Abstract
<title>Abstract</title> <p>The near-wall region of a turbulent flow maintains a self-sustaining cycleof streaks and quasi-streamwise vortices, and this cycle leaves an uneven signature onthe wall shear stress.We ask how much of the buffer layer dynamics is encoded in the time-evolving wall shear stress, or whether the wall stress is merely a passive footprint. To answer this question, we modelthe underlying dynamical system directly from wall measurements. Using snapshot data from aminimal turbulent channel at \((Re_\tau=180)\), we extract the proper orthogonal decomposition(POD) modes of the streamwise and spanwise wall shear stresses and approximate their attractorusing radial basis functions (RBFs) with trajectory-adapted kernel widths. This yields adifferentiable latent vector field that we can interrogate directly.Without any imposed supervision, the proposed ROM naturally separates the quiescent,vortex-dominated, and bursting phases of the wall cycle.In unforced long-term rollouts, the ROM trajectories stay bounded and recover theinvariant measure.Since the RBF representation is differentiable, we are able to locate weakly unstable near-equilibrium points and resolve the non-normal growth and phase-volume contraction of theattractor.Finally, we assimilate sparse, noisy wall measurements with an ensemble Kalman filter, and theROM then tracks the true flow trajectory. This demonstrates how tightly instantaneous wallshear constrains the cycle:the model recovers the invariant measure, and forecast errors driven by unobserved interiormotions remain bounded and localised within the active phase.</p>