Spectral characterization of thermo-fluid structures in wall-bounded high-pressure transcritical turbulence

Direct numerical simulations of high-pressure transcritical carbon dioxide in a differentially-heated minimal-flow-unit channel are used to examine the spatiotemporal organization of turbulence in high-pressure transcritical fluids. By applying spectral proper orthogonal decomposition with an energy inner product that weights both hydrodynamic and thermodynamic fluctuations, the leading coherent modes of the flow are characterized. Across all studied conditions, a robust, slow-band mode emerges as a wall-attached, streamwise-elongated sheet that occupies a large fraction of the channel. Within this structure, a clear co-location is observed between velocity and temperature fluctuations, particularly where the pseudo-boiling layer intersects the near-wall hot region. While increasing bulk pressure diminishes the thermal signature of this mode, the underlying hydrodynamic sheet persists. A distinct, higher-frequency branch is also observed, but only conditionally: it appears exclusively in low-supercritical-pressure, large-temperature-difference configurations. The hot wall, in contrast, displays broader spanwise spacing within the slow band but lacks this separate high-frequency mode. Taken together, these results suggest that the turbulent flow is built on a coherent-structure scaffold comprising a universal slow-band hydrodynamic sheet and a conditional, high-frequency thermal branch on the cold side. This implies that reduced-order models must retain both elements and the coupled weighting of hydrodynamic and thermodynamic perturbations to accurately capture the flow physics.