We propose a fully spatiotemporal approach for identifying spatially varying modes of oscillation in fluid dynamics simulation output by means of multitaper frequency wavenumber spectral analysis. Two-dimensional frequency wavenumber spectral analysis allows one to decompose waveforms into standing or traveling variety. The extended higher-dimensional multitaper method proposed here is shown to have improved statistical properties over conventional nonparametric spectral estimators, and is accompanied by condence intervals which estimate their uncertainty. Multitaper frequency-wavenumber analysis is applied to a canonical benchmark problem, namely, a DNS of von Karman vortex shedding of a square wall-mounted cylinder with two in flow scenarios with matching momentum-thickness Reynolds numbers Re = 1000 at the obstacle. Frequency-wavenumber analysis of a two dimensional section of these data reveals that although both the laminar and turbulent in flow scenarios show a turbulent -5/3 cascade in the wavenumber and frequency, the flow characteristics dier in that there is a significantly more prominent discrete harmonic oscillation near (f; nu) = (0.2; 0.21) in wavenumber and frequency in the laminar in flow scenario than the turbulent scenario. This frequency-wavenumber pair corresponds to a travelling wave with velocity near one near the centre path of the vortex street.