Abstract
Phillips has shown that an undulating motion of a layered medium relative to a measuring instrument will result in a σ−2 spectrum (frequency or wavenumber) over a bandwidth determined by the thickness of the layers and of the sheets separating them. We show, for any (temperature) fine-structure statisteally stationary in depth with covariance rθ(y1−y2)=<θ(y1)θ(y2)>, that the covariance of the observed time ceries can be expressed in terms of rθ and the covariance in the vertical displacement ζ, assuming ζ to he josintly normal. An explicit expression for the spectrum is given for the case that the rms value of ζ is large compared to the vertical coherence scale of the fine-structure. We tentatively conclude that the fine-structure dominates in the upper few octaves of the internal wave spectra, and then extends the spectra beyond the cutoff frequency (wavenumber). The loss of vertical coherence due to fine-structure occurs over a distance inversely proportional to frequency, in general agreement with an empirical rule proposed by Webster.
