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Variational principle in dynamics of a vortex filament
1Mechanical Engineering, Wayne State University, Detroit, Michigan 48202, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
This study presents a refined variational principle for vortex filament dynamics in fluid flow, accounting for additional terms. The new principle reveals that vortex filament length can evolve during motion, unlike previous approximations.
Area of Science:
- Fluid Dynamics
- Theoretical Physics
- Vortex Dynamics
Background:
- Previous variational principles for vortex filaments approximated dynamics by considering logarithmically large terms.
- These approximations assumed constant filament length (L) during motion, as the Hamiltonian was solely a function of L.
Purpose of the Study:
- To develop a more precise variational principle for vortex filament dynamics.
- To incorporate terms of order unity into the variational principle.
- To investigate the evolution of vortex filament length.
Main Methods:
- Derivation of a new variational principle for vortex filament dynamics.
- Building upon a recently established variational principle for arbitrary vortex motion in incompressible inviscid fluids.
- Inclusion of higher-order terms beyond logarithmic approximations.
Main Results:
- A novel variational principle for vortex filament dynamics is established.
- The refined theory reveals that vortex filament length is not constant but can evolve.
- This evolution is a characteristic feature of the more precise theoretical framework.
Conclusions:
- The developed variational principle offers a more accurate description of vortex filament dynamics.
- The dynamic evolution of filament length is a key finding, expanding upon prior approximations.
- This work advances the theoretical understanding of fluid dynamics and vortex behavior.
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