The energy flux formulation of waveguide propagation is closely related to the incoherent mode sum, and its simplicity has led to development of efficient computational algorithms for reverberation and target echo strength, but it lacks the effects of convergence or modal interference. By starting with the coherent mode sum and rejecting the most rapid interference but retaining beats on a scale of a ray cycle distance it is shown that convergence can be included in a hybrid formulation requiring minimal extra computation. Three solutions are offered by evaluating the modal intensity cross terms using Taylor expansions. In the most efficient approach the double summation of the cross terms is reduced to a single numerical sum by solving the other summation analytically. The other two solutions are a local range average and a local depth average. Favorable comparisons are made between these three solutions and the wave model Orca with, and without, spatial averaging in an upward refracting duct. As a by-product, it is shown that the running range average is very close to the mode solution excluding its fringes, given a relation between averaging window size and effective number of modes which, in turn, is related to the waveguide invariant.
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June 2013
June 05 2013
Ray convergence in a flux-like propagation formulation
Chris H. Harrison
Chris H. Harrison
a)
Centre for Maritime Research and Experimentation
, Viale San Bartolomeo 400, 19126 La Spezia, Italy
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Author to whom correspondence should be addressed. Also at: Institute of Sound and Vibration Research, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom. Electronic mail: harrison@cmre.nato.int
J. Acoust. Soc. Am. 133, 3777–3789 (2013)
Article history
Received:
November 16 2012
Accepted:
March 25 2013
Citation
Chris H. Harrison; Ray convergence in a flux-like propagation formulation. J. Acoust. Soc. Am. 1 June 2013; 133 (6): 3777–3789. https://doi.org/10.1121/1.4802642
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