633 research outputs found
On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
The main part of this contribution to the special issue of EJM-B/Fluids
dedicated to Patrick Huerre outlines the problem of the subcritical transition
to turbulence in wall-bounded flows in its historical perspective with emphasis
on plane Couette flow, the flow generated between counter-translating parallel
planes. Subcritical here means discontinuous and direct, with strong
hysteresis. This is due to the existence of nontrivial flow regimes between the
global stability threshold Re_g, the upper bound for unconditional return to
the base flow, and the linear instability threshold Re_c characterized by
unconditional departure from the base flow. The transitional range around Re_g
is first discussed from an empirical viewpoint ({\S}1). The recent
determination of Re_g for pipe flow by Avila et al. (2011) is recalled. Plane
Couette flow is next examined. In laboratory conditions, its transitional range
displays an oblique pattern made of alternately laminar and turbulent bands, up
to a third threshold Re_t beyond which turbulence is uniform. Our current
theoretical understanding of the problem is next reviewed ({\S}2): linear
theory and non-normal amplification of perturbations; nonlinear approaches and
dynamical systems, basin boundaries and chaotic transients in minimal flow
units; spatiotemporal chaos in extended systems and the use of concepts from
statistical physics, spatiotemporal intermittency and directed percolation,
large deviations and extreme values. Two appendices present some recent
personal results obtained in plane Couette flow about patterning from numerical
simulations and modeling attempts.Comment: 35 pages, 7 figures, to appear in Eur. J. Mech B/Fluid
Unbalanced instabilities of rapidly rotating stratified shear flows
The linear stability of a rotating, stratified, inviscid horizontal plane
Couette flow in a channel is studied in the limit of strong rotation and
stratification. An energy argument is used to show that unstable perturbations
must have large wavenumbers. This motivates the use of a WKB-approach which, in
the first instance, provides an approximation for the dispersion relation of
the various waves that can propagate in the flow. These are Kelvin waves,
trapped near the channel walls, and inertia-gravity waves with or without
turning points.
Although, the wave phase speeds are found to be real to all algebraic orders
in the Rossby number, we establish that the flow, whether cyclonic or
anticyclonic, is unconditionally unstable. This is the result of linear
resonances between waves with oppositely signed wave momenta. We derive
asymptotic estimates for the instability growth rates, which are exponentially
small in the Rossby number, and confirm them by numerical computations. Our
results, which extend those of Kushner et al (1998) and Yavneh et al (2001),
highlight the limitations of the so-called balanced models, widely used in
geophysical fluid dynamics, which filter out Kelvin and inertia-gravity waves
and hence predict the stability of the Couette flow. They are also relevant to
the stability of Taylor-Couette flows and of astrophysical accretion discs.Comment: 6 figure
Destabilizing Taylor-Couette flow with suction
We consider the effect of radial fluid injection and suction on
Taylor-Couette flow. Injection at the outer cylinder and suction at the inner
cylinder generally results in a linearly unstable steady spiralling flow, even
for cylindrical shears that are linearly stable in the absence of a radial
flux. We study nonlinear aspects of the unstable motions with the energy
stability method. Our results, though specialized, may have implications for
drag reduction by suction, accretion in astrophysical disks, and perhaps even
in the flow in the earth's polar vortex.Comment: 34 pages, 9 figure
High-speed shear driven dynamos. Part 2. Numerical analysis
This paper aims to numerically verify the large Reynolds number asymptotic
theory of magneto-hydrodynamic (MHD) flows proposed in the companion paper
Deguchi (2019). To avoid any complexity associated with the chaotic nature of
turbulence and flow geometry, nonlinear steady solutions of the
viscous-resistive magneto-hydrodynamic equations in plane Couette flow have
been utilised. Two classes of nonlinear MHD states, which convert kinematic
energy to magnetic energy effectively, have been determined. The first class of
nonlinear states can be obtained when a small spanwise uniform magnetic field
is applied to the known hydrodynamic solution branch of the plane Couette flow.
The nonlinear states are characterised by the hydrodynamic/magnetic roll-streak
and the resonant layer at which strong vorticity and current sheets are
observed. These flow features, and the induced strong streamwise magnetic
field, are fully consistent with the vortex/Alfv\'en wave interaction theory
proposed in Deguchi (2019). When the spanwise uniform magnetic field is
switched off, the solutions become purely hydrodynamic. However, the second
class of `self-sustained shear driven dynamos' at the zero-external magnetic
field limit can be found by homotopy via the forced states subject to a
spanwise uniform current field. The discovery of the dynamo states has
motivated the corresponding large Reynolds number matched asymptotic analysis
in Deguchi (2019). Here, the reduced equations derived by the asymptotic theory
have been solved numerically. The asymptotic solution provides remarkably good
predictions for the finite Reynolds number dynamo solutions
Self-similar shear-thickening behavior in CTAB/NaSal surfactant solutions
The effect of salt concentration Cs on the critical shear rate required for
the onset of shear thickening and apparent relaxation time of the
shear-thickened phase, has been investigated systematically for dilute
CTAB/NaSal solutions. Experimental data suggest a self-similar behavior of the
critical shear rate and relaxation time as functions of Cs. Specifically, the
former ~ Cs^(-6) whereas the latter ~ Cs^(6) such that an effective Weissenberg
number for the onset of the shear thickened phase is only weakly dependent on
Cs. A procedure has been developed to collapse the apparent shear viscosity
versus shear rate data obtained for various values of Cs into a single master
curve. The effect of Cs on the elastic modulus and mesh size of the
shear-induced gel phase for different surfactant concentrations is discussed.
