The waveguide invariant for a Pekeris waveguide.

Area of Science:

• Acoustics
• Oceanography
• Wave Propagation

Background:

• Pekeris waveguides are fundamental models in underwater acoustics.
• Accurate calculation of waveguide invariants is crucial for understanding sound propagation.
• Existing methods often rely on numerical simulations, limiting analytical insights.

Purpose of the Study:

• To derive a closed-form waveguide invariant (β) for Pekeris waveguides.
• To develop an analytical method for predicting sound propagation characteristics.
• To validate the derived formula against established numerical models.

Main Methods:

• Utilized the modal Wentzel-Kramers-Brillouin (WKB) dispersion equation.
• Employed implicit differentiation and the concept of effective boundary depth, ΔH(θ).
• Derived explicit and closed-form expressions for the waveguide invariant β.

Main Results:

• An explicit formula for β(m,n) between mode pairs was obtained.
• The derived formula for adjacent modes, β=(H+ΔH(θ))/(H/cos²θ-ΔH(θ)), showed excellent agreement with numerical results.
• An approximation β=cos²θ is valid for ΔH(θ)/H≪1.

Conclusions:

• The derived closed-form waveguide invariant offers an accurate analytical solution for Pekeris waveguides.
• This method provides a valuable alternative to computationally intensive numerical simulations.
• The findings enhance the understanding of acoustic wave propagation in stratified environments.