Zero absolute vorticity: insight from experiments in rotating laminar plane Couette flow

For pressure-driven turbulent channel flows undergoing spanwise system rotation, it has been observed that the absolute vorticity, i.e., the sum of the averaged spanwise flow vorticity and system rotation, tends to zero in the central region of the channel. This observation has so far eluded a convincing theoretical explanation, despite experimental and numerical evidence reported in the literature. Here we show experimentally that three-dimensional laminar structures in plane Couette flow, which appear under anticyclonic system rotation, give the same effect, namely, that the absolute vorticity tends to zero if the rotation rate is high enough. It is shown that this is equivalent to a local Richardson number of approximately zero, which would indicate a stable condition. We also offer an explanation based on Kelvin's circulation theorem to demonstrate that the absolute vorticity should remain constant and approximately equal to zero in the central region of the channel when going from the nonrotating fully turbulent state to any state with sufficiently high rotation.