Abstract

Motivated by experiments on a hydrodynamic regime in electron
transport, we study the effect of an oscillating electric field in
such a setting. We consider a long two-dimensional channel of, whose
geometrical simplicity allows an analytical study
as well as hopefully permitting experimental realisation. We find two,
distinctive regimes: a quasi-static flow, and a boundary layer type
behaviour. The latter includes a
splitting of the location of maximal flow velocity from the centre
towards
the edges of the boundary layer, an an increasingly reactive nature of
the response, with the phase shift of the response varying across the
channel. In which regime we are, depends on dimensionless combination of
channel width, viscosity and forcing frequency, similar to the Reynolds number.
The scaling of the total optical
conductance with channel width differs between the two regimes, while
its
frequency dependence resembles a Drude form throughout, even in the
complete absence of ohmic heating, against which, at the same time, our
results are stable. Current estimates for transport coefficients in
graphene and delafossites suggest that the boundary layer regime should
be experimentally accessible.