Reynolds stress analysis of EMHD-controlled wall turbulence. Part I. Streamwise forcing

In this work we investigate numerically turbulent flow of low electrical conductivity fluid subject to electro-magnetic (EMHD) forcing. The configuration is similar to the one considered in the experimental work of Henoch and Stace [Phys. Fluids 7, 1371 (1995)] but in a channel geometry. The lower wall of the channel is covered with alternating streamwise electrodes and magnets to create a Lorentz force in the positive streamwise direction. Two cases are considered in detail corresponding to interaction parameter values of 0.4 (case 1) and 0.1 (case 2). The effect of switching off and on the electrodes is also studied for the two cases. At the Reynolds number considered (Re_τ≈200), a drag increase was obtained for all cases, in agreement with the experiments of Henoch and Stace. A Reynolds stress analysis was performed based on a new decomposition of the gradients normal to the wall of the Reynolds stress $\overline{\mathrm{-u\prime v\prime }}.$ It was found that the vortex stretching term $\overline{{\mathrm{w\prime w}}_2\prime }$ and the spanwise variation of the stress component $\overline{\mathrm{u\prime w\prime }}$ are responsible for the drag increase. More specifically, the term $\partial \overline{\mathrm{(u\prime w\prime )}}{\mathrm{/\partial x}}_3$ is associated with secondary vortical motions in the near-wall and becomes large and positive for large shear stress in regions where fluid is moving toward the wall. In contrast, negative values are associated with regions of lower shear where fluid is being lifted away from the wall. Unlike the unperturbed flow, in the controlled flow high speed near-wall streamwise jets are present (case 1) even in the time-averaged fields. Other changes in turbulence structure are quantified using streak spacing, vortex lines, vorticity quadrant analysis, and plots of the rms value of the vorticity angle.