Coupled-mode sound propagation in a range-dependent, moving fluid

Area of Science:

• Ocean acoustics
• Fluid dynamics
• Wave propagation

Background:

• Accurate modeling of sound propagation in ocean currents is crucial for acoustic inversion.
• Existing coupled-mode theories often assume a motionless fluid, limiting their applicability in dynamic ocean environments.
• The orthogonality of normal modes, a key property in motionless fluids, is lost in the presence of currents.

Purpose of the Study:

• To develop an exact coupled-mode representation for acoustic propagation in a range-dependent waveguide with flow.
• To establish an orthogonal basis for acoustic analysis in the presence of currents.
• To derive simplified mode-coupling equations for improved acoustic inversion.

Main Methods:

• Derived an exact coupled-mode representation of the acoustic field.
• Utilized normal modes of a corresponding range-independent waveguide as a local basis.
• Rewrote linearized hydrodynamic equations in terms of a five-component state vector.
• Established orthogonality of state vectors for individual normal modes.
• Derived coupled differential equations for range-dependent mode amplitudes.

Main Results:

• Established orthogonality of state vectors, overcoming the loss of orthogonality in mode shape functions.
• Derived coupled mode equations that maintain the form of those for motionless fluids.
• Identified that range-dependent flow velocity contributes to mode coupling.
• Mode-coupling coefficients differ from the motionless case due to flow velocity variations.

Conclusions:

• The developed model provides an accurate and efficient mathematical framework for sound propagation in flowing waveguides.
• The simplified mode-coupling equations facilitate acoustic inversion in complex, range-dependent ocean environments.
• The formulation is validated against limiting cases and an exact analytic solution, confirming its robustness.