Experiments performed using different flow cells (Couette and cone-and-plate)
show that the critical shear rate, relaxation time and the maximum viscosity
attained are geometry-independent. The elastic modulus of the gel phase
inferred indirectly by employing simplified hydrodynamic instability analysis
of a sheared gel-fluid interface is in qualitative agreement with that
predicted for an entangled phase of living polymers. A qualitative mechanism
that combines the effect of Cs on average micelle length and Debye parameter
with shear-induced configurational changes of rod-like micelles is proposed to
rationalize the self-similarity of SIS formation.Comment: 27 pages, 17 figure
Molecular dynamics simulation: a tool for exploration and discovery using simple models
Emergent phenomena share the fascinating property of not being obvious
consequences of the design of the system in which they appear. This
characteristic is no less relevant when attempting to simulate such phenomena,
given that the outcome is not always a foregone conclusion. The present survey
focuses on several simple model systems that exhibit surprisingly rich emergent
behavior, all studied by MD simulation. The examples are taken from the
disparate fields of fluid dynamics, granular matter and supramolecular
self-assembly. In studies of fluids modeled at the detailed microscopic level
using discrete particles, the simulations demonstrate that complex hydrodynamic
phenomena in rotating and convecting fluids, the Taylor-Couette and
Rayleigh-B\'enard instabilities, can not only be observed within the limited
length and time scales accessible to MD, but even quantitative agreement can be
achieved. Simulation of highly counterintuitive segregation phenomena in
granular mixtures, again using MD methods, but now augmented by forces
producing damping and friction, leads to results that resemble experimentally
observed axial and radial segregation in the case of a rotating cylinder, and
to a novel form of horizontal segregation in a vertically vibrated layer.
Finally, when modeling self-assembly processes analogous to the formation of
the polyhedral shells that package spherical viruses, simulation of suitably
shaped particles reveals the ability to produce complete, error-free assembly,
and leads to the important general observation that reversible growth steps
contribute to the high yield. While there are limitations to the MD approach,
both computational and conceptual, the results offer a tantalizing hint of the
kinds of phenomena that can be explored, and what might be discovered when
sufficient resources are brought to bear on a problem.Comment: 21 pages, 20 figures (v2 - minor text addition
Flow organization and heat transfer in turbulent wall sheared thermal convection
We perform direct numerical simulations of wall sheared Rayleigh-B\'enard
(RB) convection for Rayleigh numbers up to , Prandtl number unity, and
wall shear Reynolds numbers up to . Using the Monin-Obukhov length
we identify three different flow states, a buoyancy dominated regime
(; with the thermal
boundary layer thickness), a transitional regime (; with the height of the domain), and a shear dominated
regime (). In the buoyancy dominated regime the flow
dynamics are similar to that of turbulent thermal convection. The transitional
regime is characterized by rolls that are increasingly elongated with
increasing shear. The flow in the shear dominated regime consists of very
large-scale meandering rolls, similar to the ones found in conventional Couette
flow. As a consequence of these different flow regimes, for fixed and with
increasing shear, the heat transfer first decreases, due to the breakup of the
thermal rolls, and then increases at the beginning of the shear dominated
regime. For the Nusselt number effectively scales as
, with while we find
in the buoyancy dominated regime. In the transitional regime the effective
scaling exponent is , but the temperature and velocity profiles
in this regime are not logarithmic yet, thus indicating transient dynamics and
not the ultimate regime of thermal convection
Mini-conference and related sessions on laboratory plasma astrophysics
This paper provides a summary of some major physics issues and future perspectives discussed in the Mini-Conference on Laboratory Plasma Astrophysics. This mini-conference, sponsored by the Topical Group on Plasma Astrophysics, was held as part of the American Physical Society’s Division of Plasma Physics 2003 Annual Meeting (October 27–31, 2003). Also included are brief summaries of selected talks on the same topic presented at two invited paper sessions (including a tutorial) and two contributed focus oral sessions, which were organized in coordination with the mini-conference by the same organizers. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70409/2/PHPAEN-11-5-2976-1.pd
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