Strain-coupled one-dimensional turbulence: a single-line closure, its limits, and the consequence for leading-edge noise

Abstract

Turbulence approaching a solid surface is strained before it arrives, and the distortion of its spectrum is often what governs the downstream response; yet reduced-order predictions, leading-edge-noise theory among them, still take the incoming spectrum as frozen. We develop a strain-coupled formulation of one-dimensional turbulence (ODT) that evolves strained turbulence with full spatial resolution at a cost compatible with parametric study, carrying the rapid distortion and the nonlinear relaxation together. The obstacle is that the rapid pressure-strain is non-local and three-dimensional while an ODT line resolves only the flow state along its own coordinate. Splitting the distortion physics by structure captures the phenomenology: the off-axis production and a spectrally closed rapid operator enter as continuous-in-time forcing along the model coordinate, while `eddy events' capture the on-line production and the turbulence-driven relaxation. Carried through to leading-edge noise, the evolved inflow shifts the predicted level by 5-20 dB at the energy-containing scales relative to the conventional frozen-spectrum assumption.