Rock global stability estimation by three dimensional blocks formed with statistically produced joint polygons

AbstractThe linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height $h$ and diameter $d$ immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each of its sides. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar–turbulent transition process. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes is related to a different physical mechanism. While the varicose mode has its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and has its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability: whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake region, for larger roughness elements the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio ${\it\eta}=1$ (with ${\it\eta}=d/h$) roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff–Braslow transition diagram provides qualitatively good agreement.

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Global Stability and Hopf Bifurcation for Gause-Type Predator-Prey System

Journal of Applied Mathematics ◽

10.1155/2012/260798 ◽

2012 ◽

Vol 2012 ◽

pp. 1-17 ◽

Cited By ~ 3

Author(s):

Shuang Guo ◽

Weihua Jiang

Keyword(s):

Global Stability ◽

Periodic Solutions ◽

Three Dimensional ◽

Growth Time ◽

Predator Prey ◽

Predator Prey Model ◽

Prey System ◽

Existence Of Periodic Solutions ◽

The Stability ◽

System With Time Delay

A class of three-dimensional Gause-type predator-prey model is considered. Firstly, local stability of equilibrium indicating the extinction of top-predator is obtained. Meanwhile, we construct a Lyapunov function, which is an extension of the Lyapunov functions constructed by Hsu for predator-prey system (2005), to give the global stability of the equilibrium. Secondly, we analyze the stability of coexisting equilibrium of predator-prey system with time delay when the predator catches the prey of pregnancy or with growth time. The delay can lead to periodic solutions, which is consistent with the law of growth for birds and some mammals. Further, an explicit formula is given which determines the stability of the bifurcating periodic solutions theoretically and the existence of periodic solutions is displayed by numerical simulations.

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Towards a quantitative comparison between global and local stability analysis

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.167 ◽

2017 ◽

Vol 819 ◽

pp. 147-164 ◽

Cited By ~ 6

Author(s):

L. Siconolfi ◽

V. Citro ◽

F. Giannetti ◽

S. Camarri ◽

P. Luchini

Keyword(s):

Stability Analysis ◽

Saddle Point ◽

Global Stability ◽

Local Stability ◽

Correction Term ◽

Three Dimensional ◽

Higher Order ◽

Order Correction ◽

Global Stability Analysis ◽

Local Stability Analysis

A methodology is proposed here to estimate the stability characteristics of bluff-body wakes using local analysis under the assumption of weakly non-parallel flows. In this connection, a generalisation of the classic spatio-temporal stability analysis for fully three-dimensional flows is first described. Secondly, an additional higher-order correction term with respect to the common saddle-point global frequency estimation is included in the analysis. The proposed method is first validated for the case of the flow past a circular cylinder and then applied to two fully three-dimensional flows: the boundary layer flow over a wall-mounted hemispherical body and the wake flow past a fixed sphere. In all the cases considered, both the estimated unstable eigenvalue and the spatial shape of the associated eigenmode are determined by local stability analysis, and they are compared with the reference counterparts obtained at a definitely higher computational cost by a fully three-dimensional global stability analysis. It is shown that the results of local stability analysis, when the higher-order correction term is included, are in excellent agreement with those obtained by global stability analysis. It is also shown that the retained correction term is of crucial importance in this perspective, leading to a remarkable improvement in accuracy with respect to the classical saddle-point estimation.

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Existence and Global Stability of a Periodic Solution for Discrete-Time Cellular Neural Networks

Discrete Dynamics in Nature and Society ◽

10.1155/2012/645214 ◽

2012 ◽

Vol 2012 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Haijian Shao ◽

Haikun Wei ◽

Haoxiang Wang

Keyword(s):

Neural Network ◽

Periodic Solution ◽

Global Stability ◽

Discrete Time ◽

Dimensional Space ◽

Three Dimensional ◽

Coincidence Degree ◽

Degree Theory ◽

Lyapunov Stability Theory ◽

Cellular Neural Network

A novel sufficient condition is developed to obtain the discrete-time analogues of cellular neural network (CNN) with periodic coefficients in the three-dimensional space. Existence and global stability of a periodic solution for the discrete-time cellular neural network (DT-CNN) are analysed by utilizing continuation theorem of coincidence degree theory and Lyapunov stability theory, respectively. In addition, an illustrative numerical example is presented to verify the effectiveness of the proposed results.

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Global stability for the three-dimensional logistic map

Nonlinearity ◽

10.1088/1361-6544/abcd05 ◽

2021 ◽

Vol 34 (2) ◽

pp. 894-938

Author(s):

János Dudás ◽

Tibor Krisztin

Keyword(s):

Global Stability ◽

Logistic Map ◽

Three Dimensional

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