Isopycnal mixing of tracers is important for ocean dynamics and
biogeochemistry. Previous studies have primarily focused on the
horizontal structure of mixing, but what controls its vertical structure
is still unclear. This study investigates the vertical structure of the
isopycnal tracer diffusivity diagnosed by a multiple-tracer inversion
method in an idealized basin circulation model. The first two
eigenvalues of the symmetric part of the 3D diffusivity tensor are
approximately tangent to isopycnal surfaces. The isopycnal mixing is
anisotropic, with principal directions of the large and small
diffusivities generally oriented along and across the mean flow
direction. The cross-stream diffusivity can be reconstructed from the
along-stream diffusivity after accounting for suppression of mixing by
the mean flow. In the circumpolar channel and the upper ocean in the
gyres, the vertical structure of the along-stream diffusivity follows
that of the rms eddy velocity times a depth-independent local
energy-containing scale estimated from the sea surface height. The
diffusivity in the deep ocean in the gyres instead follows the profile
of the eddy kinetic energy times a depth-independent mixing time scale.
The transition between the two mixing regimes is attributed to the
dominance of nonlinear interactions and linear waves in the upper and
deep ocean, respectively, distinguished by a nonlinearity parameter. A
formula is proposed that accounts for both regimes and captures the
vertical variation of diffusivities better than extant theories. These
results inform efforts to parameterize the vertical structure of
isopycnal mixing in coarse-resolution ocean models.