The low-frequency unsteadiness of oblique shock wave/boundary layer interactions (SBLIs) has been investigated using large-eddy simulation (LES) and high-frequency pressure measurements from experiments. Particular attention has been paid to off-centreline behaviour: the LES dataset was generated including sidewalls, and experimental pressure measurements were acquired across the entire span of the reflected shock foot. The datasets constitute the first maps of low-frequency unsteadiness in both streamwise and spanwise directions. The results reveal that significant low-frequency shock motion (with $St\approx 0.03$) occurs away from the centreline, along most of the central separation shock and in the corner regions. The most powerful low-frequency unsteadiness occurs off-centre, likely due to the separation shock being strengthened by shocks arising from the swept interactions on the sidewalls. Both simulation and experimental results exhibit asymmetry about the spanwise centre. In simulations, this may be attributed to a lack of statistical convergence; however, the fact that this is also seen in experiments is indicative that some SBLIs may exhibit some inherent asymmetry across the two spanwise halves of the separation bubble. There is also significant low-frequency power in the corner separations. The relation of the unsteadiness in the corner regions to that in the centre is investigated by means of two-point correlations: a key observation is that significant correlation does not extend across the attached flow channel between the central and corner separations.

This paper examines the kinematic behaviour of the reduced velocity gradient tensor (VGT),Ã ij , which is defined as a 2 × 2 block, from a single interrogation plane, of the full VGT A ij = ∂u i /∂x j . Direct numerical simulation data from the fully developed turbulent region of a nominally two-dimensional mixing layer are used in order to examine the extent to which information on the full VGT can be derived from the reduced VGT. It is shown that the reduced VGT is able to reveal significantly more information about regions of the flow in which strain rate is dominant over rotation. It is thus possible to use the assumptions of homogeneity and isotropy to place bounds on the first two statistical moments (and their covariance) of the eigenvalues of the reduced strain-rate tensor (the symmetric part of the reduced VGT) which in turn relate to the turbulent strain rates. These bounds are shown to be dependent upon the kurtosis of ∂u 1 /∂x 1 and another variable defined from the constituents of the reduced VGT. The kurtosis is observed to be minimised on the centreline of the mixing layer and thus tighter bounds are possible at the centre of the mixing layer than at the periphery. Nevertheless, these bounds are observed to hold for the entirety of the mixing layer, despite departures from local isotropy. The interrogation plane from which the reduced VGT is formed is observed not to affect the joint probability density functions (p.d.f.s) between the strain-rate eigenvalues and the reduced strain-rate eigenvalues despite the fact that this shear flow has a significant mean shear in the cross-stream direction. Further, it is found that the projection of the eigenframe of the strain-rate tensor onto the interrogation plane of the reduced VGT is also independent of the plane that is chosen, validating the approach of bounding the full VGT using the assumption of local isotropy.

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