Vertical profiles of scalar horizontal winds have been measured at high resolution (10m) in the 13 to 37 km region of the stratosphere. This resolution (at that range of altitude) represents the state‐of‐the‐art, and is unique. Our goal was to ascertain whether or not the internal waves of the stratosphere behave consistently with the Garrett‐Munk model which was originally created for oceanic internal waves. The power spectral densities (PSD's) of five profiles are presented and it is found that (a) they closely fit a straight line on a log‐log graph even to wavelengths as small as 40m, and (b) the average slope is −2.7 ± .2 (standard error = 0.1). We conclude that (a) stratospheric internal waves obey the Garrett‐Munk model for vertical wave numbers, and (b) there is no statistically significant evidence for a break in the curve at high wave numbers when due allowance is made for aliasing effects.

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Comparison is made of C(2)(n) profile measurements obtained with a stellar scintillometer and uhf 440-MHz radar. The scintillometer C(2)(n) was obtained at altitude positions between 5 and 18 km, each with a broad height resolution. The radar C(2)(n) was obtained at 400-m intervals with 550-m height resolution. The radar C(2)(n) measurements, when smoothed with the scintillometer weighting function, are in good agreement with the scintillometer C(2)(n) measurements.

The Mellin transform is used to diagonalize the dilation operator in a manner analogous to the use of the Fourier transform to diagonalize the translation operator. A power spectrum is also introduced for the Mellin transform which is analogous to that used for the Fourier transform. Unlike the case for the power spectrum of the Fourier transform where sharp peaks correspond to periodicities in translation, the peaks in the power spectrum of the Mellin transform correspond to periodicities in magnification. A theorem of Wiener-Khinchine type is introduced for the Mellin transform power spectrum. It is expected that the new power spectrum will play an important role extracting meaningful information from noisy data and will thus be a useful complement to the use of the ordinary Fourier power spectrum.