American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 880-887. doi: 10.3934/proc.2003.2003.880

The primitive equations formulated in mean vorticity

Cheng Wang 1,

1. 

Department of Mathematics, Indiana University, Bloomington, IN 47405-5701

Received  September 2002 Published  April 2003

The primitive equations (PEs) of large-scale oceanic flow formulated in mean vorticity is proposed. In the reformulation of the PEs, the prognostic equation for the horizontal velocity is replaced by evolutionary equations for the mean vorticity field and the vertical derivative of the horizontal velocity. The total velocity field (both horizontal and vertical) is statically determined by differential equations at each fixed horizontal point. Its equivalence to the original formulation is also presented.
Keywords: mean vorticity, Primitive equations, mean stream function., hydrostatic balance.
Mathematics Subject Classification: Primary: 35Q35; Secondary: 86A1.
Citation: Cheng Wang. The primitive equations formulated in mean vorticity. Conference Publications, 2003, 2003 (Special) : 880-887. doi: 10.3934/proc.2003.2003.880
[1]

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
[2]

Juan Li, Wenqiang Li. Controlled reflected mean-field backward stochastic differential equations coupled with value function and related PDEs. Mathematical Control and Related Fields, 2015, 5 (3) : 501-516. doi: 10.3934/mcrf.2015.5.501
[3]

Silvia Sastre-Gomez. Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2669-2680. doi: 10.3934/dcds.2017114
[4]

Chang-Shou Lin. An expository survey on the recent development of mean field equations. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 387-410. doi: 10.3934/dcds.2007.19.387
[5]

Pierre-Emmanuel Jabin. A review of the mean field limits for Vlasov equations. Kinetic and Related Models, 2014, 7 (4) : 661-711. doi: 10.3934/krm.2014.7.661
[6]

Michael Herty, Lorenzo Pareschi, Sonja Steffensen. Mean--field control and Riccati equations. Networks and Heterogeneous Media, 2015, 10 (3) : 699-715. doi: 10.3934/nhm.2015.10.699
[7]

Y. Goto, K. Ishii, T. Ogawa. Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature. Communications on Pure and Applied Analysis, 2005, 4 (2) : 311-339. doi: 10.3934/cpaa.2005.4.311
[8]

Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Mean-field backward stochastic Volterra integral equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1929-1967. doi: 10.3934/dcdsb.2013.18.1929
[9]

Bixiang Wang. Mean-square random invariant manifolds for stochastic differential equations. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1449-1468. doi: 10.3934/dcds.2020324
[10]

Wei Wang, Kai Liu, Xiulian Wang. Sensitivity to small delays of mean square stability for stochastic neutral evolution equations. Communications on Pure and Applied Analysis, 2020, 19 (4) : 2403-2418. doi: 10.3934/cpaa.2020105
[11]

Franco Flandoli, Marta Leocata, Cristiano Ricci. The Vlasov-Navier-Stokes equations as a mean field limit. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3741-3753. doi: 10.3934/dcdsb.2018313
[12]

Zhen Li, Jicheng Liu. Synchronization for stochastic differential equations with nonlinear multiplicative noise in the mean square sense. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5709-5736. doi: 10.3934/dcdsb.2019103
[13]

Jinju Xu. A new proof of gradient estimates for mean curvature equations with oblique boundary conditions. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1719-1742. doi: 10.3934/cpaa.2016010
[14]

Hailong Zhu, Jifeng Chu, Weinian Zhang. Mean-square almost automorphic solutions for stochastic differential equations with hyperbolicity. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1935-1953. doi: 10.3934/dcds.2018078
[15]

Gabriella Tarantello. Analytical, geometrical and topological aspects of a class of mean field equations on surfaces. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 931-973. doi: 10.3934/dcds.2010.28.931
[16]

Chiun-Chuan Chen, Chang-Shou Lin. Mean field equations of Liouville type with singular data: Sharper estimates. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 1237-1272. doi: 10.3934/dcds.2010.28.1237
[17]

Yves Achdou, Mathieu Laurière. On the system of partial differential equations arising in mean field type control. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 3879-3900. doi: 10.3934/dcds.2015.35.3879
[18]

Hongjie Dong, Xinghong Pan. On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4567-4592. doi: 10.3934/dcds.2021049
[19]

Michael Herty, Torsten Trimborn, Giuseppe Visconti. Mean-field and kinetic descriptions of neural differential equations. Foundations of Data Science, 2022, 4 (2) : 271-298. doi: 10.3934/fods.2022007
[20]

Yinggu Chen, Said HamadÈne, Tingshu Mu. Mean-field doubly reflected backward stochastic differential equations. Numerical Algebra, Control and Optimization, 2022  doi: 10.3934/naco.2022012

 Impact Factor: 

Tools

Metrics

  • PDF downloads (29)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy