  We construct multi-mode viscous hydrodynamics for one dimensional spinless
electrons. Depending on the scale, the fluid has six (shortest lengths), four
(intermediate, exponentially broad regime), or three (asymptotically long
scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to
anomalous scaling of physical observables and waves propagating in the fluid.
In a four-mode regime, all modes are ballistic and acquire KPZ-like broadening
with asymmetric power-law tails. "Heads" and "tails" of the waves contribute
equally to thermal conductivity, leading to $\omega^{-1/3}$ scaling of its real
part. In a three-mode regime, the system is in the universality class of
classical viscous fluid[9,24]. Self-interaction of the sound modes results in
KPZ-like shape, while the interaction with the heat mode results in asymmetric
tails. The heat mode is governed by Levy flight distribution, whose power-law
tails give rise to $\omega^{-1/3}$ scaling of heat conductivity.
