Trapped modes around freely floating bodies in a two-layer fluid channel

Area of Science:

• Fluid dynamics
• Wave mechanics
• Spectral theory

Background:

• Trapping of water waves by fixed obstacles is well-understood.
• Oscillating floating structures introduce nonlinear spectral problems.
• Previous research has not fully addressed trapped modes for freely floating bodies.

Purpose of the Study:

• To simplify the complex nonlinear spectral problem arising from floating structures.
• To identify conditions for the existence of trapped modes in two-layer fluid channels.
• To provide examples of floating bodies that support trapped modes.

Main Methods:

• Development of a convenient elimination scheme to simplify the spectral problem.
• Formulation of a linear spectral problem for a self-adjoint operator in Hilbert space.
• Analysis of symmetry assumptions in the fluid domain geometry.

Main Results:

• The nonlinear spectral problem is reduced to a linear one.
• Conditions guaranteeing trapped modes in two-layer fluid channels are established.
• Several configurations of floating bodies supporting trapped modes are identified.

Conclusions:

• The study successfully simplifies a complex fluid dynamics problem.
• Conditions for trapped modes in specific fluid geometries are now defined.
• The findings offer insights into wave phenomena around floating structures.