N. Rott, Thermoacoustics, Adv. Appl. Mech, vol.20, pp.135-175, 1980.

G. W. Swift, Thermoacoustic engines, J. Acoust. Soc. Am, vol.84, pp.1145-1178, 1988.

W. C. Ward, G. W. Swift, and J. P. Clark, Interactive analysis, design and teaching for thermoacoustics using DeltaEC (A), J. Acoust. Soc. Am, vol.123, p.3546, 2008.

G. B. Chen and T. Jin, Experimental investigation on the onset and damping behavior of the oscillation in a thermoacoustic prime mover, Cryogenics, vol.39, pp.843-846, 1999.

T. Jin, C. S. Mao, and K. Tang, Characteristics study on the oscillation onset and damping of a traveling-wave thermoacoustic prime mover, Journ. Zhejiang Univ. Science A, vol.9, pp.944-949, 2008.

G. W. Swift, Analysis and performance of a large thermoacoustic engine, J. Acoust. Soc. Am, vol.92, pp.1551-1563, 1992.

S. Zhou and Y. Matsubara, Experimental research of thermoacoustic prime-mover, Cryogenics, vol.387, pp.813-822, 1998.

Z. B. Yu, Q. Li, X. Chen, F. Z. Guo, X. J. Xie et al., Investigation on the oscillation modes in a thermoacoustic Stirling prime mover: mode stability and mode transition, Cryogenics, vol.43, pp.687-691, 2003.

G. Penelet, V. Gusev, P. Lotton, and M. Bruneau, Nontrivial influence of acoustic streaming on the efficiency of annular thermoacoustic prime movers, Phys. Let. A, vol.351, p.268273, 2006.
URL : https://hal.archives-ouvertes.fr/hal-02057446

G. Penelet, E. Gaviot, V. Gusev, P. Lotton, and M. Bruneau, Experimental investigation of transient nonlinear phenomena in an annular thermoacoustic prime-mover: observation of a double-threshold effect, Cryogenics, vol.42, pp.527-532, 2002.
URL : https://hal.archives-ouvertes.fr/hal-02057617

Z. Yu, A. J. Jaworski, and A. S. , Fishbone-like instability in a looped-tube thermoacoustic engine, J. Acoust. Soc. Am, vol.128, pp.188-194, 2010.

M. F. Hamilton, Y. A. Ilinskii, and E. A. Zabolotskaya, Nonlinear two-dimensional model for thermoacoustic engines, J. Acoust. Soc. Am, vol.111, pp.2076-2086, 2002.

S. Karpov and A. Prosperetti, A nonlinear model of thermoacoustic engines, J. Acoust. Soc. Am, vol.112, pp.1431-1444, 2002.

G. Y. Yu, E. C. Luo, W. Dai, and J. Y. Hu, Study of nonlinear processes of a large experimental thermoacoustic-Stirling heat engine by using computational fluid dynamics, J. Appl. Phys, vol.102, p.74901, 2007.

D. Shimizu and N. Sugimoto, Numerical study of thermoacoustic Taconis oscillations, J. Appl. Phys, vol.107, p.34910, 2010.

S. Karpov and A. Prosperetti, Nonlinear saturation of the thermoacoustic instability, J. Acoust. Soc. Am, vol.107, pp.3130-3147, 2000.

A. T. De-waele, Basic treatment of onset conditions and transient effects in thermoacoustic Stirling engines, J. Sound. Vib, vol.325, pp.974-988, 2009.

S. Backhaus and G. W. Swift, A thermoacoustic Stirling heat engine, Nature, vol.399, pp.335-338, 1999.

G. Penelet, V. Gusev, P. Lotton, and M. Bruneau, Experimental and theoretical study of processes leading to steady-state sound in annular thermoacoustic engines, Phys. Rev. E, vol.72, p.16625, 2005.
URL : https://hal.archives-ouvertes.fr/hal-02057449

D. Gedeon, DC gas flows in Stirling and pulse tube cryocoolers, Cryocoolers, vol.9, pp.385-392, 1997.

S. L. Garrett and R. L. Chen, Build an Acoustic Laser, vol.10, issue.3, pp.4-5, 2000.

M. Guedra and G. Penelet, On the use of a complex frequency for the description of thermoacoustic engines, Acta Acust. United Ac, vol.98, pp.232-241, 2012.
URL : https://hal.archives-ouvertes.fr/hal-02057411

V. Gusev, H. Bailliet, P. Lotton, and M. Bruneau, Asymptotic theory of nonlinear acoustic waves in a thermoacoustic prime mover, Acta Acust. United Ac, vol.86, pp.25-38, 2000.

G. Penelet, S. Job, V. Gusev, P. Lotton, and M. Bruneau, Dependence of sound amplification on temperature distribution in annular thermoacoustic engines, Acta Acust. United Ac, vol.91, pp.567-577, 2005.
URL : https://hal.archives-ouvertes.fr/hal-02057456

W. P. Arnott, H. E. Bass, and R. Raspet, General formulation of thermoacoustics for stacks having arbitrarily shaped pore cross sections, J. Acoust. Soc. Am, vol.90, pp.3228-3237, 1991.

F. P. Incropera and D. P. Dewitt, Fundamentals of Heat and Mass Transfer, 1990.

M. C. Peters and A. Hirschberg, Acoustically induced periodic vortex shedding at sharp edged open channel ends: simple vortex models, J. Sound Vib, vol.161, pp.281-299, 1993.

W. Chester, Resonant oscillations of a gas in an open-ended tube, Proc. R. Soc. Lond. A, vol.377, pp.449-467, 1981.

T. Yazaki, A. Tominaga, and Y. Narahara, Large heat transport due to spontaneous gas oscillation induced in a tube with steep temperature gradients, Journ. Heat Transfer, pp.889-894, 1983.

S. Boluriaan and P. J. Morris, Acoustic streaming: from Rayleigh to today, Intern. Journ. of Aeroacoustics, vol.2, pp.255-292, 2003.

M. Mironov, V. Gusev, Y. Auregan, P. Lotton, M. Bruneau et al., Acoustic streaming related to minor loss phenomenon in differentially heated elements of thermoacoustic devices, J. Acoust. Soc. Am, vol.112, pp.441-445, 2002.

H. Bailliet, V. Gusev, R. Raspet, and R. Hiller, Acoustic streaming in closed thermoacoustic devices, J. Acoust. Soc. Am, vol.110, pp.1808-1821, 2001.

J. R. Olson and G. W. Swift, Acoustic streaming in pulse tube refrigerators: tapered pulse tubes, Cryogenics, vol.37, pp.769-776, 1997.
DOI : 10.1016/s0011-2275(97)00037-4

S. Moreau, H. Bailliet, and J. C. Valì-ere, Effect of a stack on Rayleigh streaming cells investigated by laser Doppler velocimetry for application to thermoacoustic devices, J. Acoust. Soc. Am, vol.125, pp.3514-3517, 2009.

M. Amari, V. Gusev, and N. Joly, Transient unidirectional acoustic streaming in annular resonators, Ultrasonics, vol.42, pp.573-578, 2004.
DOI : 10.1016/j.ultras.2003.12.003

, ? d s ? x ? x s ) and in the waveguide (x s ? x ? L), for x s = 26.5 cm. The corresponding heat power supply at threshold (? ampl ? ?3 10 ?3 s ?1 ) is Q onset = 20.17 W , and the acoustic pressure amplitude at position x = L is fixed to 1 Pa. (a): spatial distribution of the second order mass flow ? m in the stack (the transverse coordinate ? s is defined as ? s = r/r s ), Spatial distribution of acoustic streaming at threshold in the stack (x s