The commonly applied self-similar solution of the problem of the converging shock wave (shock) evolution with constant compression of the medium behind the shock front results in an unlimited increase in the medium velocity in the vicinity of the implosion. In this paper, the convergence of cylindrical shocks in water is analyzed using the mass conservation law, when the water compression behind the shock front is a variable. The model predicts a finite range of radii, which depends on the adiabatic index of water and where the increase in pressure exceeds the sum of the change in the kinetic and internal energy densities behind the shock front. In this range of radii, only the finite increase in the shock and water flow velocities is realized.

1.
V. E.
Fortov
and
I. T.
Iakubov
,
The Physics of Non-Ideal Plasma
(
World Scientific Publishing Co. Private Ltd
.,
Singapore
,
2000
).
2.
R. P.
Drake
,
High Energy Physics: Fundamentals, Inertial Fusion and Experimental Astrophysics
(
Springer
,
New York
,
2006
).
3.
Y. B.
Zel'dovich
and
Y. P.
Raizer
,
Physics of Shock Waves and High – Temperature Hydrodynamic Phenomena
, 2nd ed. (
Academic
,
New York
,
1967
).
4.
A.
Grinenko
,
V. T.
Gurovich
, and
Y. E.
Krasik
, “
Implosion in water medium and its possible application for the inertial confinement fusion target ignition
,”
Phys. Plasmas
14
,
012701
(
2007
).
5.
D.
Yanuka
,
A.
Rososhek
,
S. N.
Bland
, and
Y. E.
Krasik
, “
Uniformity of cylindrical imploding underwater shockwaves at very small radii
,”
Appl. Phys. Lett.
111
,
214103
(
2017
).
6.
D.
Yanuka
,
S.
Theocharous
,
S.
Efimov
,
S. N.
Bland
,
A.
Rososhek
,
Y. E.
Krasik
,
M. P.
Olbinado
, and
A.
Rack
, “
Synchrotron based x-ray radiography of convergent shock waves driven by underwater electrical explosion of a cylindrical wire array
,”
J. Appl. Phys.
125
,
093301
(
2019
).
7.
A.
Rososhek
,
D.
Nouzman
, and
Y. E.
Krasik
, “
Addressing the symmetry of a converging cylindrical shock wave in water close to implosion
,”
Appl. Phys. Lett.
118
,
174103
(
2021
).
8.
L.
Rayleigh
, “
On the pressure developed in a liquid during the collapse of a spherical cavity
,”
Philos. Mag.
34
,
94
(
1917
).
9.
E. I.
Zababahin
and
I. E.
Zababahin
,
The Phenomena of Unlimited Cumulation
(
Nauka
,
Moscow
,
1988
) (in Russian).
10.
C.
Hunter
, “
On the collapse of an empty cavity in water
,”
J. Fluid Mech.
8
,
241
(
1960
).
11.
J. F.
Giron
,
S. D.
Ramsey
, and
R. S.
Baty
, “
Scale invariance of the homentropic inviscid Euler equations with application to the Noh problem
,”
Phys. Rev. E
101
,
053101
(
2020
).
12.
G.
Bazalitski
,
V. T.
Gurovich
,
A.
Fedotov-Gefen
,
S.
Efimov
, and
Y. E.
Krasik
, “
Simulation of converging cylindrical GPa-range shock waves generated by wire array underwater electrical explosions
,”
Shock Waves
21
,
321
(
2011
).
13.
S. P.
Lyon
and
J. D.
Johnson
, “
SESAME: The Los Alamos National Laboratory equation-of-state database
,”
Report No. LA-UR-92-3407
(
Los Alamos National Laboratory
,
1992
).
14.
S.
Ridah
, “
Shock waves in water
,”
J. Appl. Phys.
64
,
152
(
1988
).
15.
R. B.
Lazarus
, “
Self-similar solutions for converging shocks and collapsing cavities
,”
SIAM J. Numer. Anal.
18
,
316
(
1981
).
16.
L. D.
Landau
and
E. M.
Lifshitz
,
Theoretical Physics, Mechanics
(
Nauka
,
Moscow
,
2004
).
17.
M. H.
Rice
and
J. M.
Walsh
, “
Equation of state of water to 250 Kilobars
,”
J. Chem. Phys.
26
,
824
(
1957
).
18.
A. S.
Chefranov
and
S. G.
Chefranov
, “
Extrema of the kinetic energy and its dissipation rate in vortex flows
,”
Dokl. Phys.
48
(
12
),
696
(
2003
).
19.
S. G.
Chefranov
, “
Instability of cumulation in convergent cylindrical shock wave
,”
Phys. Fluids
33
,
096111
(
2021
).
20.
D.
Maler
, “
Underwater electrical explosion of wire and wire array: studies of shockwave interaction with targets
,” Ph. D. thesis (
Technion-Israel Institute of Technology
,
Haifa
,
2020
).
21.
N. N.
Kalitkin
,
Numerical Methods
(
Nauka
,
Moscow
,
1980
).
22.
F.
Toro
,
Riemann Solvers and Numerical Methods for Fluid Dynamics, in a Practical Introduction
, 3rd ed. (
Springer-Verlag
,
Berlin-Heidelberg
,
2009
).
23.
S. G.
Chefranov
and
A. S.
Chefranov
, “
Exact solution to the main turbulence problem for a compressible medium and the universal -8/3 law turbulence spectrum of breaking waves
,”
Phys. Fluids
33
,
076108
(
2021
).
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