Spectral stochastic estimation of high-Reynolds-number wall-bounded turbulence for a refined inner-outer interaction model

For wall-bounded flows, the model of Marusic et al. [Science 329, 193 (2010)] allows one to predict the statistics of the streamwise fluctuating velocity in the inner region, from a measured input signal in the logarithmic region. Normally, a user-defined large-scale portion of the input forms the large-scale content in the prediction by scaling its amplitude, as well as temporally shifting the signal to account for the physical inclination of these scales. Incoherent smaller scales are then fused to the prediction via universally expressed fluctuations that are subject to an amplitude modulation. Here we present a refined version of the model using spectral linear stochastic estimation, which eliminates a user-defined scale separation of the input. Now, an empirically derived transfer kernel comprises an implicit filtering via a scale-dependent gain and phase; this kernel captures the coherent portion in the prediction. An additional refinement of the model embodies a relative shift between the stochastically estimated scales in the prediction and the modulation envelope of the universal small scales. Predictions over a three-decade span of Reynolds numbers, Re-tau similar to O(10(3)) to O(10(6)), highlight promising applications of the refined model to high-Reynolds-number flows, in which coherent scales become the primary contributor to the fluctuating energy.