1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
On the existence of two-dimensional nonlinear steady states in plane Couette flow
Rent:
Rent this article for
USD
10.1063/1.2753982
/content/aip/journal/pof2/19/7/10.1063/1.2753982
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/7/10.1063/1.2753982
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Continuation of two-dimensional solutions with in mixed Poiseuille-Couette flow (1) as a function of , for (black curves with turning points at ) and (blue online, with turning points at ). Full line: , dashed line (almost undistinguishable from full line): , dotted line: . The nondimensional wall shear rate has been used as a measure of nonlinearity [for the laminar flow, ]. The “gap” at results from the existence of a turning point close to .

Image of FIG. 2.
FIG. 2.

(Color online) Continuation of two-dimensional solutions in mixed Poiseuille-Couette flow (1) as a function of for (black curves with the largest values), (blue online, curves centered on ), (red online, narrow curves at low ). Full line: , dashed line: , dotted line: . Solutions for do not extend to and the corresponding red dotted curve at is for . Note the convergence problems at low for and .

Image of FIG. 3.
FIG. 3.

(Color online) Continuation of two-dimensional solutions in mixed Poiseuille-Couette flow (1) as a function of for (black, family of large curves), (blue online, family of medium size curves), (red online, family of small curves corresponding to the “nose” of the surface of solutions). Full line: , dashed line (undistinguishable from full line curves): , dotted line: . The results for presented here are also undistinguishable from those (not shown here) obtained for the same resolution as that used by CE95.

Image of FIG. 4.
FIG. 4.

(Color online) Bifurcations and nonlinear continuation of two-dimensional solutions of the -perturbed plane Couette flow of MH05 with , (full line), (dashed line), and (dotted and dashed-dotted lines). has been used [the results of some of these computations done at are undistinguishable from those at ]. All solutions are steady except for the dashed-dotted line branch at (dashed-dotted, red online), for which the phase speed reaches 0 when it meets the dotted steady branches. The vertical dashed-triple dotted line corresponds to the path followed in the continuation presented in Fig. 5. Continuation was stopped at large energy (strong nonlinearity) due to insufficient numerical resolution.

Image of FIG. 5.
FIG. 5.

Nonlinear continuation of two-dimensional solutions of the -perturbed plane Couette flow of MH05 with respect to , for , and . The dashed line corresponds to the phase speed of the solutions and the full line to their kinetic energy. The starting point of the continuation corresponds to the Hopf bifurcation of the perturbed Couette flow, which occurs at for . Continuation was stopped at large energy (strong nonlinearity) due to insufficient numerical resolution.

Image of FIG. 6.
FIG. 6.

Bifurcations and nonlinear continuation of steady two-dimensional solutions of the -perturbed plane Couette flow without the artifact mean flow perturbation for (full line), (dashed line), and (dashed-dotted line) when the perturbation term is added to the part of the equations only. . Continuation was stopped at large energy (strong nonlinearity) due to insufficient numerical resolution.

Image of FIG. 7.
FIG. 7.

Nonlinear continuation of steady two-dimensional solutions of the -perturbed plane Couette flow without the artifact mean flow perturbation as a function of , for (full line), (dotted line), (dashed line), and (dashed-dotted line). .

Loading

Article metrics loading...

/content/aip/journal/pof2/19/7/10.1063/1.2753982
2007-07-31
2014-04-20
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the existence of two-dimensional nonlinear steady states in plane Couette flow
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/7/10.1063/1.2753982
10.1063/1.2753982
SEARCH_EXPAND_ITEM