We present simultaneous in situ measurements of a long-period inertio-gravity wave and of clear air turbulence events associated with wave propagation. The energy budget of the wave-turbulence interaction shows that a long period and of short vertical wavelength may propagate upward over several wavelengths close to the shear instability conditions. This result allows one to interpret the spatiotemporal structure of CAT layers as reported in the literature and in particular their horizontal and vertical extent, their thickness, and their persistence.