  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. 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. The RadioAstron observations at wavelengths of
18cm, 6cm, and 1.3cm 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. The RadioAstron images reveal a wealth of structural
detail in the jet of S5 0836+710 on angular scales ranging from 0.02mas to
200mas. Brightness temperatures in excess of $10^{13}$\,K are measured in the
jet, requiring Doppler factors of $\ge 100$ 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.
