Direct numerical simulations are performed to investigate the countergradient transport of heat and momentum in homogeneous shear turbulence under stable thermal stratification. The simulations are conducted at a Reynolds number of $\mathrm{Re}=5000$, with Richardson numbers set to 0, 0.1, and 0.2. The clustering method is employed to analyze $Q1$ and $Q3$ structures, which drive the countergradient transport in the quadrant classification of vertical heat flux and momentum. The structural characteristics and spatial distributions of these structures are systematically evaluated and compared with previous research findings. The results reveal that most countergradient transport originates from structures larger than the Corrsin scale, and their volumetric contribution increases with stratification intensity. Furthermore, the paired $Q1$ and $Q3$ structures are characterized by analogous spatial patterns and exhibit a strong association with vortical structures. Specifically, the countergradient transport of heat is driven by the interaction between the cold and hot fluid parcels or the vortex-induced rotation, whereas the countergradient transport of momentum is solely attributed to the vortex-induced rotation. These findings provide improved insight into the dynamics of countergradient transport under stable thermal stratification and highlight the critical role of vortical structures in driving these processes.

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• Shear flows
• Turbulence
• Buoyancy
• Direct numerical simulations
• Navier-Stokes equation
• Statistical methods