  We provide numerical evidence that a Kelvin-Helmholtz instability occurs in
the Dirac fluid of electrons in graphene and can be detected in current
experiments. This instability appears for electrons in the viscous regime
passing though a micrometer-scale obstacle and affects measurements on the time
scale of nanoseconds. A possible realization with a needle-shaped obstacle is
proposed to produce and detect this instability by measuring the electric
potential difference between contact points located before and after the
obstacle. We also show that, for our setup, the Kelvin-Helmholtz instability
leads to the formation of whirlpools similar to the ones reported in Bandurin
et al. [Science 351, 1055 (2016)]. To perform the simulations, we develop a
lattice Boltzmann method able to recover the full dissipation in a fluid of
massless particles.
