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The heat and mass transfer characteristics of a simple shear flow over a surface covered with staggered herringbone structures are numerically investigated using the lattice Boltzmann method. Two flow motions are identified. The first is a spiral flow oscillation above the herringbone structures that advect heat and mass from the top plane to herringbone structures. The second is a flow recirculation in the grooves between the ridges that advect heat and mass from the area around the tips of the structures to their side walls and the bottom surfaces. These two basic flow motions couple together to form a complex transport mechanism. The results show that when advective heat and mass transfer takes effect at relatively large Reynolds and Schmidt numbers, the dependence of the total transfer rate on Schmidt number follows a power law, with the exponent being the same as that in the Dittus–Boelter equation for turbulent heat transfer. As the Reynolds number increases, the dependence of the total transfer rate on the Reynolds number also approaches a power law, and the exponent is close to that in the Dittus–Boelter equation.