Simulations of complex turbulent shear flows, including both transverse strain and wall-normal body forces, are presented. Transverse strain creates cross-flow skewing of the mean velocity vectors that reduces momentum and heat transfer rates. In contrast, unstable wall-normal body forces generate large-scale, embedded streamwise vortices that increase vertical mixing and heat transfer rates. We vary two control parameters (related to the magnitude of imposed transverse strain and body force) in turbulent channel flow to evaluate effective methods to control vertical mixing and heat transfer.