References
Kirchhoff, G., Vorlesungen über Mathematische Physik: Mechanik, B.G. Teubner, Leipzig, 1877 p. 257.
Fröhlich, J. and Ruelle, D., ‘Statistical mechanics of vortices in an inviscid 2D fluid’, Commun. Math. Phys. 87 (1982) 1–36.
Shnirelman, A.I., ‘Lattice theory and flows of ideal incompressible fluid’, Russ. J. Math. Phys. 1 (1993) 105–114.
Novikov, E.A., ‘Dynamics and statistics of a system of vortices’, JETP 41 (1975) 937–943.
Abo-Shaeer, J.R., Raman, C. and Ketterle, W., ‘Formation and decay of vortex lattices in Bose-Einstein condensates at finite temperatures’, Phys. Rev. Lett. 88 (2002).
Onsager, L., ‘Statistical hydrodynamics’, Nuovo Cimento Suppl. 6 (1949) 279–287.
Eckhardt, B., ‘Integrable four vortex motion’, Phys. Fluids 31 (1988) 2796–2801.
Thess, A., ‘Instabilities in 2D spatially periodic flows. II. Square eddy lattice’, Phys. Fluids A 4 (1992) 1396–1407.
Saffman, P.G. and Szeto, R., ‘Equilibrium shapes of a pair of equal uniform vortices’, Phys. Fluids 23 (1980) 2339–2342.
Saffman, P.G. and Tanveer, S., ‘The touching pair of equal and opposite uniform vortices’, Phys. Fluids 25 (1982) 1929–1930.
Lamb, H., Hydrodynamics, Cambridge University Press, 6th edn, 1932 p. 223.
Kraichnan, R.H. and Montgomery, D., ‘2D turbulence’, Rep. Prog. Phys. 43 (1980) 547–619.
Gatignol, R., ‘Théorie cinétique des gaz à répartition discrète de vitesses’, Z. Flugwissenschaften 18 (1970) 93–99.
Chu, K.-H., ‘Approximate Solutions for Physical Problems Related to Microchannels and Rarefied Gases’, Post-Dr Report (in English), Peking University, Beijing, May 2001.
Bobylev, A.V. and Cercignani C., ‘Discrete velocity models without nonphysical invariants’, J. Statist. Phys. 97 (1999) 677–686.
Chu, A.K.-H., ‘Note on the dispersion relations of ultrasound propagation’, Meccanica 34 (1999) 59–62.
Monaco, R. and Preziosi, L. Fluid Dynamic Applications of the Discrete Boltzmann Equation, World Scientific, Singapore, 1991.
Povitsky, A., ‘Numerical study of wave propagation in a nonuniform compressible flow’, Phys. Fluids 14 (2002) 2657–2672.
Pierrehumbert, R.T., ‘A family of vortex pairs with distributed vorticity’, J. Fluid Mech. 99 (1982) 129–144.
Kopiev, V.F. and Chernyshev, S.A., ‘Vortex ring eigen-oscillations as a source of sound’, J. Fluid Mech. 341 (1997) 19–57.
Inoue, O., ‘Sound generation by the leapfrogging between two coaxial vortex rings’, Phys. Fluids 14 (2002) 3361–3364.
Bühler, O., ‘Statistical mechanics of strong and weak point vortices in a cylinder’, Phys. Fluids 14 (2002) 2139–2149.
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Chu, R.KH. Propagation of Sound in Hard-Sphere-like Vortex Gases Using Discrete Kinetic Approach. Meccanica 39, 285–290 (2004). https://doi.org/10.1023/B:MECC.0000022839.93151.b1
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DOI: https://doi.org/10.1023/B:MECC.0000022839.93151.b1