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The spatiotemporal dynamics of a turbulent boundary layer subjected to an unsteady pressure gradient are studied. A dynamic sequence of favourable to adverse pressure gradients (FAPGs) is imposed by deforming a section of the wind tunnel ceiling, transitioning the pressure gradient from zero to a strong FAPG within 0.07 s. At the end of the transient, the acceleration parameter is K=6x10^-6 in the favourable pressure gradient (FPG) region and K=-4.8x10^-6 in the adverse pressure gradient (APG) region. The resulting unsteady response of the boundary layer is compared with equivalent steady pressure gradient cases in terms of turbulent statistics and coherent structures. While the steady FAPG effects, as shown by Parthasarathy & Saxton-Fox (2023), caused upstream stabilisation in the FPG, a milder APG response downstream, and the formation of an internal layer, the unsteady case presented in this paper shows a reduced stabilisation in the FPG region, a stronger APG response and a weaker internal layer. This altered response is hypothesised to stem from the different spatiotemporal pressure gradient histories experienced by turbulent structures when the pressure gradient changes at a time scale comparable to their convection. 

A statically deformable ceiling was used at the Turbulence Dynamic Research facility at the University of Illinois at Urbana-Champaign. This facility was used to impose static spatially varying pressure gradients in a favorable-adverse (FAPG) arrangement. This study focuses on the FPG region of this flowfield which experiences a rapid spatial variation of its pressure gradient over 6.2𝛿. Non-time-resolved particle imaging velocimetry data were captured for 6 pressure gradients and 6 Reynolds numbers. This manuscript focuses on 𝑅𝑒𝜏 = 953 and four pressure gradient cases that have maximum acceleration parameters of 𝐾𝑚𝑎𝑥 × 106 = 0, 2.43, 4.77, and 5.97. The Reynolds stresses and turbulent kinetic energy of the boundary layer were investigated. The results were analyzed for the occurrence of relaminarization and it was concluded that no relaminarization occurred in any of the cases. The Reynolds stresses showed behavior suggestive of an internal layer, including knee points in 𝑢′𝑢′. However, no conclusive evidence was found to support this hypothesis. 

Simple, laminar wake flows require many Fourier modes to represent their dynamics, even though they are perfectly periodic with a single period. The spatial form of the Fourier modes alternate between having a maximum value in the center of the wake for odd harmonics and having a zero crossing in the center of the wake for even harmonics of the primary frequency. We demonstrate that the harmonic organization and the alternating shapes of the Fourier modes for simple wakes are direct results of the skewness of the wake, which changes sign at the center of the wake flow and also at different positions in the streamwise direction. Having a non-zero skewness guarantees that more than one Fourier mode is required to represent the dynamics, even for a perfectly periodic signal, and the spatial variation of the skewness explains the alternating structure of the Fourier modes’ shapes. We demonstrate these relationships through a one-dimensional analysis of how Fourier modes relate to skewness in a model problem and by examining the skewness and Fourier modes of a low Reynolds number flow past a flat plate at an angle of attack of 35 degrees. 

The spectral and spatial behavior of the wake of a small cylinder immersed in a turbulent boundary layer at different wall-normal heights is studied and compared to a canonical turbulent boundary layer. Time-resolved particle image velocimetry measurements were taken downstream of the position where the cylinder is immersed. Measurements were also taken in of the unperturbed turbulent boundary layer in the same region without the cylinder for the same freestream velocity. The pre-multiplied energy spectra was computed for the seven cases and compared. Changes to the spectral content of the wake and of the boundary layer were observed for cases where the cylinder was nearer to the wall, while little interaction was observed for cases with the cylinder outside of the boundary layer thickness. Spectral proper orthogonal decomposition modes were calculated at wavelengths relevant to the wake vortex shedding and to the energetic turbulent structures and modifications to the modes were observed for cases with strong interaction. Vortex detection methods were used to visualize the wake and suggested that both a breakdown of periodicity of the vortex spacing and an overall spatial meandering of the wake may be responsible for the spectral modifications observed. 

The preferential organisation of coherent vortices in a turbulent boundary layer in relation to local large-scale streamwise velocity features was investigated. Coherent vortices were identified in the wake region using the Triple Decomposition Method (originally proposed by Kolář) from 2D particle image velocimetry (PIV) data of a canonical turbulent boundary layer. Two different approaches, based on conditional averaging and quantitative statistical analysis, were used to analyze the data. The large-scale streamwise velocity field was first conditionally averaged on the height of the detected coherent vortices and a change in the sign of the average large scale streamwise fluctuating velocity was seen depending on the height of the vortex core. A correlation coefficient was then defined to quantify this relationship between the height of coherent vortices and local large-scale streamwise fluctuating velocity. Both of these results indicated a strong negative correlation in the wake region of the boundary layer between vortex height and large-scale velocity. The relationship between vortex height and full large-scale velocity isocontours was also studied and a conceptual model based on the findings of the study was proposed. The results served to relate the hairpin vortex model of Adrian et al. to the scale interaction results reported by Mathis et al., and Chung and McKeon.