Turbulent Flows in Electron Hydrodynamics: Conductivity and Vorticity

TL;DR

This paper investigates turbulent flows in electron hydrodynamics, analyzing conductivity and vorticity in different geometries, revealing nonlinear effects and vorticity behavior near edges.

Contribution

It provides new insights into turbulence in electron fluids, including nonlinear conductivity corrections and vorticity distribution in specific geometries.

Findings

Conductivity correction scales as W^4 in nonlinear flows.

Vorticity spans a wide range near the edges of the geometry.

Velocity and magnetic fields reflect vorticity behavior.

Abstract

In this article, we attempt to understand various aspects of turbulent flows in electron hydrodynamics. We analyze a rectangular channel geometry in the presence of an electric field and a Corbino geometry in the presence of a magnetic field. In the former geometry, we analyze the conductivity of the fluid as well as the frequency spectrum of perturbations about the Poiseuille flow. While the normal Poiseuille flow has an associated conductivity which scales as $W^2$, we find a correction which scales as $W^4$ in the case of non-linear flows, where $W$ is the characteristic length of the system. In the Corbino geometry, we analyze the velocity, vorticity and magnetic fields. We find that the vorticity can span across a wide range near the edge of the geometry, a behavior that can be reflected in the velocity and magnetic fields.