Variational principle for frozen-in vorticity interacting with sound waves

Area of Science:

• Fluid Dynamics and Hydrodynamics
• Theoretical Physics
• Nonlinear Dynamics

Background:

• Conservative hydrodynamic models are fundamental in describing fluid behavior.
• Understanding the interaction between vortex structures and acoustic waves is crucial.
• Canonical formalism provides a powerful framework for continuous media.

Purpose of the Study:

• To investigate the general properties of conservative hydrodynamic-type models.
• To derive a variational formulation for the dynamics of vortex structures and acoustic waves.
• To establish a foundation for developing approximate dynamical models.

Main Methods:

• Application of canonical formalism to liquid continuous media.
• Development of a variational principle incorporating Eulerian fields (density, momentum) and vortex line shapes.
• Analysis of the motion and interaction of frozen-in localized vortex structures and acoustic waves.

Main Results:

• A novel variational formulation is established for the described system.
• The formulation includes fluid density, canonical momentum, and generalized vorticity shapes as dynamical variables.
• The derived variational principle is suitable for creating reduced-order dynamical models.

Conclusions:

• The developed variational principle offers a new perspective on hydrodynamic model dynamics.
• This approach facilitates the creation of simplified models with fewer degrees of freedom.
• The findings have implications for theoretical fluid dynamics and computational modeling.