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.
Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations
Rent:
Rent this article for
USD
10.1063/1.4811297
/content/aip/journal/chaos/23/3/10.1063/1.4811297
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/3/10.1063/1.4811297
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Bifurcation diagram of (upper panel) and (lower panel) as a function of the Reynolds number Re, for two pre-crisis attractors (black) and (red). After crisis, and merge to form an enlarged attractor (black).

Image of FIG. 2.
FIG. 2.

Upper panel: bifurcation diagram of as a function of the Reynolds number Re for . Lower panel: the two largest Lyapunov exponents as a function of Re.

Image of FIG. 3.
FIG. 3.

Poincaré points of the quasiperiodic attractors QPA (black) and QPA (red) for Re = 51.4 (left-side panels) and chaotic attractors CA and CA for Re = 51.52 (right-side panels) projected using Fourier modes and .

Image of FIG. 4.
FIG. 4.

Poincaré points of the HCA in the hyperchaotic regime projected using Fourier modes (upper panel) and (middle panel). The lower panel shows an enlargement of the hyperchaotic attractor projected using Fourier mode .

Image of FIG. 5.
FIG. 5.

Time series of the kinetic energy E (upper panels) and the enstrophy Ω (lower panels) in the chaotic regime (Re = 51.52) and the hyperchaotic regime (Re = 51.525). The arrows indicate the selected values of used to detect Lagrangian coherent structures (Figs. 8 and 9 ).

Image of FIG. 6.
FIG. 6.

Left-side panels: Poincaré points of the HCS (gray) and chaotic attractors CA (black) and CA (red) in the chaotic regime (Re = 51.52) projected using Fourier modes (upper panels) and (middle panels). The lower panel shows an enlargement of the middle panel. Right-side panels: Poincaré points of the HCS (gray), and chaotic saddles CS (black) and CS (red), in the hyperchaotic regime (Re = 51.525).

Image of FIG. 7.
FIG. 7.

The forward-time FTLE field of Re = 51.52 at  = 15 000 for (upper panel), and (lower panel), superposed by forward-time hyperbolic LCSs (yellow lines).

Image of FIG. 8.
FIG. 8.

The FTLE field of the hyperchaotic attractor (Re = 51.525) at  = 4500 (upper panel),  = 7000 (middle panel), and  = 8500 (bottom panel), superposed by forward-time LCSs (yellow) and backward-time LCSs (white).

Image of FIG. 9.
FIG. 9.

The FTLE field for Re = 51.52, at  = 3960 (upper panel),  = 6316 (middle panel), and  = 15 000 (bottom panel), superposed by forward-time LCSs (yellow) and backward-time LCSs (white).

Image of FIG. 10.
FIG. 10.

Probability distribution function of the FTLE field for Re = 51.52< Re (left-side panels) and Re= 51.525 > Re (right-side panels). The continuous line represents laminar periods, the dotted line corresponds to the high-variability periods, and the dashed line represents strong bursts.

Image of FIG. 11.
FIG. 11.

Power spectra of the time series of (upper panel) and (lower panel) at Re = 51.4. The frequencies indicated in the figure are and .

Loading

Article metrics loading...

/content/aip/journal/chaos/23/3/10.1063/1.4811297
2013-07-09
2014-04-23
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/3/10.1063/1.4811297
10.1063/1.4811297
SEARCH_EXPAND_ITEM