arXiv subjects

Paul Manneville

Publications and source records attributed to Paul Manneville.

21 records · Page 2Linked to original sources

arXiv2011

Pattern fluctuations in transitional plane Couette flow

In wide enough systems, plane Couette flow, the flow established between two parallel plates translating in opposite directions, displays alternatively turbulent and laminar oblique bands in a given range of Reynolds numbers R. We show that in periodic domains that contain a few bands, for given values of R and size, the orientation and the wavelength of this pattern can fluctuate in time. A procedure is defined to detect well-oriented episodes and to determine the statistics of their lifetimes. The latter turn out to be distributed according to exponentially decreasing laws. This statistics is interpreted in terms of an activated process described by a Langevin equation whose deterministic part is a standard Landau model for two interacting complex amplitudes whereas the noise arises from the turbulent background.

physics.flu-dyn↗

arXiv2010

On modelling transitional turbulent flows using under-resolved direct numerical simulations: The case of plane Couette flow

Direct numerical simulations have proven of inestimable help to our understanding of the transition to turbulence in wall-bounded flows. While the dynamics of the transition from laminar flow to turbulence via localised spots can be investigated with reasonable computing resources in domains of limited extent, the study of the decay of turbulence in conditions approaching those in the laboratory requires consideration of domains so wide as to exclude the recourse to fully resolved simulations. Using Gibson's C++ code ChannelFlow, we scrutinize the effects of a controlled lowering of the numerical resolution on the decay of turbulence in plane Couette flow at a quantitative level. We show that the number of Chebyshev polynomials describing the cross-stream dependence can be drastically decreased while preserving all the qualitative features of the solution. In particular, the oblique turbulent band regime experimentally observed in the upper part of the transitional range is extremely robust. In terms of Reynolds numbers, the resolution lowering is seen to yield a regular downward shift of the upper and lower thresholds Rt and Rg where the bands appear and break down. The study is illustrated with the results of two preliminary experiments.

nlin.PS↗

arXiv2008

Understanding the sub-critical transition to turbulence in wall flows

Contrasting with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become turbulent in a much wilder way, most often marked by the coexistence of laminar and turbulent domains at intermediate Reynolds numbers, well below the range where (viscous) instabilities can show up. There can even be no unstable mode at all, as for plane Couette flow (pCf) or for Poiseuille pipe flow (Ppf) that currently are the subject of intense research. Though the mechanisms involved in the transition to turbulence in wall flows are now better understood, statistical properties of the transition itself are yet unsatisfactorily assessed. A review of the situation is given. An alternative to the temporal theory of the transition to turbulence in terms of chaotic transients in such globally subcritical flows is proposed, which invokes spatio-temporal intermittence and the theory of first order (thermodynamic) phase transitions.

physics.flu-dyn↗