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The role of higher vorticity moments in a variational formulation of Barotropic flows on a rotating sphere
1. | Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, United States |
2. | Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187 |
[1] |
Joachim Escher, Boris Kolev, Marcus Wunsch. The geometry of a vorticity model equation. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1407-1419. doi: 10.3934/cpaa.2012.11.1407 |
[2] |
Delia Ionescu-Kruse. Variational derivation of the Camassa-Holm shallow water equation with non-zero vorticity. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 531-543. doi: 10.3934/dcds.2007.19.531 |
[3] |
Walter A. Strauss. Vorticity jumps in steady water waves. Discrete and Continuous Dynamical Systems - B, 2012, 17 (4) : 1101-1112. doi: 10.3934/dcdsb.2012.17.1101 |
[4] |
Cheng Wang. The primitive equations formulated in mean vorticity. Conference Publications, 2003, 2003 (Special) : 880-887. doi: 10.3934/proc.2003.2003.880 |
[5] |
Cheng Wang. Convergence analysis of the numerical method for the primitive equations formulated in mean vorticity on a Cartesian grid. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1143-1172. doi: 10.3934/dcdsb.2004.4.1143 |
[6] |
Thomas Y. Hou, Zuoqiang Shi. Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1449-1463. doi: 10.3934/dcds.2012.32.1449 |
[7] |
Vikas S. Krishnamurthy. The vorticity equation on a rotating sphere and the shallow fluid approximation. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6261-6276. doi: 10.3934/dcds.2019273 |
[8] |
H. Beirão da Veiga. Vorticity and regularity for flows under the Navier boundary condition. Communications on Pure and Applied Analysis, 2006, 5 (4) : 907-918. doi: 10.3934/cpaa.2006.5.907 |
[9] |
Jifeng Chu, Joachim Escher. Steady periodic equatorial water waves with vorticity. Discrete and Continuous Dynamical Systems, 2019, 39 (8) : 4713-4729. doi: 10.3934/dcds.2019191 |
[10] |
Octavian G. Mustafa. On isolated vorticity regions beneath the water surface. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1523-1535. doi: 10.3934/cpaa.2012.11.1523 |
[11] |
Vishal Vasan, Katie Oliveras. Pressure beneath a traveling wave with constant vorticity. Discrete and Continuous Dynamical Systems, 2014, 34 (8) : 3219-3239. doi: 10.3934/dcds.2014.34.3219 |
[12] |
Sho Matsumoto, Jonathan Novak. A moment method for invariant ensembles. Electronic Research Announcements, 2018, 25: 60-71. doi: 10.3934/era.2018.25.007 |
[13] |
Verónica Anaya, Mostafa Bendahmane, David Mora, Ricardo Ruiz Baier. On a vorticity-based formulation for reaction-diffusion-Brinkman systems. Networks and Heterogeneous Media, 2018, 13 (1) : 69-94. doi: 10.3934/nhm.2018004 |
[14] |
Adrian Constantin. Dispersion relations for periodic traveling water waves in flows with discontinuous vorticity. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1397-1406. doi: 10.3934/cpaa.2012.11.1397 |
[15] |
Mats Ehrnström. Deep-water waves with vorticity: symmetry and rotational behaviour. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 483-491. doi: 10.3934/dcds.2007.19.483 |
[16] |
Calin Iulian Martin. Dispersion relations for periodic water waves with surface tension and discontinuous vorticity. Discrete and Continuous Dynamical Systems, 2014, 34 (8) : 3109-3123. doi: 10.3934/dcds.2014.34.3109 |
[17] |
Philippe Bonneton, Nicolas Bruneau, Bruno Castelle, Fabien Marche. Large-scale vorticity generation due to dissipating waves in the surf zone. Discrete and Continuous Dynamical Systems - B, 2010, 13 (4) : 729-738. doi: 10.3934/dcdsb.2010.13.729 |
[18] |
Hugo Beirão da Veiga. Navier-Stokes equations: Some questions related to the direction of the vorticity. Discrete and Continuous Dynamical Systems - S, 2019, 12 (2) : 203-213. doi: 10.3934/dcdss.2019014 |
[19] |
J. F. Toland. Energy-minimising parallel flows with prescribed vorticity distribution. Discrete and Continuous Dynamical Systems, 2014, 34 (8) : 3193-3210. doi: 10.3934/dcds.2014.34.3193 |
[20] |
Calin I. Martin. On three-dimensional free surface water flows with constant vorticity. Communications on Pure and Applied Analysis, 2022, 21 (7) : 2415-2431. doi: 10.3934/cpaa.2022053 |
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