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A nonlinear ensemble-variational (EnVar) data assimilation is performed inorder to estimate the unknown flow field over a slender cone at Mach-6, fromisolated wall-pressure measurements. The cost functional accounts fordiscrepancies in wall-pressure spectra and total intensity between theexperiment and the prediction using direct numerical simulations (DNS), as wellas our relative confidence in the measurements and the estimated state. Wedemonstrate the robustness of the predicted flow by direct propagation ofposterior statistics. The approach provides a unique first look at the flowbeyond the sensor data, and rigorously accounts for the role of nonlinearityunlike previous efforts that adopted ad-hoc inflow syntheses. Away from thewall, two- and three-dimensional assimilated states both show rope-likestructures, qualitatively similar to independent schlieren visualizations.Despite this resemblance, and even though the planar second modes are the mostunstable upstream, three-dimensional (3D) waves must be included in theassimilation in order to accurately reproduce the wall-pressure measurementsrecorded in the Ludwieg-Tube facility. The results highlight the importance ofthree-dimensionality of the field and of the base-state distortion on theinstability waves in this experiment, and motivate future measurements thatprobe the 3D nature of the flow field.

Assimilation of wall-pressure measurements in high-speed flow over a cone