Airborne measurements were conducted above the UK during May and June 2000 in order to investigate turbulence and mixing in the tropopause region. Measurements of temperature frequently exhibited a periodic series of ramps that resembled a sawtooth pattern. These repeating structures were only observed in or near patches of intense shear-generated turbulence associated with the jet-stream. In each observed case the temperature ramps had the same orientation with respect to the wind shear. The temperature increased gradually in the direction of the shear, dropped suddenly, and the pattern repeated with wavelengths of about 1 to 1.2 km. Numerical simulation was applied to demonstrate that the observed temperature ramps are a signature of growing Kelvin-Helmholtz waves that are just beginning to overturn in transition to turbulence. The fluctuations in wind became increasingly three-dimensional along the direction of the shear with coherent oscillations that are consistent with the shear-aligned vortices found in laboratory experiments and numerical simulations.