Dispersive properties of a fluctuating parabolic waveguide

Abstract

The acoustic field of the fluctuating parabolic waveguide was expressed as an eigenmode expansion of the Green function. The field was assumed to be negligibly influenced by the boundary conditions and the source/observer locations were on the waveguide axis. Variations in pressure, arrival time, and angle for each mode, m, and source frequency, ω, were examined for fluctuations in axis velocity, C0, and waveguide curvature parameter, a. The results showed the measurable quantities to be approximately ten orders of magnitude more sensitive to fluctuations in the waveguide curvature parameter than to fluctuations in axis velocity. The arrival time asymptotic behavior was tA/t0 ∼ O(exp(−ωm2/4ω2)) for large source frequencies, ω ≫ ωm = (2m + 1)aC02, and fluctuations in the waveguide curvature parameter resulted in negligible variation in arrival time. For source frequencies near the mode-dependent cutoff frequency, ωm, arrival times showed extreme sensitivity to fluctuations in the waveguide curvature parameter. Mode-dependent arrival angles were least sensitive to fluctuations in the curvature parameter near grazing angles of π/4 radians. Fluctuations in pressure exhibited similar sensitivity to the waveguide parameters and intrinsic high-order moments.