Context : Detailed studies of relativistic jets in active galactic nuclei ( AGN ) require high-fidelity imaging at the highest possible resolution .
This can be achieved using very long baseline interferometry ( VLBI ) at radio frequencies , combining worldwide ( global ) VLBI arrays of radio telescopes with a space-borne antenna on board a satellite .

Aims : We present multiwavelength images made of the radio emission in the powerful quasar S5 0836 + 710 , obtained using a global VLBI array and the antenna Spektr-R of the RadioAstron mission of the Russian Space Agency , with the goal of studying the internal structure and physics of the relativistic jet in this object .

Methods : The RadioAstron observations at wavelengths of 18 cm , 6 cm , and 1.3 cm are part of the Key Science Program for imaging radio emission in strong AGN .
The internal structure of the jet is studied by analyzing transverse intensity profiles and modeling the structural patterns developing in the flow .

Results : The RadioAstron images reveal a wealth of structural detail in the jet of S5 0836+710 on angular scales ranging from 0.02 mas to 200 mas .
Brightness temperatures in excess of 10 ^ { 13 } K are measured in the jet , requiring Doppler factors of \geq 100 for reconciling them with the inverse Compton limit .
Several oscillatory patterns are identified in the ridge line of the jet and can be explained in terms of the Kelvin-Helmholtz ( KH ) instability .
The oscillatory patterns are interpreted as the surface and body wavelengths of the helical mode of the KH instability .
The interpretation provides estimates of the jet Mach number and of the ratio of the jet to the ambient density , which are found to be M _ { \mathrm { j } } \approx 12 and \eta \approx 0.33 .
The ratio of the jet to the ambient density should be conservatively considered an upper limit because its estimate relies on approximations .

Conclusions :