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Bénard-von Kármán vortex street in dipolar Bose-Einstein Condensate (BEC) trapped by a square-like potential is investigated numerically. In the frame of mean-field theory, the nonlinear dynamic of the dipolar BEC can be described by the so-called two-dimensional Gross-Pitaevskii (GP) equation with long-range interaction. In this paper, we only consider the case that all the dipoles are polarized along the z-axis, which is perpendicular to the plane of disc-shaped BEC. Firstly, the stationary state of the BEC is obtained by the imaginary-time propagation approach. Secondly, the nonlinear dynamic of the BEC, when a moving Gaussian potential exists in such a system, is numerically investigated by the time-splitting Fourier spectral method, in which the stationary state obtained before is set to be the initial state. The results show that when the velocity of the cylindrical obstacle potential reaches a critical value, which depends on interaction strength and the shape of the potential, the vortex-antivortex pairs will be generated alternately in the super-flow behind the obstacle potential. However, in general, such a vortex-antivortex pair structure is dynamically unstable. When the velocity of the obstacle potential increases to a certain value and for a suitable potential width, a stable vortex structure called Bénard-von Kármán vortex street will be formed. While this phenomenon emerges, the vortices in pairs created by the obstacle potential have the same circulation. The pairs with opposite circulations are alternately released from the moving obstacle potential. For larger potential width and velocity, the shedding pattern becomes irregular. We also numerically investigate the effects of the dipole interaction strength, the width and the velocity of the obstacle potential on the vortex structures arising in the wake flow. As a result, the phase graph is presented by lots of numerical calculations for a group of given physical parameters. Thirdly, the drag force on the obstacle potential is also calculated and the mechanical mechanism of vortex pair is analyzed. Finally, we discuss how to find the phenomenon of Bénard-von Kármán vortex street in dipolar BEC experimentally.
[1] Wang D S, Song S W, Xiong B, Liu W M 2011 Phys. Rev. A 84 053607
[2] Ji A C, Liu W M, Song J L, Zhou F 2008 Phys. Rev. Lett. 101 010402
[3] Abrikosov A A, Eksp Z 1957 Phys. JETP 5 1174
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[6] Bénard H, Acad C R 1908 Science 147 839
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[16] Qi R, Yu X L, Li Z B, Liu W M 2009 Phys. Rev. Lett. 102 185301
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[22] Cai Y Y, Matthias R, Lei Z, Bao W Z 2010 Phys. Rev. A 82 043623
[23] Nath R, Pedri P, Santos L 2009 Phys. Rev. Lett. 102 050401
[24] Giovanazzi S, Gorlitz A, Pfau T 2002 Phys. Rev. Lett. 89 130401
[25] Pedri P, Santos L 2005 Phys. Rev. Lett. 95 200404
[26] Bao W, Chem L L, Lim F Y 2006 J. Comput. Phys. 219 836
[27] Bao W, Wang H 2006 J. Comput. Phys. 217 612
[28] Mou S, Guo K X, Xiao B 2014 Superlattices Microstruct. 65 309
