American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 611-620. doi: 10.3934/proc.2005.2005.611

Variational analysis of energy-enstrophy theories on the sphere

Chjan C. Lim 1, and  Da Zhu 1,

1. 

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, United States, United States

Received  September 2004 Revised  April 2005 Published  September 2005

Kraichnan's energy-enstrophy theory for 2D inviscid flows on the sphere is discussed within a variational framework. We will give necessary and sufficient conditions for the existence and uniqueness for the extremals of the energy with zero circulation under different values of the temperature parameter $\beta$. The unboundedness of the augmented energy functional in this model when $\beta$ is located in the certain intervals will be shown and related to energy catastrophe of the energy-enstrophy model.
Keywords: unboundedness., energy-enstrophy, variational analysis.
Mathematics Subject Classification: Primary: 76B47, 82B20; Secondary: 65C0.
Citation: Chjan C. Lim, Da Zhu. Variational analysis of energy-enstrophy theories on the sphere. Conference Publications, 2005, 2005 (Special) : 611-620. doi: 10.3934/proc.2005.2005.611
[1]

S. Danilov. Non-universal features of forced 2D turbulence in the energy and enstrophy ranges. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : 67-78. doi: 10.3934/dcdsb.2005.5.67
[2]

Aseel Farhat, M. S Jolly, Evelyn Lunasin. Bounds on energy and enstrophy for the 3D Navier-Stokes-$\alpha$ and Leray-$\alpha$ models. Communications on Pure and Applied Analysis, 2014, 13 (5) : 2127-2140. doi: 10.3934/cpaa.2014.13.2127
[3]

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
[4]

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
[5]

Shengji Li, Chunmei Liao, Minghua Li. Stability analysis of parametric variational systems. Numerical Algebra, Control and Optimization, 2011, 1 (2) : 317-331. doi: 10.3934/naco.2011.1.317
[6]

Lixia Wang, Shiwang Ma. Unboundedness of solutions for perturbed asymmetric oscillators. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 409-421. doi: 10.3934/dcdsb.2011.16.409
[7]

YunKyong Hyon, James E. Fonseca, Bob Eisenberg, Chun Liu. Energy variational approach to study charge inversion (layering) near charged walls. Discrete and Continuous Dynamical Systems - B, 2012, 17 (8) : 2725-2743. doi: 10.3934/dcdsb.2012.17.2725
[8]

Riccardo March, Giuseppe Riey. Analysis of a variational model for motion compensated inpainting. Inverse Problems and Imaging, 2017, 11 (6) : 997-1025. doi: 10.3934/ipi.2017046
[9]

G. Mastroeni, L. Pellegrini. On the image space analysis for vector variational inequalities. Journal of Industrial and Management Optimization, 2005, 1 (1) : 123-132. doi: 10.3934/jimo.2005.1.123
[10]

Sergio Amat, Pablo Pedregal. On a variational approach for the analysis and numerical simulation of ODEs. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1275-1291. doi: 10.3934/dcds.2013.33.1275
[11]

Mingqi Xiang, Giovanni Molica Bisci, Binlin Zhang. Variational analysis for nonlocal Yamabe-type systems. Discrete and Continuous Dynamical Systems - S, 2020, 13 (7) : 2069-2094. doi: 10.3934/dcdss.2020159
[12]

Robert I McLachlan, Christian Offen. Backward error analysis for variational discretisations of PDEs. Journal of Geometric Mechanics, 2022  doi: 10.3934/jgm.2022014
[13]

Jumpei Inoue, Kousuke Kuto. On the unboundedness of the ratio of species and resources for the diffusive logistic equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2441-2450. doi: 10.3934/dcdsb.2020186
[14]

Sobhan Seyfaddini. Unboundedness of the Lagrangian Hofer distance in the Euclidean ball. Electronic Research Announcements, 2014, 21: 1-7. doi: 10.3934/era.2014.21.1
[15]

Andrzej Nowakowski. Variational analysis of semilinear plate equation with free boundary conditions. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3133-3154. doi: 10.3934/dcds.2015.35.3133
[16]

Yan Tang. Convergence analysis of a new iterative algorithm for solving split variational inclusion problems. Journal of Industrial and Management Optimization, 2020, 16 (2) : 945-964. doi: 10.3934/jimo.2018187
[17]

Alexandre Caboussat, Roland Glowinski. Numerical solution of a variational problem arising in stress analysis: The vector case. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1447-1472. doi: 10.3934/dcds.2010.27.1447
[18]

Khalid Addi, Samir Adly, Hassan Saoud. Finite-time Lyapunov stability analysis of evolution variational inequalities. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1023-1038. doi: 10.3934/dcds.2011.31.1023
[19]

Patricia Bauman, Guanying Peng. Analysis of minimizers of the Lawrence-Doniach energy for superconductors in applied fields. Discrete and Continuous Dynamical Systems - B, 2019, 24 (11) : 5903-5926. doi: 10.3934/dcdsb.2019112
[20]

Xing Wang, Nan-Jing Huang. Stability analysis for set-valued vector mixed variational inequalities in real reflexive Banach spaces. Journal of Industrial and Management Optimization, 2013, 9 (1) : 57-74. doi: 10.3934/jimo.2013.9.57

 Impact Factor: 

Tools

Metrics

  • PDF downloads (49)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy