  Boundary-layer transition is accompanied by a significant increase in skin
friction whose origin is rigorously explained using the stochastic Lagrangian
formulation of the Navier-Stokes equations. This formulation permits the exact
analysis of vorticity dynamics in individual realizations of a viscous
incompressible fluid flow. The Lagrangian reconstruction formula for vorticity
is here extended for the first time to Neumann boundary conditions (Lighthill
source). We can thus express the wall vorticity, and therefore the wall stress,
as the expectation of a stochastic Cauchy invariant in backward time, with
contributions from (a) wall-vorticity flux (Lighthill source) and (b) interior
vorticity that has been evolved by nonlinear advection, viscous diffusion,
vortex stretching and tilting. We consider the origin of stress maxima in the
transitional region, examining a sufficient number of events to represent the
increased skin friction. The stochastic Cauchy analysis is applied to each
event to trace the origin of the wall vorticity. We find that the Lighthill
source, vortex tilting, diffusion and advection of outer vorticity make minor
contributions. They are less important than spanwise stretching of near-wall
spanwise vorticity, which is the dominant source of skin-friction increase
during laminar-to-turbulent transition. Our analysis should assist more
generally in understanding drag generation and reduction strategies and flow
separation in terms of near-wall vorticity dynamics.
