Modulation of vorticity flux from wall-pressure footprints via continuous data assimilation

This study makes a twofold contribution regarding vorticity flux modulation by wall-pressure ‘footprints’. First, we present a continuous data assimilation (DA) framework for reconstructing flow fields from wall-pressure observations by embedding an adjoint-derived scalar source into the pressure Poisson equation. By leveraging elliptic pressure–velocity coupling, the method propagates wall-driven corrections across the domain, and avoids the costly global backward integration of four-dimensional variational DA while retaining phase-aware control of vorticity production and modal energy. Second, we validate the framework on a three-dimensional turbulent flow over a NACA0012 aerofoil at 12 Superscript ring 12 ∘ $12^{\\circ}$ , using synthetic wall-pressure data from high-fidelity large eddy simulations (LES). The DA strategy mitigates unresolved transition physics in coarse simulations by suppressing premature separation, restoring attachment, and recovering key flow metrics with near-LES fidelity. Spectral and wavelet analyses further demonstrate that the reconstruction captures both the scale-dependent energy distribution and the spatial coherence of the dominant structures. Two complementary mechanisms are identified: (i) an oscillator-like mechanism, where phase-locked tangential pressure gradients couple with normal vorticity gradients to modulate near-wall vorticity through linear and nonlinear interactions; and (ii) an amplifier-like mechanism, where trailing-edge inputs propagate upstream via scale-dependent elliptic coupling, exciting receptivity modes, and triggering transition cascades through Orr mechanisms and resolvent-matched instabilities. The sensor coverage study reveals scale-dependent sensitivity: streamwise-elongated motions remain robust under sparse arrays, whereas spanwise-dominated structures require near-wall sensing. These findings broaden the scope of continuous DA for wall-bounded flow reconstructions, offering a computationally efficient way to incorporate wall-pressure observations into existing solvers for enhanced accuracy.