1,811 research outputs found
Boundary condition and geometry engineering in electronic hydrodynamics
We analyze the role of boundary geometry in viscous electronic hydrodynamics.
We address the twin questions of how boundary geometry impacts flow profiles,
and how one can engineer boundary conditions -- in particular the effective
slip parameter -- to manipulate the flow in a controlled way. We first propose
a micropatterned geometry involving finned barriers, for which we show by an
explicit solution that one can obtain effectively no-slip boundary conditions
regardless of the detailed microscopic nature of the channel surface. Next we
analyse the role of mesoscopic boundary curvature on the effective slip length,
in particular its impact on the Gurzhi effect. Finally we investigate a
hydrodynamic flow through a circular junction, providing a solution, which
suggests an experimental set-up for determining the slip parameter. We find
that its transport properties differ qualitatively from the case of ballistic
conduction, and thus presents a promising setting for distinguishing the two.Comment: 9 pages, 15 figures, 5 appendice
Travelling waves in two-dimensional plane Poiseuille flow
The asymptotic structure of laminar modulated travelling waves in two-dimensional high-Reynolds-number plane Poiseuille flow is investigated on the upper-energy branch. A finite set of independent slowly varying parameters are identified which parameterize the solution of the Navier–Stokes equations in this subset of the phase space. Our parameterization of the weakly stable modes describes an attracting manifold of maximum-entropy configurations. The complementary modes, which have been neglected in this parameterization, are strongly damped. In order to seek a closure, a countably infinite number of modulation equations are
derived on the long viscous time scale: a single equation for averaged kinetic energy and momentum; and the remaining equations for averaged powers of vorticity. Only a finite number of these vorticity modulation equations are required to determine the finite number of unknowns. The new results show that the evolution of the slowly varying amplitude parameters is determined by the vorticity field and that the phase velocity responds to these changes in the amplitude in accordance with the kinetic energy and momentum. The
new results also show that the most crucial physical mechanism in the production of vorticity is the interaction between vorticity and kinetic energy, this interaction being responsible for the existence of the attractor
On the instability of the magnetohydrodynamic pipe flow subject to a transverse magnetic field
The linear stability of a fully-developed liquid-metal MHD pipe flow subject
to a transverse magnetic field is studied numerically. Because of the lack of
axial symmetry in the mean velocity profile, we need to perform a BiGlobal
stability analysis. For that purpose, we develop a two-dimensional complex
eigenvalue solver relying on a Chebyshev-Fourier collocation method in physical
space. By performing an extensive parametric study, we show that in contrast to
Hagen-Poiseuille flow known to be linearly stable for all Reynolds numbers, the
MHD pipe flow with transverse magnetic field is unstable to three-dimensional
disturbances at sufficiently high values of the Hartmann number and wall
conductance ratio. The instability observed in this regime is attributed to the
presence of velocity overspeeds in the so-called Roberts layers and the
corresponding inflection points in the mean velocity profile. The nature and
characteristics of the most unstable modes are investigated, and we show that
they vary significantly depending on the wall conductance ratio. A major result
of this paper is that the global critical Reynolds number for the MHD pipe flow
with transverse magnetic field is , and it occurs for a perfectly
conducting pipe wall and the Hartmann number
- …