Experiments on fully developed turbulent flow in a channel which is rotating at a steady rate about a spanwise axis are described. The Coriolis force components in the region of two-dimensional mean flow affect both local and global stability. Three stability-related phenomena were observed or inferred: (i) the reduction (increase) of the rate of wall-layer streak bursting in locally stabilized (destabilized) wall layers; (ii) the total suppression of transition to turbulence in a stabilized layer; (iii) the development of large-scale roll cells on the de-stabilized side of the channel by growth of a Taylor-Gortler vortex instability.An appropriate local stability parameter is the Richardson number formulated by Bradshaw (1969) for this case and the analogous cases of flow over curved walls and of shear-layer flow with density stratification. Local effects of rotational stabilization, such as reduction of the turbulent stress in wall layers, can be related to the local Richardson number in a simple way. This paper not only investigates this effect, but also, by methods of flow visualization, exposes some of the underlying structure changes caused by rotation.

The stability of laminar and turbulent channel flow is examined for cases where Coriolis forces are introduced by steady rotation about an axis perpendicular to the plane of mean flow. Linearized equations of motion are derived for small disturbances of the Taylor type. Conditions for marginal stability in laminar Couette and Poiseuille flow correspond, in part, to the analogous solutions of buoyancy-driven convection instabilities in heated fluid layers, and to those of Taylor instabilities in the flow between rotating cylinders. In plane Poiseuille flow with rotation, the critical disturbance mode occurs at a Reynolds number of Rec= 88.53 and rotation number Ro= 0.5. At higher Reynolds numbers, unstable conditions canexist over the range of rotation numbers given by 0 < Ro< 3, provided the undisturbed flow remains laminar. A two-layer model is devised to investigate the onset of longitudinal instabilities in turbulent flow. The linear disturbance equations are solved essentially in their laminar form, whereby the velocity gradient of laminar flow is replaced by a numerically computed profile for the gradient of the turbulent mean velocity. The turbulent stress levels in the stable and unstable flow regions are represented by integrated averages of the eddy viscosity. Onset of instability for Reynolds numbers between 6000 and 35 000 is predicted to occur at Ro= 0.022, a value in remarkable agreement with the experimentally observed appearance of roll instabilities in rotating turbulent channel flow.

Underwater towing experiments were carried out with a rectangular airfoil of aspect ratio 5.3 at 4° and 8°a ngles of attack and at chord-based Reynolds numbers between 2.2 x 10 5 and 7.5 x 10 5 . Tangential velocity measurements in the downstream region between 100 and 1000 chord lengths indicate rates of vortex decay proportional to r 7/8 at 8°, whereas previous flight tests show that the decay rate approaches £~1 /2 far downstream. The observed behavior is explained in terms of an analytical solution that includes time dependence of the turbulent eddy viscosity, V T ~ t m . It shows that, for m > 0, an isolated turbulent vortex decays faster than t~1 /2 . In this case, the decay is accompanied by increasing v r , or levels of turbulence, which corresponds to turbulent nonequilibrium flow. The special case of vortex decay with equilibrium flow (m = 0) leads to the well-known decay rate 2 . Since, in towing tank experiments at low Reynolds number, turbulent vortex decay may occur predominantly in nonequilibrium, it is doubtful that such tests correctly predict the late stage of decay of aircraft trailing vortices, when turbulence is the only dissipating mechanism. Nomenclaturea = core radius b = wing span c -wing chord AH = head loss in boundary layer p = pressure p m = fluid pressure as r -> oo p(0) = pressure on the vortex axis r = radius measured from vortex axis t = time At = time difference in velocity measurement T = time parameter, T -F^ t/c 2 U ^ -towing speed v = tangential velocity component v a = tangential velocity at r = a w = axial velocity component vv 0 = axial velocity on vortex axis z = downstream distance behind airfoil ex = angle of attack /? = constant of proportionality, Eq. (6) F = circulation F a = circulation at core radius F^ = circulation of wing 0, A0 = angle in velocity measurement v = kinematic viscosity V T = eddy viscosity (v T /v) a = eddy viscosity at core radius p = fluid density Superscripts m = exponent in expression for time-dependent V T , Eq. (7)Subscripts a = conditions at the core radius, r = a v e = effective viscosity (v T /v) 0 = eddy viscosity level after rollup 0 = conditions on the vortex axis, r -0 oo = conditions at r = GO