Turbulence at an aerofoil leading edge: the linearity boundary and its generation mechanism

Abstract

Turbulence approaching an aerofoil leading edge is strained and blocked in the final few nose radii. Rapid-distortion theory assumes that the pre-impact field is a linear image of the upstream turbulence; we test that assumption directly. Grid turbulence is computed over a NACA~0012 aerofoil and sampled on three congruent surfaces around the nose, giving the cross-spectral tensor between upstream and pre-impact stations. Relative to a no-aerofoil control, the linearity spectrum falls by a factor of three already at the energy-containing scales ($κ= k\,r_{\mathrm{LE}} \approx 0.3$), showing that a substantial part of the pre-impact turbulence is generated locally rather than inherited. The same location appears in physical space: the anisotropy invariant $III_b$ changes sign from prolate to oblate within the last few per cent of chord, departing the plane-strain rapid-distortion prediction. The change is produced by pressure--strain redistribution, which drains the strain-amplified wall-normal stress into the other components; the term is absent in the control and becomes active once the accumulated strain is rapid. Across a fourteen-fold range of nose radius the sign change occurs at $x \approx -1.5\,r_{\mathrm{LE}}$ and the generated turbulence is spanwise-dominated. At second order the mapping remains usable: when inserted into a standard Amiet prediction it improves agreement with measured leading-edge noise, and the same coefficients transfer to independent published cases when only nose radius and free-stream speed are supplied.