scholarly journals Variational formulation of macro-particle plasma simulation algorithms

2014 ◽  
Vol 21 (5) ◽  
pp. 055708 ◽  
Author(s):  
B. A. Shadwick ◽  
A. B. Stamm ◽  
E. G. Evstatiev
Keyword(s):  
Variational Formulation ◽  
Plasma Simulation ◽  
Simulation Algorithms

scholarly journals Variational formulations of steady rotational equatorial waves

2020 ◽  
Vol 10 (1) ◽  
pp. 534-547
Author(s):  
Jifeng Chu ◽  
Joachim Escher
Keyword(s):  
Linear Stability ◽  
Stream Function ◽  
Water Waves ◽  
Variational Formulation ◽  
Energy Functional ◽  
Equatorial Waves ◽  
Second Variation ◽  
Governing Equations ◽  
The Second Variation ◽  
Variational Formulations

Abstract When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

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