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Nonlinear acoustics and shock formation in lossless barotropic Green--Naghdi fluids
Oscillating nonlinear acoustic shock waves
1. | Bogolyubov Institute for Theoretical Physics, 03143 Kiev, Ukraine |
2. | GreenHydrogen, DK-6000 Kolding, Denmark |
3. | Department of Physics and Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark |
4. | Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark |
References:
[1] |
B. O. Enflo and C. M. Hedberg, Theory of Nonlinear Acoustics in Fluids, $1^{st}$ edition, Kluwer Academic, Dordrecht, 2002. |
[2] |
W. Chester, Resonant oscillations in closed tubes, J. Fluid Mech., 18 (1964), 44-64.
doi: 10.1017/S0022112064000040. |
[3] |
I. Christov, C. I. Christov and P. M. Jordan, Modeling weakly nonlinear acoustic wave propagation, Q. Jl Mech. Appl. Math., 60 (2007), 473-495.
doi: 10.1093/qjmam/hbm017. |
[4] |
I. Christov, C. I. Christov and P. M. Jordan, Corrigendum and addendum: Modeling weakly nonlinear acoustic wave propagation, Q. Jl Mech. Appl. Math., 68 (2015), 231-233.
doi: 10.1093/qjmam/hbu023. |
[5] |
S. M. Hagsäter, T. G. Jensen, H. Bruus and J. P. Kutter, Acoustic resonances in piezo-actuated microfluidic chips: Full-image micro-piv experiments and numerical simulations, Lab Chip, 7 (2007), 1336-1344. |
[6] |
S. M. Hagsäter, A. Lenshof, P. Skafte-Pedersen, J. P. Kutter, T. Laurell and H. Bruus, Acoustic resonances in straight micro channels: Beyond the 1d-approximation, Lab Chip, 8 (2008), 1178-1184. |
[7] |
M. F. Hamilton and C. L. Morfey, In: M.F. Hamilton and D.T. Blackstock, (eds.), Nonlinear Acoustics, Chap. 3, Academic Press, San Diego, (1998), 41-64. |
[8] |
P. M. Jordan, An analytical study of Kuznetsov's equation: Diffusive solitons, shock formation, and solution bifurcation, Physics Letters A, 326 (2004), 77-84.
doi: 10.1016/j.physleta.2004.03.067. |
[9] |
P. M. Jordan, G. V. Norton, S. A. Chin-Bing and A. Warn-Varnas, On the propagation of nonlinear acoustic waves in viscous and thermoviscous fluids, European Journal of Mechanics B-Fluids, 34 (2012), 56-63.
doi: 10.1016/j.euromechflu.2012.01.016. |
[10] |
B. Kaltenbacher, Mathematics of nonlinear acoustics, Evolutiuon equations and control theory, 4 (2015), 447-491.
doi: 10.3934/eect.2015.4.447. |
[11] |
R. S. Keiffer, R. McNorton, P. M. Jordan and I. C. Christov, Dissipative acoustic solitons under a weakly-nonlinear, Lagrangian-averaged Euler-$\alpha$ model of single-phase lossless fluids, Wave Motion, 48 (2011), 782-790.
doi: 10.1016/j.wavemoti.2011.04.013. |
[12] |
V. P. Kuznetsov, Equations of nonlinear acoustics, Sov. Phys. Acoust., 16 (1971), 467-470. |
[13] |
S. Makarov and M. Ochmann, Nonlinear and thermoviscous phenomena in acoustics, part I, Acustica, 82 (1996), 579-606. |
[14] |
NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/, Release 1.0.10 of 2015-08-07. Online companion to [OLBC10]. |
[15] |
W. L. Nyborg, Acoustic streaming, Physical Acoustics, 2 (1965), 265-331.
doi: 10.1016/B978-0-12-395662-0.50015-1. |
[16] |
A. R. Rasmussen, M. P. Sørensen, Yu. B. Gaididei and P. L. Christiansen, Interacting wave fronts and rarefaction waves in a second order model of nonlinear thermoviscous fluids, Acta Appl. Math., 115 (2011), 43-61.
