  We introduce a geometric analysis of turbulent mixing in density-stratified
flows based on the alignment of the density gradient in two orthogonal bases
that are locally constructed from the velocity gradient tensor. The first basis
connects diapycnal mixing to rotation and shearing motions, building on the
recent 'rortex-shear decomposition' in stratified shear layers (Jiang et al.,
J. Fluid Mech. 947, A30, 2022), while the second basis connects mixing to the
principal axes of the viscous dissipation tensor. Applying this framework to
datasets taken in the stratified inclined duct laboratory experiment reveals
that density gradients in locations of high shear tend to align preferentially
(i) along the direction of minimum dissipation and (ii) normal to the plane
spanned by the rotex and shear vectors. The analysis of the local alignment
across increasingly turbulent flows offers new insights into the intricate
relationship between the density gradient and dissipation, and thus diapycnal
mixing.
