A region-based stochastic reduced-order model for resolvent analysis and directional coupling in a turbulent axisymmetric wake

We present an interpretable reduced-order model for a turbulent axisymmetric wake in region space. Time-resolved planar particle image velocimetry snapshots are partitioned into fixed recirculation (R), shear-layer (S), and outer-wake (O) regions, and each region is represented by its integrated in-plane fluctuation energy. This yields a compact three-state description that remains directly tied to the main wake regions. A linear region-to-region map is identified from the data and combined with measured multivariate residual forcing in a discrete resolvent framework to reconstruct band-dependent spectra and directional coupling. Resolvent analysis, spectral Granger causality, and coupling-direction diagnostics reveal three frequency-dependent regimes, including a recirculation-led very-low-frequency regime, a transitional bubble-pumping regime with broader regional participation, and a shear-led vortex-shedding regime in which cross-region forcing covariance has its strongest influence. Across all bands, only about one-third of the forcing power aligns with the most amplified forcing direction, showing that linear operator gain alone cannot explain the observed spectra. These results demonstrate that a low-order wake model can remain physically interpretable while capturing both the identified linear region-to-region dynamics and the multiregion forcing structure that shapes the measured spectral response.