# American Institute of Mathematical Sciences

February  2005, 5(1): i-i. doi: 10.3934/dcdsb.2005.5.1i

## Introduction: Recent advances in vortex dynamics and turbulence

 1 Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, United States 2 University of Washington, Department of Applied Mathematics, Box 352420, Seattle, WA 98195-2420

Published  November 2004

As the subject of vortex dynamics and its applications to two-dimensional fluid flows mature, we have witnessed an explosion in the number of research works in the field. It is the aim of this special issue to collate some of this recent advance and at the same time point to several new directions. One of these new directions is the re-entry of equilibrium statistical mechanics into the field. Many years after the classical papers of Onsager, Kraichnan, Leith, Montgomery, Lundgren, Pointin and Chorin, we are at a point where the Kraichnan, Batchelor and Leith energy-enstrophy theories in two-dimensional turbulence have been studied from new analytical and numerical points of views. A second emerging direction is in the use of a particular type of large-scale scientific computing in vortex statistics, namely Monte-Carlo simulations of vortex gas in the plane and sphere which explore an extended range of parameter values such as temperature and chemical potentials.
Citation: Chjan C. Lim, Ka Kit Tung. Introduction: Recent advances in vortex dynamics and turbulence. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : i-i. doi: 10.3934/dcdsb.2005.5.1i
 [1] Eleftherios Gkioulekas, Ka Kit Tung. On the double cascades of energy and enstrophy in two dimensional turbulence. Part 1. Theoretical formulation. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 79-102. doi: 10.3934/dcdsb.2005.5.79 [2] Patrick Fischer, Charles-Henri Bruneau, Hamid Kellay. Multiresolution analysis for 2D turbulence. part 2: A physical interpretation. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 717-734. doi: 10.3934/dcdsb.2007.7.717 [3] Marcel Lesieur. Two-point closure based large-eddy simulations in turbulence. Part 2: Inhomogeneous cases. Discrete and Continuous Dynamical Systems, 2010, 28 (1) : 227-241. doi: 10.3934/dcds.2010.28.227 [4] Patrick Fischer. Multiresolution analysis for 2D turbulence. Part 1: Wavelets vs cosine packets, a comparative study. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 659-686. doi: 10.3934/dcdsb.2005.5.659 [5] Luis Vega. The dynamics of vortex filaments with corners. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1581-1601. doi: 10.3934/cpaa.2015.14.1581 [6] Eleftherios Gkioulekas, Ka Kit Tung. On the double cascades of energy and enstrophy in two dimensional turbulence. Part 2. Approach to the KLB limit and interpretation of experimental evidence. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 103-124. doi: 10.3934/dcdsb.2005.5.103 [7] Zhongyi Huang, Peter A. Markowich, Christof Sparber. Numerical simulation of trapped dipolar quantum gases: Collapse studies and vortex dynamics. Kinetic and Related Models, 2010, 3 (1) : 181-194. doi: 10.3934/krm.2010.3.181 [8] Pedro J. Torres, R. Carretero-González, S. Middelkamp, P. Schmelcher, Dimitri J. Frantzeskakis, P.G. Kevrekidis. Vortex interaction dynamics in trapped Bose-Einstein condensates. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1589-1615. doi: 10.3934/cpaa.2011.10.1589 [9] Zhiguo Xu, Weizhu Bao, Shaoyun Shi. Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2265-2297. doi: 10.3934/dcdsb.2018096 [10] François Baccelli, Augustin Chaintreau, Danny De Vleeschauwer, David R. McDonald. HTTP turbulence. Networks and Heterogeneous Media, 2006, 1 (1) : 1-40. doi: 10.3934/nhm.2006.1.1 [11] James Montaldi, Amna Shaddad. Generalized point vortex dynamics on $\mathbb{CP} ^2$. Journal of Geometric Mechanics, 2019, 11 (4) : 601-619. doi: 10.3934/jgm.2019030 [12] Xavier Perrot, Xavier Carton. Point-vortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 971-995. doi: 10.3934/dcdsb.2009.11.971 [13] Eric Falcon. Laboratory experiments on wave turbulence. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 819-840. doi: 10.3934/dcdsb.2010.13.819 [14] W. Layton, R. Lewandowski. On a well-posed turbulence model. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 111-128. doi: 10.3934/dcdsb.2006.6.111 [15] Yifei Lou, Sung Ha Kang, Stefano Soatto, Andrea L. Bertozzi. Video stabilization of atmospheric turbulence distortion. Inverse Problems and Imaging, 2013, 7 (3) : 839-861. doi: 10.3934/ipi.2013.7.839 [16] Mimi Dai. Phenomenologies of intermittent Hall MHD turbulence. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021285 [17] Jair Koiller. Getting into the vortex: On the contributions of james montaldi. Journal of Geometric Mechanics, 2020, 12 (3) : 507-523. doi: 10.3934/jgm.2020018 [18] Fanghua Lin, Juncheng Wei. Superfluids passing an obstacle and vortex nucleation. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 6801-6824. doi: 10.3934/dcds.2019232 [19] P.K. Newton. N-vortex equilibrium theory. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 411-418. doi: 10.3934/dcds.2007.19.411 [20] Alexandre Boritchev. Decaying turbulence for the fractional subcritical Burgers equation. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 2229-2249. doi: 10.3934/dcds.2018092

2020 Impact Factor: 1.327