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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.more » « lessFree, publicly-accessible full text available July 27, 2025
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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.more » « less
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Modal analysis techniques have proven useful in understanding and modeling turbulent phenomena. However, these techniques are more efficient in parallel flows where Fourier transforms can be taken along homogeneous directions. We suggest that quasi-1D methods can be applied to mildly non-canonical flows by using a curvilinear coordinate system. For a given base flow, we identify a curvilinear coordinate system that allows the Fourier-transformed equations of motion to be simplified into a quasi-1D system that can be efficiently analyzed.more » « less
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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.more » « less