BACKGROUND Patients with peripheral artery disease have an increased risk of cardiovascular morbidity and mortality. Antiplatelet agents are widely used to reduce these complications. METHODS This was a multicentre, double-blind, randomised placebo-controlled trial for which patients were recruited at 602 hospitals, clinics, or community practices from 33 countries across six continents. Eligible patients had a history of peripheral artery disease of the lower extremities (previous peripheral bypass surgery or angioplasty, limb or foot amputation, intermittent claudication with objective evidence of peripheral artery disease), of the carotid arteries (previous carotid artery revascularisation or asymptomatic carotid artery stenosis of at least 50%), or coronary artery disease with an ankle-brachial index of less than 0·90. After a 30-day run-in period, patients were randomly assigned (1:1:1) to receive oral rivaroxaban (2·5 mg twice a day) plus aspirin (100 mg once a day), rivaroxaban twice a day (5 mg with aspirin placebo once a day), or to aspirin once a day (100 mg and rivaroxaban placebo twice a day). Randomisation was computer generated. Each treatment group was double dummy, and the patient, investigators, and central study staff were masked to treatment allocation. The primary outcome was cardiovascular death, myocardial infarction or stroke; the primary peripheral artery disease outcome was major adverse limb events including major amputation. This trial is registered with ClinicalTrials.gov, number NCT01776424, and is closed to new participants. FINDINGS Between March 12, 2013, and May 10, 2016, we ; HR 0·67, 95% CI 0·45-1·00, p=0·05). The median duration of treatment was 21 months. The use of the rivaroxaban plus aspirin combination increased major bleeding compared with the aspirin alone group (77 [3%] of 2492 vs 48 [2%] of 2504; HR 1·61, 95% CI 1·12-2·31, p=0·0089), which was mainly gastrointestinal. Similarly, major bleeding occurred in 79 (3%) of 2474 patients with rivaroxaban 5 mg, and in 48 (2%) of 2504 in the aspirin alone group (HR 1·68, 95% CI 1·17-2·40; p=0·0043). INTERPRETATION Low-dose rivaroxaban taken twice a day plus aspirin once a day reduced major adverse cardiovascular and limb events when compared with aspirin alone. Although major bleeding was increased, fatal or critical organ bleeding was not. This combination therapy represents an important advance in the management of patients with peripheral artery disease. Rivaroxaban alone did not significantly reduce major adverse cardiovascular events compared with asprin alone, but reduced major adverse limb events and increased major bleeding. FUNDING Bayer AG. Methods This was a multicentre, double-blind, randomised placebo-controlled trial for which patients were recruited at 602 hospitals, clinics, or community practices from 33 countries across six continents. Eligible patients had a history of peripheral artery disease of the lower extremities (previous peripheral bypass surgery or angioplasty, limb or foot amputation, i...

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.

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Incompressible flow over a backward-facing step is studied in order to investigate the flow characteristics in the separated shear-layer, the reattachment zone, and the redeveloping boundary layer after reattachment. Two different step-heights are used: h/δs = 2.2 and h/δs = 3.3. The boundary layer at separation is turbulent for both cases. Turbulent intensities and shear stress reach maxima in the reattachment zone, followed by rapid decay near the surface after reattachment. Downstream of reattachnent, the flow returns very slowly to the structure of an ordinary turbulent boundary layer. In the reattached layer the conventional normalization of outerlayer eddy viscosity by U∞ δ* does not collapse the data. However, it was found that normalization by U∞ (δ − δ*) does collapse the data to within ± 10% of a single curve as far downstream as x/xR ≈ 2, the last data station. This result illustrates the strong downstream persistence of the energetic turbulence structure created in the separated shear layer.

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.

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Two experiments (δ/R = 0.05 and 0.10) were performed to determine how boundary-layer turbulence is affected by strong convex curvature. The flow passed from a flat surface, over convex surface with 90° of turning, and then onto a flat recovery surface. The pressure gradient along the test surface was forced to be zero.After the sudden introduction of curvature, the shear stress in the outer part of the boundary layer is sharply diminished. The wall shear also drops off quickly downstream. When the surface suddenly becomes flat again, the wall-shear and the shear-stress profiles recover very slowly towards flat-wall conditions. The shear-stress profiles in the curved region for both experiments collapse when $-\overline{uv}/u^2_{\tau}$ is plotted vs. distance from the wall normalized on wall radius, n/R. The strong-curvature data of So & Mellor also fall on the same curve. Thus suggests an asymptotic state for the shear-stress profiles of strongly curved boundary layers where R rather than boundary-layer thickness controls the active turbulence lengthscales. In this asymptotic region, the active shear-layer thickness is less than its initial value at the start of curvature. In the recovery region, the width of the active shear layer regrows slowly within the original velocity-gradient boundary layer, like a developing boundary layer under a free stream with a velocity gradient normal to the wall.

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