Quelques références

Livres.

Majda--Bertozzi: Vorticity and incompressible flow --- Cambridge Texts In Applied Mathematics, 2002.
Cottet--Koumoutsakos : Vortex method: theory and practice --- Cambridge University Press, 2000. Téléchargeable : http://www.cse-lab.ethz.ch/index.php/publications
Ting--Klein: Viscous Vortical Flows. Springer-Verlag 1991.
Newton: The N-Vortex Problem: Analytical Techniques 2000.
Marchioro-Pulvirienti. Vortex methods in two-dimensional fluid dynamics. Lecture note in physics. Springer-Verlag, Berlin 1984.
Chorin. Vorticity and turbulence. Springer 1994.

Publications.

Méthodes vortex et aspects numériques.

A.J. Chorin (1978) Vortex Sheet Approximation of Boundary Layers, J. Comp. Phys., 27, 428-442.
I. Mortazavi, P. Micheau, A. Giovannini. Numerical convergence of the Random Vortex Method for complex flows. ESAIM Proceedings, 11 (1997), 521-538.
I. Mortazavi, P. Micheau, A. Giovannini. L'étude de la convergence numérique d'une méthode vortex pour un écoulement à grand nombre de Reynolds. Compt. Rendus Acad. Sciences, 330 (2002), 1-8.

C. Mimeau , F. Gallizio, I. Mortazavi and G.-H. Cottet. Vortex penalization method for bluff body flows. Intern. Journal for Numerical Methods in Fluids, , 79, pp. 53-83, 2015.
C. Mimeau, G.-H. Cottet and I. Mortazavi. Direct numerical simulation of three-dimensional bluff-body flows by a vortex penalization method. Computers & Fluids, 136 (2016) 331-347.

Méthodes vortex et aspects théoriques sans bord.

E.G. Puckett, The Random Vortex Method with Vorticity Creation : Introduction and Guide to Parameter Selection, Lectures in Appl. Math. AMS, 28, pp. 567-584 (1991).
0. Hald, Convergence of a random method with creation of vorticity. SIAM J. Sci. and Stat. Comput., 7(4), 1373-1386.
N. Fournier, M. Hauray, S. Mischler. Propagation of chaos for the 2D viscous vortex model. J. Eur. Math. Soc., (2014).
P.--E. Jabin, Z. Wang, Quantitative estimates of propagation of chaos for stochastic systems with W^{-1,infty} kernels. Soumis (2017).
F. Flandoli, M. Gubinelli, E. Priola. Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations. Stochastic Processes and Their Appl. (2011).

Méthodes vortex et aspects théoriques avec bords.

G. Benfatto, M. Pulvirenti, Convergence of Chorin-Marsden product formula in the half plane, Comm. Math. Phys., 106 (2), 1986, 427-458.
C. Boldrighini, P. Butta. Navier-Stokes equation on a flat cylinder with vorticity production on the boundary. Nonlinearity (2011).
B. Jourdain, S. Méléard. Probabilitic interpretation and particle methode for vortex equations with Neumann's boundary condition. Proc Edinburgh Maths Soc. (2004).
D. Arsénio, E. Dormy, C. Lacave. The vortex method for 2D ideal flows in exterior domains. Soumis (2017).

Interactions de vortex

D.G. Dritschel. A general theory for two-dimensional vortex interactions. J. Fluid Mech., 293, 269--303 (2006).
B.H. Burgess, G.D. Dritschel, D. G., R.K. Scott. Vortex scaling ranges in two-dimensional turbulence. Phys of Fluid (2017).
Vidéos du Computational Science and Engineering Laboratory de l'ETH Zurich (voir en particulier, The Secret Life of Vortices).