ultrason. Sonochem.
15
,
598
604
(
2008
).
156.
V. K.
Kedrinskii
, “
Creation of special shock tubes and investigation of cumulation of liquid cylindrical shells in a rotating system
,”
J. Appl. Mech. Technol. Phys.
63
,
1
6
(
2022
).
157.
M. P.
Brenner
,
S.
Hilgenfeldt
, and
D.
Lohse
, “
Single-bubble sonoluminescence
,”
Rev. Mod. Phys.
74
,
425
484
(
2002
).
158.
G.
Gimenez
, “
The simultaneous study of light emissions and shock waves produced by cavitation bubbles
,”
J. Acoust. Soc. Am.
71
,
839
846
(
1982
).
159.
H.
Nazari-Mahroo
,
K.
Pasandideh
,
H. A.
Navid
, and
R.
Sadighi-Bonabi
, “
Influence of liquid compressibility on the dynamics of single bubble sonoluminescence
,”
Phys. Lett. A
382
,
1962
1967
(
2018
).
160.
. P.
Hoeppe
,
M.
Osterhoff
,
A.
Aghel Maleki
,
J. M.
Rosselló
,
M.
Vassholz
,
J.
Hagemann
,
T.
Engler
,
D.
Schwarz
,
A.
Rodriguez-Fernandez
,
U.
Boesenberg
,
J.
Möller
,
R.
Shayduk
,
J.
Hallmann
,
A.
Madsen
,
R.
Mettin
, and
T.
Salditt
, “
The collapse of a sonoluminescent cavitation bubble imaged with X-ray free-electron laser pulses
,”
New J. Phys.
26
,
033002
(
2024
).
161.
Y.-P.
Lee
,
S. W.
Karng
,
J.-S.
Jeon
, and
H.-Y.
Kwak
, “
Shock pulse from a sonoluminescing gas bubble
,”
J. Phys. Soc. Jpn.
66
,
2537
2540
(
1997
).
162.
J.
Holzfuss
,
M.
Rüggeberg
, and
A.
Billo
, “
Shock wave emissions of a sonoluminescing bubble
,”
Phys. Rev. Lett.
81
,
5434
5437
(
1998
).
163.
J.
Holzfuss
, “
Acoustic energy radiated by nonlinear spherical oscillations of strongly driven bubbles
,”
Proc. R Soc. A
466
,
1829
1847
(
2010
).
164.
A.
Shima
, “
The natural frequency of a bubble oscillating in a viscous compressible liquid
,”
J. Basic Eng.
92
,
555
561
(
1970
).
165.
C.
Hunter
, “
On the collapse of an empty cavity in water
,”
J. Fluid Mech.
8
,
241
263
(
1960
).
166.
V. A.
Akulichev
, “
Pulsation of cavitation voids
,” in
High-Intensity Ultrasonic Fields
, edited by
L. D.
Rozenberg
(
Springer US
,
Boston, MA
,
1971
).
167.
V. S.
Moholkar
,
S.
Rekveld
, and
M. M.
Warmoeskerken
, “
Modeling of the acoustic pressure fields and the distribution of the cavitation phenomena in a dual frequency sonic processor
,”
Ultrasonics
38
,
666
670
(
2000
).
168.
D.
Fuster
,
C.
Dopazo
, and
G.
Hauke
, “
Liquid compressibility effects during the collapse of a single cavitating bubble
,”
J. Acoust. Soc. Am.
129
,
122
131
(
2011
).
169.
M.
Mahdi
,
M.
Shams
, and
R.
Ebrahimi
, “
Effects of heat transfer on the strength of shock waves emitted upon spherical bubble collapse
,”
Int. J. Numer. Methods Heat Fluid Flow
20
,
372
391
(
2010
).
170.
D. B.
Preso
,
D.
Fuster
,
A. B.
Sieber
,
D.
Obreschkow
, and
M.
Farhat
, “
Vapor compression and energy dissipation in a collapsing laser-induced bubble
,”
Phys. Fluids
36
,
033342
(
2024
).
171.
X.
Zhang
,
C.
Yang
,
C.
Wang
,
Y.
Zhang
, and
Y.
Zhang
, “
Dynamics of an oscillating cavitation bubble within a narrow gap
,”
Phys. Fluids
35
,
103302
(
2023
).
172.
L.
