We introduce a noninvasive, quantitative magnetic resonance imaging (MRI) wind-tunnel measurement in flowing gas (>10 m s(-1)) at high Reynolds numbers (Re>10(5)). The method pertains to liquids and gases, is inherently three dimensional, and extends the range of Re to which MRI is applicable by orders of magnitude. There is potential for clear time savings over traditional pointwise techniques. The mean velocity and turbulent diffusivity of gas flowing past a bluff obstruction and a wing section at realistic stall speeds were measured. The MRI data are compared with computational fluid dynamics.

The combined effects of favourable pressure gradient and streamline curvature were studied experimentally using an approximately homogeneous uniformly sheared turbulence. The shear flow was initially generated in a straight wind tunnel, where the turbulence was allowed to develop a fixed stress anisotropy, and then subsequently directed into a curved wind-tunnel test section. Streamwise pressure gradients were applied by convergence of the curved tunnel walls in the plane of the mean shear. In one set of experiments, convergence was applied in the first half of the curved test section, but not in the second half. In another set of experiments, the convergence was applied in the second half of the curved test section, but not in the first. This arrangement permitted the study of application and removal of streamwise pressure gradient to curved shear flow. Measurements showing the response of the turbulence stresses to the changing mean strain rates are reported and are consistent with previous studies which show that stabilizing curvature diminishes the turbulence energy and stresses. The addition of the streamwise strain rate associated with favourable pressure gradient was observed to have the effect of further diminishing the turbulence activity and its overall anisotropy. However, the important shear component of the anisotropy was increased above what it would be under the influence of curvature alone. The removal of streamwise strain rate caused the turbulence to recover a structure similar to that measured for uniformly curved shear flow; although this adjustment included an increase in the shear component of anisotropy prior to its gradual relaxation.The principal direction of the Reynolds stress tensor was found to be closely related to the principal direction of the mean strain rate tensor in the present flows. This result was also found to be valid in the outer layer of accelerating curved boundary layers. A relationship between the direction of the principal mean strain rate and the mean flow curvature and streamwise strain rate was formulated to explain how each influences the state of turbulence stress.

In this work, particular and general solutions to Airy’s inhomogeneous equation are obtained when the forcing function is one of Airy’s functions of the first and second kind, and the standard Nield-Kuznetsov function of the first kind. Particular solutions give rise to special integrals that involve products of Airy’s and Nield-Kuznetsov functions. Evaluation of the resulting integrals is facilitated by expressing their integrands in asymptotic series. Corresponding expressions for the Nield-Kuznetsov function of the second kind are obtained.

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In this work, particular and general solutions to Airy’s inhomogeneous equation are obtained when the forcing function is one of Airy’s functions of the first and second kind, and the standard Nield-Kuznetsov function of the first kind. Particular solutions give rise to special integrals that involve products of Airy’s and Nield-Kuznetsov functions. Evaluation of the resulting integrals is facilitated by expressing their integrands in asymptotic series. Corresponding expressions for the Nield-Kuznetsov function of the second kind are obtained.