doi: 10.1007/s10440-010-9581-7. |
[17] |
Anders Rønne Rasmussen, Thermoviscous Model Equations in Nonlinear Acoustics, Ph.D Thesis, Department of Mathematics, Technical University of Denmark in Kongens Lyngby, Denmark, 2009. |
show all references
References:
[1] |
B. O. Enflo and C. M. Hedberg, Theory of Nonlinear Acoustics in Fluids, $1^{st}$ edition, Kluwer Academic, Dordrecht, 2002. |
[2] |
W. Chester, Resonant oscillations in closed tubes, J. Fluid Mech., 18 (1964), 44-64.
doi: 10.1017/S0022112064000040. |
[3] |
I. Christov, C. I. Christov and P. M. Jordan, Modeling weakly nonlinear acoustic wave propagation, Q. Jl Mech. Appl. Math., 60 (2007), 473-495.
doi: 10.1093/qjmam/hbm017. |
[4] |
I. Christov, C. I. Christov and P. M. Jordan, Corrigendum and addendum: Modeling weakly nonlinear acoustic wave propagation, Q. Jl Mech. Appl. Math., 68 (2015), 231-233.
doi: 10.1093/qjmam/hbu023. |
[5] |
S. M. Hagsäter, T. G. Jensen, H. Bruus and J. P. Kutter, Acoustic resonances in piezo-actuated microfluidic chips: Full-image micro-piv experiments and numerical simulations, Lab Chip, 7 (2007), 1336-1344. |
[6] |
S. M. Hagsäter, A. Lenshof, P. Skafte-Pedersen, J. P. Kutter, T. Laurell and H. Bruus, Acoustic resonances in straight micro channels: Beyond the 1d-approximation, Lab Chip, 8 (2008), 1178-1184. |
[7] |
M. F. Hamilton and C. L. Morfey, In: M.F. Hamilton and D.T. Blackstock, (eds.), Nonlinear Acoustics, Chap. 3, Academic Press, San Diego, (1998), 41-64. |
[8] |
P. M. Jordan, An analytical study of Kuznetsov's equation: Diffusive solitons, shock formation, and solution bifurcation, Physics Letters A, 326 (2004), 77-84.
doi: 10.1016/j.physleta.2004.03.067. |
[9] |
P. M. Jordan, G. V. Norton, S. A. Chin-Bing and A. Warn-Varnas, On the propagation of nonlinear acoustic waves in viscous and thermoviscous fluids, European Journal of Mechanics B-Fluids, 34 (2012), 56-63.
doi: 10.1016/j.euromechflu.2012.01.016. |
[10] |
B. Kaltenbacher, Mathematics of nonlinear acoustics, Evolutiuon equations and control theory, 4 (2015), 447-491.
doi: 10.3934/eect.2015.4.447. |
[11] |
R. S. Keiffer, R. McNorton, P. M. Jordan and I. C. Christov, Dissipative acoustic solitons under a weakly-nonlinear, Lagrangian-averaged Euler-$\alpha$ model of single-phase lossless fluids, Wave Motion, 48 (2011), 782-790.
doi: 10.1016/j.wavemoti.2011.04.013. |
[12] |
V. P. Kuznetsov, Equations of nonlinear acoustics, Sov. Phys. Acoust., 16 (1971), 467-470. |
[13] |
S. Makarov and M. Ochmann, Nonlinear and thermoviscous phenomena in acoustics, part I, Acustica, 82 (1996), 579-606. |
[14] |
NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/, Release 1.0.10 of 2015-08-07. Online companion to [OLBC10]. |
[15] |
W. L. Nyborg, Acoustic streaming, Physical Acoustics, 2 (1965), 265-331.
doi: 10.1016/B978-0-12-395662-0.50015-1. |
[16] |
A. R. Rasmussen, M. P. Sørensen, Yu. B. Gaididei and P. L. Christiansen, Interacting wave fronts and rarefaction waves in a second order model of nonlinear thermoviscous fluids, Acta Appl. Math., 115 (2011), 43-61.
doi: 10.1007/s10440-010-9581-7. |
[17] |
Anders Rønne Rasmussen, Thermoviscous Model Equations in Nonlinear Acoustics, Ph.D Thesis, Department of Mathematics, Technical University of Denmark in Kongens Lyngby, Denmark, 2009. |
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