Likhterov
, “
High-frequency acoustic noise emitted by initial impact of solid sphere falling onto liquid surface
,”
Phys. Fluids
10
,
321
323
(
1998
).
173.
A.
Berman
and
L.
Likhterov
, “
Spectrum asymptotics of high-frequency acoustic emission generated by surface explosion
,”
Phys. Fluids
13
,
1508
1512
(
2001
).
174.
Y. C.
Kim
,
P.
Blanloeuil
,
D. D.
Li
,
R. A.
Taylor
, and
T. J.
Barber
, “
Acoustically driven translation of a single bubble in pulsed traveling ultrasonic waves
,”
Phys. Fluids
35
,
033315
(
2023
).
175.
J. B.
Keller
and
I. I.
Kolodner
, “
Damping of underwater explosion bubble oscillations
,”
J. Appl. Phys.
27
,
1152
1161
(
1956
).
176.
A.
Prosperetti
, “
Bubble phenomena in sound fields: Part one
,”
Ultrasonics
22
,
69
77
(
1984
).
177.
L.
Rayleigh
, “
Aerial plane waves of finite amplitude
,”
Proc. R. Soc. London. Ser. A
84
,
247
284
(
1910
).
178.
R. J.
LeVeque
,
Numerical Methods for Conservation Laws
, 2nd ed.,
Lectures in mathematics
(
Birkhäuser
,
Basel Berlin
,
2008
).
179.
D. L.
Chapman
, “
VI. On the rate of explosion in gases
,”
London, Edinburgh, Dublin Philos. Mag. J. Sci.
47
,
90
104
(
1899
).
180.
E.
Jouguet
, “
Sur la propagation des réactions chimiques dans les gaz
,”
J. de Mathématiques Pures et Appliquées
1
,
347
425
(
1905
).
181.
B.
Riemann
, “
Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite
,”
Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen
8
,
43
66
(
1860
).
182.
L. E.
Kinsler
,
Fundamentals of Acoustics
, 4th ed. (
Wiley
,
New York, NY
,
2000
).
183.
R. H.
Randall
,
An Introduction to Acoustics
, Dover ed. (
Dover Publications
,
Mineola, NY
,
2005
).
184.
V. K.
Kedrinskii
,
Hydrodynamics of Explosions: Experiment and Models
(
Springer
,
Berlin, Heidelberg, New York
,
2005
).
185.
D. T.
Blackstock
, “
On plane, spherical, and cylindrical sound waves of finite amplitude in lossless fluids
,”
J. Acoust. Soc. Am.
36
,
217
219
(
1964
).
186.
A.-M.
Zhang
,
S.-M.
Li
,
P.
Cui
,
S.
Li
, and
Y.-L.
Liu
, “
A unified theory for bubble dynamics
,”
Phys. Fluids
35
,
033323
(
2023
).
187.
W.
Wagner
and
A.
Pruß
, “
The IAPWS Formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use
,”
J. Phys. Chem. Ref. Data
31
,
387
535
(
2002
).
188.
F.
Harlow
and
A.
Amsden
, “
Fluid dynamics
,”
Monograph LA-4700
(
Los Alamos National Laboratory
,
1971
).
189.
O. L.
Métayer
,
J.
Massoni
, and
R.
Saurel
, “
Élaboration des lois d'état d'un liquide et de sa vapeur pour les modèles d'écoulements diphasiques
,”
Int. J. Therm. Sci.
43
,
265
276
(
2004
).
190.
J.
Chandran
and
A.
Salih
, “
A modified equation of state for water for a wide range of pressure and the concept of water shock tube
,”
Fluid Phase Equilibria
483
,
182
188
(
2019
).
191.
G.
Tammann
, “
Über Zustandsgleichungen im Gebiete kleiner Volumen
,”
Annalen der Phys.
342
,
975
1013
(
1912
).
192.
G. M.
Kontogeorgis
,
R.
Privat
, and
J.-N.
Jaubert
, “
Taking another look at the van der Waals equation of state–Almost 150 years later
,”
J. Chem. Eng. Data
64
,
4619
4637
(
2019
).
193.
E. A.
Neppiras
, “
Acoustic cavitation
,”
Phys. Rep.
61
,
159
251
(
1980
).
194.
P. M.
Tilmann
, “
Nonlinear sound-scattering by small bubbles
,” in
Cavitation and Inhomogeneities in Underwater Acoustics
, edited by
W.
