Velocity–vorticity correlations related to the gradients of the Reynolds stresses in parallel turbulent wall flows

By using the momentum equations in ‘‘vorticity’’ form, relations between velocity–vorticity correlations and gradients of the Reynolds stresses are established for a two-dimensional turbulent channel flow. Employing these relations, the approximate formulas of Phillips [Phys. Fluids, 30, 2354 (1987)] and recently obtained experimental data allow for unmeasured velocity–vorticity correlation profiles to be deduced. The results herein indicate that the contributions to the gradients of the diagonal stresses are dominated by the correlation involving the spanwise vorticity component, while the contributions to the off-diagonal stresses are shared almost equally between the correlations involving the spanwise and normal vorticity components.