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Title: Extra-wide-angle parabolic equations in motionless and moving media
Authors: Ostashev, Vladimir E.
Muhlestein, Michael B.
Wilson, D. Keith.
Keywords: Sound-waves
Differential equations, Parabolic
Publisher: Cold Regions Research and Engineering Laboratory (U.S.)
Engineer Research and Development Center (U.S.)
Series/Report no.: Miscellaneous Paper (Engineer Research and Development Center (U.S.)) ; no. ERDC/CRREL MP-21-22
Is Version Of: Ostashev, Vladimir E., Michael B. Muhlestein, and D. Keith Wilson. "Extra-wide-angle parabolic equations in motionless and moving media." The Journal of the Acoustical Society of America 145, no. 2 (2019): 1031-1047.
Abstract: Wide-angle parabolic equations (WAPEs) play an important role in physics. They are derived by an expansion of a square-root pseudo-differential operator in one-way wave equations, and then solved by finite-difference techniques. In the present paper, a different approach is suggested. The starting point is an extra-wide-angle parabolic equation (EWAPE) valid for small variations of the refractive index of a medium. This equation is written in an integral form, solved by a perturbation technique, and transformed to the spectral domain. The resulting split-step spectral algorithm for the EWAPE accounts for the propagation angles up to 90° with respect to the nominal direction. This EWAPE is also generalized to large variations in the refractive index. It is shown that WAPEs known in the literature are particular cases of the two EWAPEs. This provides an alternative derivation of the WAPEs, enables a better understanding of the underlying physics and ranges of their applicability, and opens an opportunity for innovative algorithms. Sound propagation in both motionless and moving media is considered. The split-step spectral algorithm is particularly useful in the latter case since complicated partial derivatives of the sound pressure and medium velocity reduce to wave vectors (essentially, propagation angles) in the spectral domain.
Description: Miscellaneous Paper
Gov't Doc #: ERDC/CRREL MP-21-22
Rights: Approved for Public Release; Distribution is Unlimited
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