The U-2 aircraft was instrumented and flown in the stratosphere during the Stratosphere-Troposphere Exchange Project's experiments on April 1984 to provide a set of simultaneous measurements by fast responding sensors that would aid in the identification of the modes of cross-jet transport. The measurements confirm the preexperimental deductions that transport is dominated by waves, not by large-scale circulations. Monotonic gradients of trace constituents normal to the jet axis, with upper stratospheric tracers increasing poleward and tropospheric tracers increasing equatorward, are augmented by large-scale confluence as the jet intensifies during cyclogenesis. These gradients are rotated, intensified, and significantly increased in area as their mixing ratio surfaces are folded by the differential transport of a very low frequency, transverse wave. The quasi-horizontal transport produces a laminar structures with stable rich in upper stratospheric tracers alternating vertically with less stable layers rich in tropospheric tracers. The transport proceeds toward irreversibility as higher frequency, shear-gravity waves extend the folding to small horizontal scales. It becomes irreversible when these short waves actually fold the isentropic surfaces and small-scale mixing develops. The progression to higher wave numbers is a discrete, not a continuous, casade with major gaps in the observed horizontal wavelengths. The wave modes are identified by matching the observed amplitudes and phases against those obtained by linear perturbation theory. Prior to mixing, the wave-generated perturbations maintain the correlations produced by advecting the larger-scale mean gradients; thus the high resolution measurements support the linear turbulence closure assumption. ¿American Geophysical Union 1991