In a curved channel streamwise vortices, often called Dean vortices, may develop above a critical Reynolds number owing to centrifugal effects. Similar vortices can occur in a rotating plane channel due to Coriolis effects if the axis of rotation is normal to the mean flow velocity and parallel to the walls. In this paper the flow in a curved rotating channel is considered. It is shown from linear stability theory that there is a region for which centrifugal effects and Coriolis effects almost cancel each other, which increases the critical Reynolds number substantially. The flow visualization experiments carried out show that a complete cancellation of Dean vortices can be obtained for low Reynolds number. The rotation rate for which this occurs is in close agreement with predictions from linear stability theory. For curved channel flow a secondary instability of travelling wave type is found at a Reynolds number about three times higher than the critical one for the primary instability. It is shown that rotation can completely cancel the secondary instability.

Experimental results are reported from hot-wire measurements in a narrow gap, curved air channel with a spanwise aspect ratio of 29. The Reynolds numbers (Re) covered a range from 2 to 6.5 times the critical Re, i.e., the Re for which the flow becomes centrifugally unstable according to linear stability theory. For the lowest Re studied, the measurements showed a regular flow pattern of streamwise vortices, whereas at higher Re interaction occurred between vortex pairs. The streamwise disturbance velocity increased rapidly near the inlet section, thereafter the disturbance amplitude overshot before it finally reached a saturated level of the nonlinear stage. At even higher Re a secondary instability in the form of traveling waves appeared on top of the primary instability and was found to be localized between one pair of vortices at the inflow region from the concave wall.

An experimental study is reported of the flow in a high-aspect-ratio curved air channel with spanwise system rotation, utilizing hot-wire measurements and smoke visualization. The experiments were made at two different Dean numbers (De), approximately 2 and 4.5 times the critical De for which the flow becomes unstable and develops streamwise vortices. For the lower De without system rotation the primary Dean instability appeared as steady longitudinal vortices. It was shown that negative spanwise system rotation, i.e. the Coriolis force counteracts the centrifugal force, could cancel the primary Dean instability and that for high rotation rates it could give rise to vortices on the inner convex channel wall. For positive spanwise system rotation, i.e. when the Coriolis force enhanced the centrifugal force, splitting and merging of vortex pairs were observed. At the higher De secondary instabilities occurred in the form of travelling waves. The effect of spanwise system rotation on the secondary instability was studied and was found to reduce the amplitude of the twisting and undulating motions for low negative rotation. For low positive rotation the amplitude of the secondary instabilities was unaffected for most regions in parameter space.

In this paper, we use nonlinear calculations to study curved boundary-layer flows with pressure gradients and self-similar suction or blowing. For an accelerated outer flow, stabilization occurs in the linear region while the saturation amplitude of vortices is larger than for flows with a decelerating outer flow. The combined effects of boundary-layer suction and a favourable pressure gradient can give a significant stabilization of the flow. Streamwise vortices can be amplified on both concave and convex walls for decelerated Falkner-Skan flow with an overshoot in the velocity profile. The disturbance amplitude is generally lower far downstream compared with profiles without overshoot. the wall jet without freestream as described by Glauert [4]. Libby and Liu have shown that there exists at least four branches for adverse pressure gradients and Zaturska and Banks [5] found a new branch related to favourable pressure gradients. Solutions to the Falkner-Skan equation in the form of overshoot velocity profiles have also been included in the textbooks by White [6] and Sobey [7].Overshoot profiles are unstable on both concave and convex walls and streamwise vortices can develop. On curved walls the Görtler number is the appropriate parameter for the stability problem. The Görtler number is defined as Go = Re √ , the curvature parameter = /R, where R is the radius of curvature of the wall and = √ x/U ∞ is the boundary-layer thickness, where x is the streamwise coordinate and is the kinematic viscosity. The Reynolds number is defined as Re = U ∞ / , where U ∞ is the freestream velocity. Streamwise vortices in curved boundary layers have been studied frequently both numerically and experimentally, for a review see Hall [8], Saric [9], and Floryan [10]. However, studies of streamwise vortices in wall jet flows are more sparse. The first parallel neutral stability calculations were made by Kahawita [11] for the Glauert wall jet without freestream. Non-parallel linear stability theory was used by Floryan [12,13], followed by Matsson [14] who studied the influence of system rotation and self-similar suction or blowing on wall jets. Wadey [15] used asymptotic methods for linear theory to study Görtler vortices in wall jet flows for large spanwise wavenumbers. It was found that curved wall jets on both concave and convex walls were more stable to streamwise vortices than boundary-layer flows.An experimental study of streamwise vortices appeared for wall jet flow on a concave wall, see Matsson [16], followed by nonlinear simulations of the same flow by Le Cunff and Zebib [17]. The simulations were able to capture the primary instability of streamwise vortices in the experiments. They also found that for low Görtler numbers the disturbance amplitude initially could be increased but the amplitude further downstream attained an amplitude which was lower than the starting level. However, at higher Görtler numbers the streamwise vortices increased exponentially in amplitude followed by a maximum and an almost constant level furt...

Hot-wire anemometry, smoke visualization and nonlinear calculations were used to study the wall jet on a cylinder with rotation. It was found that streamwise vortices are amplified in convex wall jet flow without rotation and that the maximum amplitude was higher than for the concave case. Furthermore, the transition region was located downstream compared with the concave wall jet. Rotation was found to destabilize the convex wall jet, i.e., the transition region appeared upstream compared with nonrotation.