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This work investigates the spatio-temporal evolution of coherentstructures inthe wake of a generic high-speed train. Spectral properorthogonal decompositionis used to extract energy spectra and empiricalmodes of the fluctuating field.The spectrum of the symmetriccomponent shows overall higher energy and morepronounced low-rankbehavior compared to the antisymmetric one, with the mostdominantsymmetric mode at $\omega=3.437$ characterized by vortex sheddingin thenear wake and constant streamwise wavenumber structures in thefar wake. Themode bispectrum further reveals the dominant role of selfinteraction of thesymmetric component, leading to first harmonic andsubharmonic triads of thefundamental frequency. Then, the stability ofthe wake flow is analyzed based ontwo-dimensional local analysis. Theabsolute frequency of the near-wakeeigenmode is determined based onspatio-temporal analysis, then tracked alongthe streamwise direction tofind out the global frequency, which indicate amarginally stable globalmode oscillating at a frequency very close to thedominant SPOD mode.The global mode wavemaker is then located, and thestructuralsensitivity is calculated based on the direct and adjoint modesderivedfrom a local spatial analysis, with the maximum value localizedwithinthe recirculation region close to the train tail. Finally, the globalmodeshape is computed by tracking the most spatially unstable eigenmode,and thealignment with the SPOD mode is computed as a function ofstreamwise location.By combining data-driven and theoreticalapproaches, the mechanisms of coherentstructures in complex wakeflows are well identified and isolated.

Linear stability and spectral modal decomposition of three-dimensional turbulent wake flow of a generic high-speed train