Controlling secondary flows in Taylor-Couette flow using stress-free boundary conditions

Taylor-Couette (TC) flow, the flow between two independently rotating and co-axial cylinders, is known to have pinned secondary flows known as Taylor rolls. We study the possibility of affecting these secondary structures using one- and two-dimensional patterns of stress-free and no-slip boundary conditions on the inner cylinder. For this, we perform direct numerical simulations of TC flow with pure inner cylinder rotation at three different shear Reynolds numbers up to $Re_s=3 \times 10^4$, fixing the radius ratio to $\eta=0.909$. We find that one-dimensional azimuthal patterns do not have a significant effect on the flow. However, one-dimensional axial patterns disrupt the rolls by interfering with the Reynolds stress that is responsible for secondary structures and decrease the torque substantially. Two-dimensional spiral inhomogeneities lie somewhere between the previous two cases. It affects the torque and imparts axial velocity thus moving the pinned secondary flows. We quantify the roll's movement for various angles and the widths of the spiral pattern, and find that the maximum speed is a non-monotonic function of pattern angle and pattern frequency. Finally, we find that two-dimensional checkerboard patterns do not affect the flow or the torque substantially.