Lauterborn
(
Springer
Berlin Heidelberg, Berlin, Heidelberg
,
1980
), pp.
113
118
.
195.
Y. A.
Ilinskii
,
E. A.
Zabolotskaya
,
T. A.
Hay
, and
M. F.
Hamilton
, “
Models of cylindrical bubble pulsation
,”
J. Acoust. Soc. Am.
132
,
1346
1357
(
2012
).
196.
F.
Denner
and
S.
Schenke
, “
APECSS: A software library for cavitation bubble dynamics and acoustic emissions
,”
J. Open Source Softw.
8
,
5435
(
2023
).
197.
I.
Johnston
, “
The noble-abel equation of state: thermodynamic derivations for ballistics modelling
,”
Technical Report No. DSTO-TN-0670
(
Defence Science and Technology Organisation
,
2005
).
198.
E. F.
Toro
,
Riemann Solvers and Numerical Fluid Dynamics: A Practical Introduction
, 3rd ed. (
Springer
,
2009
).
199.
A.
Prosperetti
,
L. A.
Crum
, and
K. W.
Commander
, “
Nonlinear bubble dynamics
,”
J. Acoust. Soc. Am.
83
,
502
514
(
1988
).
200.
D.
Qin
,
S.
Lei
,
B.
Chen
,
Z.
Li
,
W.
Wang
, and
X.
Ji
, “
Numerical investigation on acoustic cavitation characteristics of an air-vapor bubble: Effect of equation of state for interior gases
,”
Ultrason. Sonochem.
97
,
106456
(
2023
).
201.
H.
Nazari-Mahroo
,
K.
Pasandideh
,
H.
Navid
, and
R.
Sadighi-Bonabi
, “
Influence of liquid density variation on the bubble and gas dynamics of a single acoustic cavitation bubble
,”
Ultrasonics
102
,
106034
(
2020
).
202.
A.
Prosperetti
, “
The thermal behaviour of oscillating gas bubbles
,”
J. Fluid Mech.
222
,
587
(
1991
).
203.
L.
Stricker
,
A.
Prosperetti
, and
D.
Lohse
, “
Validation of an approximate model for the thermal behavior in acoustically driven bubbles
,”
J. Acoust. Soc. Am.
130
,
3243
3251
(
2011
).
204.
G.
Zhou
and
A.
Prosperetti
, “
Modelling the thermal behaviour of gas bubbles
,”
J. Fluid Mech.
901
,
R3
(
2020
).
205.
G.
Zhou
, “
Modeling the thermal behavior of an acoustically driven gas bubble
,”
J. Acoust. Soc. Am.
149
,
923
933
(
2021
).
206.
E.
Samiei
,
M.
Shams
, and
R.
Ebrahimi
, “
Numerical study on mass transfer effects on spherical cavitation bubble collapse in an acoustic field
,” in
ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Volume
3
(
ASMEDC
,
Istanbul, Turkey
,
2010
), pp.
425
433
.
207.
E. L.
Lee
,
H. C.
Hornig
, and
J. W.
Kury
, “
Adiabatic Expansion of High Explosive Detonation Products
,”
Technical Report No. UCRL-50422
(
University of California Radiation Lab. at Livermore
,
Livermore, CA
,
1968
).
208.
G.
Baudin
and
R.
Serradeill
, “
Review of Jones-Wilkins-Lee equation of state
,”
EPJ Web Conf.
10
,
00021
(
2010
).
209.
M.
Riley
, “
Analytical solutions for predicting underwater explosion gas bubble behaviour
,”
Technical Report DRDC Atlantic TM 2010–237
(
Defence R&D Canada – Atlantic, Dartmouth, NS, Canada
,
2010
).
210.
Y.
Gao
,
S.
Wang
,
J.
Zhang
,
X.
Jia
,
C.
Liang
, and
F.
Ma
, “
Effects of underwater explosion depth on shock wave overpressure and energy
,”
Phys. Fluids
34
,
037108
(
2022
).
211.
X.
Jia
,
S.
Wang
,
J.
Xu
,
J.
Zhang
,
Y.
Gao
, and
F.
Ma
, “
Nonlinear characteristics and corrections of near-field underwater explosion shock waves
,”
Phys. Fluids
34
,
046108
(
2022
).
212.
