Abstract
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 the 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 principle 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 above the thermocline in
the gyres, the vertical structure of the along-stream diffusivity
follows that of the rms eddy velocity, with the depth-independent
constant of proportionality a local energy-containing scale defined by
the peak of the surface eddy kinetic energy (EKE) spectrum. The
diffusivity below the thermocline in the gyres instead follows the
profile of the EKE 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. A scaling 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.