[29] Finne A P, Araki T, Blaauwgeers R, Eltsov V B, Kopnin N B, Kruslus M, Skrbek L, Tsubota M, Volovikand G E 2003 Nature 424 1022
[30] Nore C, Huepe C, Brachet M E 2000 Phys. Rev. Lett. 84 2191
[31] Volovik G E 2003 JETP Lett. 78 533
[32] Inouye S, Gupta S, Rosenband T, Chikkatur A P, orlitz A G, Gustavson T L, Leanhardt A E, Pritchard D E, Ketterle W 2001 Phys. Rev. Lett. 87 080402
[33] Neely T W, Samson E C, Bradley A S, Davis M J 2010 Phys. Rev. Lett. 104 160401
[34] Stagg G W, Allen A J, Barenghi C F, Parker N G 2015 J. Phys.: Conf. Ser. 594 012044
[35] Reeves M T, Anderson B P, Bradley A S 2012 Phys. Rev. A 86 053621
[36] Kadokura T, Yoshida J, Saito H 2014 Phys. Rev. A 90 013612
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[1] Wang D S, Song S W, Xiong B, Liu W M 2011 Phys. Rev. A 84 053607
[2] Ji A C, Liu W M, Song J L, Zhou F 2008 Phys. Rev. Lett. 101 010402
[3] Abrikosov A A, Eksp Z 1957 Phys. JETP 5 1174
[4] Abo-Shaeer J R, Raman C, Vogels J M, Ketterle W 2001 Sci. 292 476
[5] Wang L X, Dong B, Chen G P, Han W, Zhang S G, Shi Y R, Zhang X F 2016 Phys. Lett. A 380 435
[6] Bénard H, Acad C R 1908 Science 147 839
[7] von Kármán T, Gottingen N G W 1911 Math. Phys. Kl. 509 721
[8] Williamson C H K 1996 Annu. Rev. Fluid Mech. 28 477
[9] Barenghi C F 2008 Physica D 237 2195
[10] Kwon W J, Moon G, Choi J, Seo S W, Shin Y 2016 Phys. Rev. Lett. 24 117
[11] Sasaki K, Suzuki N, Saito H 2010 Phys. Rev. Lett. 104 150404
[12] Kwon W J, Moon G, Choi J, Seo S W, Shin Y 2014 Phys. Rev. A 90 063627
[13] Kwon W J, Seo S W, Shin Y 2015 Phys. Rev. A 92 033613
[14] Kwon W J, Seo S W, Shin Y 2015 Phys. Rev. A 91 053615
[15] Sasaki K, Suzuki N, Saito H 2010 Phys. Rev. A 83 033602
[16] Qi R, Yu X L, Li Z B, Liu W M 2009 Phys. Rev. Lett. 102 185301
[17] Liang Z X, Zhang Z D, Liu W M 2005 Phys. Rev. Lett. 94 050402
[18] Ji A C, Sun Q, Xie X C, Liu W M 2009 Phys. Rev. Lett. 102 023602
[19] Yi S, You L 2000 Phys. Rev. A 61 041604
[20] Marinescu M, You L 1998 Phys. Rev. Lett. 81 4596
[21] Deb B, You L 2001 Phys. Rev. A 64 022717
[22] Cai Y Y, Matthias R, Lei Z, Bao W Z 2010 Phys. Rev. A 82 043623
[23] Nath R, Pedri P, Santos L 2009 Phys. Rev. Lett. 102 050401
[24] Giovanazzi S, Gorlitz A, Pfau T 2002 Phys. Rev. Lett. 89 130401
[25] Pedri P, Santos L 2005 Phys. Rev. Lett. 95 200404
[26] Bao W, Chem L L, Lim F Y 2006 J. Comput. Phys. 219 836
[27] Bao W, Wang H 2006 J. Comput. Phys. 217 612
[28] Mou S, Guo K X, Xiao B 2014 Superlattices Microstruct. 65 309
[29] Finne A P, Araki T, Blaauwgeers R, Eltsov V B, Kopnin N B, Kruslus M, Skrbek L, Tsubota M, Volovikand G E 2003 Nature 424 1022
[30] Nore C, Huepe C, Brachet M E 2000 Phys. Rev. Lett. 84 2191
[31] Volovik G E 2003 JETP Lett. 78 533
[32] Inouye S, Gupta S, Rosenband T, Chikkatur A P, orlitz A G, Gustavson T L, Leanhardt A E, Pritchard D E, Ketterle W 2001 Phys. Rev. Lett. 87 080402
[33] Neely T W, Samson E C, Bradley A S, Davis M J 2010 Phys. Rev. Lett. 104 160401
[34] Stagg G W, Allen A J, Barenghi C F, Parker N G 2015 J. Phys.: Conf. Ser. 594 012044
[35] Reeves M T, Anderson B P, Bradley A S 2012 Phys. Rev. A 86 053621
[36] Kadokura T, Yoshida J, Saito H 2014 Phys. Rev. A 90 013612
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