A.
Prosperetti
and
A.
Lezzi
, “
Bubble dynamics in a compressible liquid. Part 1. First-order theory
,”
J. Fluid Mech.
168
,
457
478
(
1986
).
213.
A.
Lezzi
and
A.
Prosperetti
, “
Bubble dynamics in a compressible liquid. Part 2. Second-order theory
,”
J. Fluid Mech.
185
,
289
321
(
1987
).
214.
T. B.
Benjamin
, “
Pressure waves from collapsing cavities
,” in
Second Symposium on Naval Hydrodynamics: Hydrodynamic Noise, Cavity Flow
, edited by
R.
Cooper
(
National Academy of Sciences–National Research Council
,
1958
).
215.
J. B.
Keller
and
M.
Miksis
, “
Bubble oscillations of large amplitude
,”
J. Acoust. Soc. Am.
68
,
628
633
(
1980
).
216.
X.
Wang
,
X.
Zhang
,
S.
Li
,
C.
Zhang
,
Y.
Zhang
,
Q.
Jiang
,
J.
Li
,
S.
Zheng
, and
Y.
Zhang
, “
Primary resonance characteristics of a cylindrical bubble based on the multi-scale method
,”
Phys. Fluids
36
,
023333
(
2024
).
217.
J.
Dormand
and
P.
Prince
, “
A family of embedded Runge-Kutta formulae
,”
J. Comput. Appl. Math.
6
,
19
26
(
1980
).
218.
R. D.
Fay
, “
Plane sound waves of finite amplitude
,”
J. Acoust. Soc. Am.
3
,
222
241
(
1931
).
219.
M. F.
Hamilton
and
D. T.
Blackstock
, “
On the coefficient of nonlinearity β in nonlinear acoustics
,”
J. Acoust. Soc. Am.
83
,
74
77
(
1988
).
220.
K. A.
Naugol'nykh
, “
Absorption of finite-amplitude waves
,” in
High-Intensity Ultrasonic Fields
, edited by
L. D.
Rozenberg
(
Springer US
,
Boston, MA
,
1971
).
221.
I.
Rudnick
, “
Theory of the attenuation of very high amplitude sound waves
,” Technical Report (
Soundrive Engine Company
,
Los Angeles, CA
,
1952
).
222.
C. B.
Laney
,
Computational Gasdynamics
(
Cambridge University Press
,
Cambridge; New York, NY
,
1998
).
223.
S.
Schenke
,
F.
Sewerin
,
B.
van Wachem
, and
F.
Denner
, “
Explicit predictor–corrector method for nonlinear acoustic waves excited by a moving wave emitting boundary
,”
J. Sound Vib.
527
,
116814
(
2022
).
224.
G. B.
Whitham
,
Linear and Nonlinear Waves
(
John Wiley & Sons, Inc
.,
Hoboken, NJ
,
1999
).
225.
D. T.
Blackstock
, “
Connection between the Fay and Fubini solutions for plane sound waves of finite amplitude
,”
J. Acoust. Soc. Am.
39
,
1019
1026
(
1966
).
226.
W.
Lauterborn
,
T.
Kurz
, and
I.
Akhatov
, “
Nonlinear acoustics in fluids
,” in
Springer Handbook of Acoustics
, edited by
T. D.
Rossing
(
Springer New York
,
New York, NY
,
2007
), pp.
257
297
.
227.
L.
Rayleigh
, “
On the pressure developed in a liquid during the collapse of a spherical cavity
,”
Philosoph. Mag.
34
,
94
98
(
1917
).
228.
G.
ter Haar
, “
Ultrasonic imaging: Safety considerations
,”
Interface Focus
1
,
686
697
(
2011
).
229.
Y.
Fan
,
H.
Li
, and
D.
Fuster
, “
Time-delayed interactions on acoustically driven bubbly screens
,”
J. Acoust. Soc. Am.
150
,
4219
4231
(
2021
).
230.
L.
Fu
,
X.-X.
Liang
,
S.
Wang
,
S.
Wang
,
P.
Wang
,
Z.
Zhang
,
J.
Wang
,
A.
Vogel
, and
C.
Yao
, “
Laser induced spherical bubble dynamics in partially confined geometry with acoustic feedback from container walls
,”
Ultrason. Sonochem.
101
,
106664
(
2023
).
You do not currently have access to this content.