A new roll-type instability has been discovered experimentally. When fluid between two closely spaced, parallel plates is oscillated about an axis midway between the plates, it exhibits an instability that takes the form of longitudinal rolls aligned perpendicular to the axis of rotation. The basic-state oscillatory shear flow, before the onset of rolls, may be viewed as driven by the $\dot{\bm \Omega}\times \hat{\bm r}$ term of the Navier–Stokes equation in the oscillatory reference frame. A regime diagram is presented in a parameter space defined by the maximum amplitude of angular oscillation, α, and the non-dimensional frequency, Φ = ωd2/ν. The equilibrium wavelength of the rolls scales with d, the gap spacing between the plates, and it increases as Φ increases. Supercritical to a weak-roll onset, an abrupt transition to stronger roll amplitude occurs. Photographs of the cell after an impulsive start show the roll development and initial increase in roll wavelength. A variety of phenomena are observed, including wavelength selection via defect creation and elimination, front propagation, secondary wave instabilities, and the transition to turbulence. We also present solutions of the Navier–Stokes equation for the basic-state shear flow in a near-axis approximation. We develop a simple resonance model which shows some promise in understanding the low-α, high-Φ behaviour of strong rolls. A theoretical analysis of this instability is presented by Hall (1994).
Physiologic blood flow is turbulent
