Turbulence control via geometry modifications and electromagnetic fields

摘要

We examine five numerical data bases from spectral element simulations of turbulent channel flow with one of the walls subject to either geometric modification or covered by streamwise electromagnetic strips. Two of the cases correspond to drag decreasing and the other three to drag increasing states, compared to the smooth unperturbed wall. The fact that the divergence of the Reynolds stress tensor equals the average Lamb vector motivates us to write the Reynolds stress gradient that dominates over a flat wall, i.e. {partial deriv}(u' v'){top}(-)/{partial deriv}x_2, as the sum of the streamwise component of the Lamb vector and the spanwise variation of the turbulent stress T_3={partial deriv}(u' v'){top}(-)/{partial deriv}x_3. The streamwise component of the Lamb vector consists of a vortex stretching term, i.e. (ω'(ω_2)'){top}(-), and a vortex transport term. We analyze the contributions associated with vortex transport, vortex stretching, and spanwise variations of the stress component (u' ω'){top}(-). We found that an increase of the vortex stretching term is associated with an increase of the Reynolds stress and shear stress. For a non-smooth wall, T_3 achieves large positive and negative values at the valleys and the tips of the roughness elements, respectively. The above analysis suggests two ways of reducing the drag: The first is to prevent the appearance of normal vorticity, and the second to create valleys at the wall so that the T_3 component becomes negative. In addition to this standard approach, we invoke the concept of turbulent charge, which is the divergence of the Lamb vector. We present the spatial distribution of this quantity and briefly analyze its connection to the problem of drag reduction.