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The relationship between the frictional drag and the velocity-vorticity correlations in wall-bounded turbulent flows is derived from the mean vorticity equation. A formula for the skin friction coefficient is proposed and evaluated with regards to three canonical wall-bounded flows: turbulent boundary layer, turbulent channel flow, and turbulent pipe flow. The frictional drag encompasses four terms: advective vorticity transport, vortex stretching, viscous, and inhomogeneous terms. Drag-reduced channel flow with the slip condition is used to test the reliability of the formula. The advective vorticity transport and vortex stretching terms are found to dominate the contributions to the frictional drag.


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