Fig. 8

Flow and buoyancy correlations of the coupled Earth dynamo model. a The modulus of the variance-normalized hydrodynamic covariance matrix, showing the correlation between the toroidal flow coefficients at the core surface (y-axis) and the buoyancy field coefficients at various depth levels (x-axis). Correlations are shown up to spherical harmonic degree 10. Coefficients are ordered according to a one-dimensional scheme where all admissible values of the degree n are grouped together for a given value of the order m, leading to iso-m blocks of decreasing size along the diagonal of the matrix. The two blue tracks have (n,m) _x =(1,1), (n,m) _y =(2,1) (track 1) and (n,m) _x =(7,7), (n,m) _y =(10,7) (track 2). b Same as a, for the toroidal flow coefficients at various depth levels. Due to boundary conditions, the sole non-zero line at the inner-core boundary is the one corresponding to (n,m) _x =(1,0). The two red tracks have (n,m) _x =(n,m) _y =(1,0) (track 1) and (n,m) _x =(6,5), (n,m) _y =(10,5) (track 2). c Modulus of correlation along the tracks defined above. ICB and CMB stand for inner-core boundary and core-mantle boundary, respectively