The Spectral Gap

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Abstract
The primary problem we discussed is how to distinguish by means of spectral analysis the different types of dynamics believed to be dominant on different scales in the atmosphere; in particular, synoptic scales (dominated by rotation), mesoscale (waves or buoyancy), and microscale (‘turbulence’). The group rapidly concluded that they did not know how to do this, even in principle, and this report describes their observations on the subject.For this purpose, spectra should be plotted (Figure 1) such that the area under a given portion of the graph is directly proportional to the contribution to the mean‐square fluctuation. All spectra are based on an average over an ensemble of realizations of the relevant field: 1. by combining records taken on separate occasions, or 2. by subdividing a continuous record into separate parts, or 3. by taking a Fourier series for a single record and smoothing the result, (which is ultimately equivalent to no. 2 above).

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