Abstract
The polynomial chaos method is applied to the problem of predicting the probability density functions of complex modal amplitudes and acoustic pressure in the presence of water column sound speed fluctuations in shallow water waveguides. Results for both the intrusive implementation of the polynomial chaos technique, where the governing coupled mode differential equations for the complex modal amplitudes are augmented with the random states of the chaos expansion, and the non-intrusive method, where legacy codes can be run over an ensemble of ocean realizations and the results fitted by a truncated chaos expansion, are shown. Both methods give good agreement with Monte Carlo histograms of the modal amplitudes and the pressure field for slight water column variability, but the non-intrusive formulation shows more robustness for larger variability. The relative merits of PC expansions for the complex modal amplitudes vs the log amplitudes for the complex pressure amplitudes are also discussed.
Published Version
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