Interpretation of Internal Wave Measurements in the Presence of Fine-Structure

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  • 1 Applied Physics Laboratory, University of Washington, Seattle, 98195
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Abstract

Philips has pointed out that the measurement of the internal wave spectrum and coherence in a stratified medium is distinctly altered when the profile contains fine-scale layers. Garrett and Munk demonstrated that the measured spectrum can be explicitly calculated in terms of the internal wave distribution and the statistics of the layered medium with the result P0=P+F, where P is the true spectrum and F the fine-structure contamination. The present study is based on a formal modification of the Garrett and Munk method, tailored to describe a medium for which the layers occur, in effect, as a nonstationary Poisson process in the vertical dimension, i.e., a randomly layered ocean. The fine-structure contamination is discussed in detail for the case of a Gaussian internal wave distribution, with a band-limited power law spectrum Pq for ω1<ω<ωn. Above the cutoff (Väisälä) frequency, ωn, the result is F≈omega;−2, in agreement with Phillips and the “fine-structure approximation” of Garrett and Munk. The continuation of F to frequencies below the cutoff, where internal wave energy P is present, depends only on the exponent q and yields the ratio γ=FP−1≈ω(q−1)/2 between these two overlapping spectra. Coherence at vertical spacing Y is treated in similar fashion, based on the Garrett and Munk formula R0=(RGF−1)(1+γ)−1, where GF−1 is termed the fine-structure coherence (FSC). The FSC is calculated and shown to depend only on parameters which are measured, together with the coherence, in a given experiment. For typical ocean internal wave parameters, the FSC is estimated to be negligible for sensor spacings greater than the rms displacement. Application of these results is illustrated with an example of real ocean data.

Abstract

Philips has pointed out that the measurement of the internal wave spectrum and coherence in a stratified medium is distinctly altered when the profile contains fine-scale layers. Garrett and Munk demonstrated that the measured spectrum can be explicitly calculated in terms of the internal wave distribution and the statistics of the layered medium with the result P0=P+F, where P is the true spectrum and F the fine-structure contamination. The present study is based on a formal modification of the Garrett and Munk method, tailored to describe a medium for which the layers occur, in effect, as a nonstationary Poisson process in the vertical dimension, i.e., a randomly layered ocean. The fine-structure contamination is discussed in detail for the case of a Gaussian internal wave distribution, with a band-limited power law spectrum Pq for ω1<ω<ωn. Above the cutoff (Väisälä) frequency, ωn, the result is F≈omega;−2, in agreement with Phillips and the “fine-structure approximation” of Garrett and Munk. The continuation of F to frequencies below the cutoff, where internal wave energy P is present, depends only on the exponent q and yields the ratio γ=FP−1≈ω(q−1)/2 between these two overlapping spectra. Coherence at vertical spacing Y is treated in similar fashion, based on the Garrett and Munk formula R0=(RGF−1)(1+γ)−1, where GF−1 is termed the fine-structure coherence (FSC). The FSC is calculated and shown to depend only on parameters which are measured, together with the coherence, in a given experiment. For typical ocean internal wave parameters, the FSC is estimated to be negligible for sensor spacings greater than the rms displacement. Application of these results is illustrated with an example of real ocean data.

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