Fig. 4.

Geometric interpretations of spatially decomposed helicity contributions. Panel a: geometrical interpretation of the spatial contribution Clmn ⋅ Blmn of a spatial (wavelet) decomposition of the helicity. The red box represents the spatial sub-domain given by the triplet lmn. Each point in this red domain contributes a winding with the rest of the field in the plane in which it is contained. Because Clmn ⋅ Blmn is a sum over the whole red domain, the set of planes containing the red domain provide winding contributions to the sum, as indicated in the figure. Panel b: winding contribution obtained by spatially decomposing the field B inside the two-point correlation function. It represents the winding of the red curve γ (localised in the plane as represented by the vector B at that point) and the field lines in the sub-plane indicated in green.
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