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Spectral proper orthogonal decomposition (SPOD) is an increasingly popularmodal analysis method in the field of fluid dynamics due to its specificproperties: a linear system forced with white noise should have SPOD modesidentical to response modes from resolvent analysis. The SPOD, coupled with theWelch method for spectral estimation, may require long time-resolved data sets.In this work, a linearised Ginzburg-Landau model is considered in order tostudy the method's convergence. SPOD modes of the white-noise forced equationare computed and compared with corresponding response resolvent modes. Thequantified error is shown to be related to the time length of Welch blocks(spectral window size) normalised by a convective time. Subsequently, analgorithm based on a temporal data shift is devised to further improve SPODconvergence and is applied to the Ginzburg-Landau system. Next, its efficacy isdemonstrated in a numerical database of a boundary layer subject to bypasstransition. The proposed approach achieves substantial improvement in modeconvergence with smaller spectral window sizes with respect to the standardmethod. Furthermore, SPOD modes display growing wall-normal and span-wisevelocity components along the stream-wise direction, a feature which had notyet been observed and is also predicted by a global resolvent calculation. Theshifting algorithm for the SPOD opens the possibility for using the method ondatasets with time series of moderate duration, often produced by largesimulations.

Improved convergence of the spectral proper orthogonal decomposition through time shifting