Qian SHI, Yu CHEN, Xilin XIE . Interplay of surface geometry and vorticity dynamics in incompressible flows on curved surfaces[J]. Applied Mathematics and Mechanics, 2017 , 38(9) : 1191 -1212 . DOI: 10.1007/s10483-017-2238-8

[1] Bouchet, F. and Venaille, A. Statistical mechanics of two-dimensional and geophysical flows. Physics Reports-Review Section of Physics Letters, 515, 227-295(2012)
[2] Hu, D., Zhang, P. W., and E, W. N. Continuum theory of a moving membrane. Physical Review E, 75, 041605(2007)
[3] Scriven, L. E. Dynamicns of a fluid interface:equation of motion for Newtonian surface fluids. Chemical Engineering Science, 12, 98-108(1960)
[4] Aris, R. Vectors, and the Basic Equations of Fluid Mechanics, Dover Publication, New York (1962)
[5] Rivera, M. K., Aluie, H., and Ecke, R. E. The direct enstrophy cascade of two-dimensional soap film flows. Physics of Fluids, 26, 055105(2014)
[6] Couder, Y., Chomaz, J. M., and Rabaud, M. On the hydrodynamics of soap films. Physica D, 37, 384-405(1989)
[7] Prasad, V. and Weeks, E. R. Two-dimensional to three-dimensional transition in soap films demonstrated by microrheology. Physical Review Letters, 102, 178302(2009)
[8] Vorobieff, P. and Ecke, R. E. Cylinder wakes in flowing soap films. Physical Review E, 60, 2953-2956(1999)
[9] Yang, Y. H., Yin, X. Z., and Lu, X. Y. Experimental methods in a soap film tunnel. Journal of Experiments in Fluid Mechanics, 19, 36-41(2005)
[10] Boffetta, G. and Ecke, R. E. Two-dimensional turbulence. Annual Review of Fluid Mechanics, 44, 427-451(2012)
[11] Rivera, M., Vorobieff, P., and Ecke, R. E. Turbulence in flowing soap films:velocity, vorticity, and thickness fields. Physical Review Letters, 81, 1417-1420(1998)
[12] Shelley, M. J. and Zhang, J. Flapping and bending bodies interacting with fluid flows. Annual Review of Fluid Mechanics, 43, 449-465(2011)
[13] Bowick, M. J. and Giomi, L. Two-dimensional matter:order, curvature and defects. Advances in Physics, 58, 449-563(2009)
[14] Nelson, D. R. Toward a tetravalent chemistry of colloids. Nano Letters, 2, 1125-1129(2002)
[15] Reuther, S. and Voigt, A. The interplay of curvature and vortices in flow on curved surfaces. SIAM Multiscale Modeling and Simulation, 13, 632-643(2015)
[16] Zermelo, E. Hydrodynamical investigations of vortex motions in the surface of a sphere. Z. Math. Phys., 47, 201-237(1902)
[17] Turner, A. M., Vitelli, V., and Nelson, D. R. Vortices on curved surfaces. Reviews of Modern Physics, 82, 1302-1347(2010)
[18] Nitschke, I., Voigt, A., and Wensch, J. A finite element approach to incompressible two-phase flow on manifolds. Journal of Fluid Mechanics, 708, 418-438(2012)
[19] Boudaoud, A., Couder, Y., and Amar, M. B. Self-adaptation in vibrating soap films. Physical Review Letters, 82, 3847-3850(1999)
[20] Acharige, S. K., Elias, F., and Derec, C. Soap film vibration:origin of the dissipation. Soft Matter, 10, 8341-8348(2014)
[21] Song, P., Hu, D., and Zhang, P. W. Numerical simulation of fluid membranes in two-dimensional space. Communications in Computational Physics, 3, 794-821(2008)
[22] Afenchenko, V. O., Ezersky, A. B., and Kiyashko, S. V. Rabinovich, M. I., and Weidman, P. D. The generation of two-dimensional vortices by transverse oscillation of a soap film. Physics of Fluids, 10, 390-399(1998)
[23] Oron, A., Davis, S. H., and Bankoff, S. G. Long-scale evolution of thin liquid films. Reviews of Modern Physics, 69, 931-980(1997)
[24] Ida, M. P. and Miksis, M. J. The dynamics of thin films I:general theory. SIAM Journal on Applied Mathematics, 58, 456-473(1998)
[25] Chomaz, J. M. The dynamics of a viscous soap film with soluble surfactant. Journal of Fluid Mechanics, 442, 387-409(2001)
[26] Roberts, A. J. and Li, Z. Q. An accurate and comprehensive model of thin fluid flows with inertia on curved substrates. Journal of Fluid Mechanics, 553, 33-73(2006)
[27] Chomaz, J. M. and Cathalau, B. Soap films as two-dimensional classical fluids. Physical Review A, 41, 2243-2245(1990)
[28] Ogawa, N. Curvature-dependent diffusion flow on a surface with thickness. Physical Review E, 81, 061113(2010)
[29] Xie, X. L., Chen, Y., and Shi, Q. Some studies on mechanics of continuous mediums viewed as differential manifolds. Science China-Physics Mechanics and Astronomy, 56, 432-456(2013)
[30] Wu, J. Z., Ma, H. Y., and Zhou, M. D. Vorticity and Vortex Dynamics, Spring-Verlag, New York (2006)
[31] Xie, X. L. Modern Tensor Analysis with Applications in Continuum Mechanics, Fudan Univerisity Press, Shanghai (2014)
[32] Dubrovin, B. A., Fomenko, A. T., and Novikov, S. P. Modern Geometry-Methods and Applications, Springer-Verlag, New York (2011)
[33] Chen, Y. and Xie, X. L. Vorticity vector-potential method for 3D viscous incompressible flows. Journal of Computational Physics, 312, 50-81(2016)
[34] Hussain, H. S. and Hussain, F. Experiments on subharmonic resonance in a shear layer. Journal of Fluid Mechanics, 304, 343-372(1995)
[35] Narayanan, S. and Hussain, F. Measurements of spatiotemporal dynamics in a forced plane mixing layer. Journal of Fluid Mechanics, 320, 71-115(1996)
[36] Xie, X. L., Ma, W. W., and Zhou, H. L. Coherent structures in countercurrent axisymmetric shear flows. Acta Mechanica Sinica, 19, 11-32(2003)