Studying the internal structure of extragalactic jets is crucial for understanding their physics . The Japanese-led space VLBI project VSOP has presented an opportunity for such studies , by reaching baseline lengths of up to 36,000 km and resolving structures down to an angular size of \approx 0.3 mas at 5 GHz . VSOP observations of the jet in 0836+710 at 1.6 and 5 GHz have enabled tracing of the radial structure of the flow on scales from 2 mas to 200 mas along the jet and determination of the wavelengths of individual oscillatory modes responsible for the formation of the structure observed . We apply linear stability analysis to identify the oscillatory modes with modes of Kelvin-Helmholtz instability that match the wavelengths of the structures observed . We find that the jet structure in 0836+710 can be reproduced by the helical surface mode and a combination of the helical and elliptic body modes of Kelvin-Helmholtz instability . Our results indicate that the jet is substantially stratified and different modes of the instability grow inside the jet at different distances to the jet axis . The helical surface mode can be driven externally , and we discuss the implications of the driving frequency on the physics of the active nucleus in 0836+710 .