A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion

Area of Science:

• Fluid Dynamics
• Mechanical Engineering
• Applied Mathematics

Background:

• Analyzing fluid flow in moving containers is complex.
• Existing models often treat vessel and fluid dynamics separately.
• Free surface behavior adds significant challenges.

Purpose of the Study:

• To develop a unified variational principle for 2D incompressible rotational fluid flow.
• To simultaneously determine fluid motion and vessel dynamics.
• To incorporate free surface effects within a moving vessel framework.

Main Methods:

• Utilizing a stream function to represent fluid motion.
• Employing the planar Euclidean group to model vessel motion.
• Applying Euler-Poincaré variational principles.
• Developing novel methods for pressure boundary conditions and free surface variations.

Main Results:

• A comprehensive variational formulation is established.
• Automatic generation of coupled equations for vessel path and fluid flow.
• Novel treatment of pressure boundary conditions and free surface dynamics.

Conclusions:

• The derived variational principle offers a unified approach to fluid-structure interaction problems.
• This method simplifies the analysis of complex free surface flows in dynamic environments.
• The formulation paves the way for advanced simulations in marine engineering and robotics.