scholarly journals The origin of hysteresis in the flag instability

2011 ◽  
Vol 691 ◽  
pp. 583-593 ◽  
Author(s):  
Christophe Eloy ◽  
Nicolas Kofman ◽  
Lionel Schouveiler
Keyword(s):  
Numerical Simulations ◽  
Hysteresis Loop ◽  
Nonlinear Stability ◽  
Slender Body ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Stability Analyses ◽  
Aeroelastic Instability ◽  
Large Hysteresis ◽  
Cantilevered Plate

AbstractThe flapping flag instability occurs when a flexible cantilevered plate is immersed in a uniform airflow. To this day, the nonlinear aspects of this aeroelastic instability are largely unknown. In particular, experiments in the literature all report a large hysteresis loop, while the bifurcation in numerical simulations is either supercritical or subcritical with a small hysteresis loop. In this paper, the discrepancy is addressed. First, weakly nonlinear stability analyses are conducted in the slender-body and two-dimensional limits, and, second, new experiments are performed with flat and curved plates. The discrepancy is attributed to inevitable planeity defects of the plates in the experiments.

Linear and Weakly Nonlinear Stability Analyses of Cooperative Car-Following Models

2014 ◽  
Vol 15 (5) ◽  
pp. 2001-2013 ◽  
Author(s):  
Julien Monteil ◽  
Romain Billot ◽  
Jacques Sau ◽  
Nour-Eddin El Faouzi
Keyword(s):  
Nonlinear Stability ◽  
Weakly Nonlinear ◽  
Car Following ◽  
Stability Analyses

Weakly Nonlinear Stability Analyses of Prototype Reaction-Diffusion Model Equations

SIAM Review ◽  
1994 ◽  
Vol 36 (2) ◽  
pp. 176-214 ◽  
Author(s):  
David J. Wollkind ◽  
Valipuram S. Manoranjan ◽  
Limin Zhang
Keyword(s):  
Diffusion Model ◽  
Nonlinear Stability ◽  
Reaction Diffusion ◽  
Weakly Nonlinear ◽  
Stability Analyses ◽  
Reaction Diffusion Model ◽  
Model Equations

The Weakly Nonlinear Stability of the Two-Dimensional Jet and Wake

1986 ◽  
Vol 55 (1) ◽  
pp. 106-114 ◽  
Author(s):  
Shinichiro Yanase ◽  
Kaoru Fujimura ◽  
Jiro Mizushima ◽  
Kanefusa Gotoh
Keyword(s):  
Nonlinear Stability ◽  
Two Dimensional ◽  
Weakly Nonlinear

SIGNIFICANCE OF AVERAGING COEFFICIENTS IN STABILITY ANALYSIS OF SHALLOW WAKE FLOWS

2007 ◽  
Vol 12 (3) ◽  
pp. 357-368
Author(s):  
Andrei Kolyshkin
Keyword(s):  
Stability Analysis ◽  
Shallow Water ◽  
Nonlinear Stability ◽  
Water Depth ◽  
Coherent Structures ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Wake Flows ◽  
Water Flows ◽  
Shallow Water Flows

Flows behind obstacles (such as islands) are shallow if the transverse scale of the flow is much larger than water depth. Field, laboratory and numerical data show that the flow pattern in shallow wakes exhibits a complex eddy‐like motion. Experimental and theoretical analyses provide evidence for the presence of two‐dimensional coherent structures in shallow water flows and show that the development of shallow wakes is different from the wakes in deep water due to the following reasons: first, the development of three‐dimensional instabilities is prevented by limited water depth and second, bottom friction acts as a stabilizing mechanism for suppressing the transverse growth of perturbations. Several authors have used the linear and weakly nonlinear stability theory in order to understand when shallow flows become unstable. Two‐dimensional depth‐averaged Saint‐Venant equations are usually used for the analysis. One of the main assumptions in shallow water theory is the independence of the velocity distribution on the vertical coordinate. In many cases, however, this assumption may not be valid. This paper presents an attempt to evaluate the influence of the assumption on the results of linear stability analysis of shallow wake flows with bottom friction. Momentum correction coefficients β 1 and β 2 are used in order to take into account the non‐uniformity of the velocity distribution in the vertical direction. Linear stability calculations show that the stability boundary is quite sensitive to the variation of the parameters β 1 and β 2. The role of the linear and weakly nonlinear stability analysis on the formation of two‐dimensional coherent structures in shallow water flows is discussed.

Nucleation of superconductivity in decreasing fields. II

1994 ◽  
Vol 5 (4) ◽  
pp. 469-494 ◽  
Author(s):  
S. J. Chapman
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Nonlinear Stability ◽  
Bifurcation Point ◽  
Superconducting State ◽  
Landau Theory ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Stability Analyses

The bifurcation from a normally conducting to a superconducting state as an external magnetic field is lowered is examined using the Ginzburg–Landau theory. Linear and weakly nonlinear stability analyses are performed near the bifurcation point, and the implications of the results for each of three examples is considered.

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