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Fig. 6 | Progress in Earth and Planetary Science

Fig. 6

From: Deep magnetic field stretching in numerical dynamos

Fig. 6

Intense high-latitude normal polarity magnetic flux patch (HN) in dynamo model 1 (Fig. 5): radial magnetic field B r (colors) and the tangential flow \(\vec {u}_{h}\) (arrows) at a mid-depth and at b the top of the free stream just below the Ekman boundary layer. The velocity arrows in a and b have the same scale. The following quantities are all at mid-depth: c radial vorticity ω r , d tangential divergence δ h , e tangential advection SV, f tangential stretching SV, g radial advection SV, h radial stretching SV, and i total frozen-flux SV. Also in j, the radial flow u r (colors) and the tangential magnetic field \(\vec {B}_{h}\) (arrows) are shown. All variables are non-dimensional. The mid-depth patch in a is shifted with respect to the outer boundary patch in b by δ𝜗=1.88° and δφ=−1.88° with an auto-correlation of 0.68. The local statistics for this patch are as follows: Ad r /Ad h =0.62; St r /St h =1.69; St h /Ad h =0.39; St/Ad=0.78; \(\mathcal {P}/\mathcal {T}=0.41\); and \(\|u_{r}\|/\|\vec {u}_{h}\|=0.62\)

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