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Vertical spectra of temperature perturbations are due to (i) internal wave displacement in the mean profile and (ii) fine-structure that would still be measured in the absence of internal waves. The former is probably confined to low wavenumbers, but at a lower energy level could be responsible for some of the reported fine-structure. The latter is distorted by the internal waves and differs from the true fine-structure spectrum by an amount proportional to the mean-square strain of internal waves.
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Christopher Garrett (1973) studied this question.
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