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Notes on McIntyre (1980)

On the meaning of ‘displacement’

“If the disturbance motion is the dominant motion, the meaning of ‘displacement’ is fairly obvious ab initio and is such that if [the Eulerian mean] is the time mean at a fixed point, then [the Lagrangian mean] is the time mean following a single fluid parcel, at least approximately.” (p. 131)

On the divergence of the Lagrangian-mean flow

“The classical Lagrangian-mean motion is evidently divergent; and it can be shown directly from (12) [Taylor expansion of the Stokes correction] that the effect is O(a*^2) and therefore comparable with all other mean effects of the waves even when their amplitude *a is arbitrarily small”

Question: So why Moore (1970) proves that the Lagrangian-mean flow is nondivergent?