  Recent observations of non-local transport in ultraclean 2D materials raised
the tantalizing possibility of accessing hydrodynamic correlated transport of
many-electron state. However, it has been pointed out that non-local transport
can also arise from impurity scattering rather than interaction. At the crux of
the ambiguity is the focus on linear effects, i.e. Ohm's law, which cannot
easily differentiate among different modes of transport. Here we propose
experiments that can reveal rich hydrodynamic features in the system by tapping
into the non-linearity of the Navier-Stokes equation. Three experiments we
propose will each manifest unique phenomenon well-known in classical fluids:
the Bernoulli effect, Eckart streaming, and Rayleigh streaming. Analysis of
known parameters confirms that the proposed experiments are feasible and the
hydrodynamic signatures are within reach of graphene-based devices.
Experimental realization of any one of the three phenomena will provide a
stepping stone to formulating and exploring the notions of nonlinear electron
fluid dynamics with an eye to celebrated examples from classical non-laminar
flows, e.g. pattern formation and turbulence.
