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Recent treatments of flute-mode-type turbulence in closed magnetic flux surface geometry align the coordinates to the magnetic field, leaving the field with one nonvanishing contravariant component. Magnetic shear leads to strong deformation of coordinate cells in the plane perpendicular to the field, impacting the results. To remedy this one can apply shifts in the drift angle coordinate, the one which remains purely periodic. All operations involving polarization and nonlinear advection are then performed locally on an orthogonal grid, allowing arbitrarily sheared and shaped magnetic geometries in computations.
B. Scott (Thu,) studied this question.