Stability analysis of Navier–Stokes system

2019 ◽  
Vol 16 (10) ◽  
pp. 1950157 ◽  
Author(s):  
Manoj Kumar ◽  
T. N. Mishra ◽  
B. Tiwari
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Linear Stability ◽  
Stokes System ◽  
Equilibrium Points ◽  
Navier Stokes ◽  
Bifurcation Parameter ◽  
Numerical Examples ◽  
Deviation Vector

Stability analysis of dynamical system is very useful and is able to classify the role of stable and unstable equilibrium points. In this work, Naiver–Stokes system has been studied by using KCC theory. The Jacobi stability and dynamics of the deviation vector near equilibrium points have been also studied. Further, the effect of bifurcation parameter on stability of Navier–Stokes system has been observed and found the limiting conditions for bifurcation. Numerical examples of particular interest have been taken to compare the results of Jacobi stability and linear stability. It is observed that Jacobi stability on the basis of KCC theory is more efficient than the linear stability.

Non-parallel linear stability analysis of the vertical boundary layer in a differentially heated cavity

1997 ◽  
Vol 352 ◽  
pp. 265-281 ◽  
Author(s):  
A. M. H. BROOKER ◽  
J. C. PATTERSON ◽  
S. W. ARMFIELD
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Navier Stokes ◽  
Parabolized Stability Equations ◽  
The Stability ◽  
Flow Quantity ◽  
Energy Equations ◽  
Made In

A non-parallel linear stability analysis which utilizes the assumptions made in the parabolized stability equations is applied to the buoyancy-driven flow in a differentially heated cavity. Numerical integration of the complete Navier–Stokes and energy equations is used to validate the non-parallel theory by introducing an oscillatory heat input at the upstream end of the boundary layer. In this way the stability properties are obtained by analysing the evolution of the resulting disturbances. The solutions show that the spatial growth rate and wavenumber are highly dependent on the transverse location and the disturbance flow quantity under consideration. The local solution to the parabolized stability equations accurately predicts the wave properties observed in the direct simulation whereas conventional parallel stability analysis overpredicts the spatial amplification and the wavenumber.

Linear stability analysis and metastable solutions for a phase-field model

1999 ◽  
Vol 129 (3) ◽  
pp. 571-600 ◽  
Author(s):  
A. Jiménez-Casas ◽  
A. Rodríguez-Bernal
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Phase Field ◽  
Field Model ◽  
Equilibrium Points ◽  
Phase Field Model ◽  
One Dimensional ◽  
Stability And Instability ◽  
The One

We study the linear stability of equilibrium points of a semilinear phase-field model, giving criteria for stability and instability. In the one-dimensional case, we study the distribution of equilibria and also prove the existence of metastable solutions that evolve very slowly in time.

scholarly journals On Stability Analysis of Higher-Order Rational Difference Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Abdul Khaliq ◽  
H. S. Alayachi ◽  
M. S. M. Noorani ◽  
A. Q. Khan
Keyword(s):  
Stability Analysis ◽  
Equilibrium Points ◽  
Global Behavior ◽  
Real Numbers ◽  
Positive Real ◽  
Numerical Examples ◽  
Local Asymptotic Stability ◽  
Recursive Sequence ◽  
Rational Difference Equation ◽  
Theoretical Results

In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence wn+1=wn−pα+βwn/γwn+δwn−r, where γwn≠−δwn−r for r∈0,∞, α, β, γ, δ∈0,∞, and r>p≥0. With initial values w−p,w−p+1,…,w−r,w−r+1,…,w−1, and w0 are positive real numbers. Some numerical examples are given to verify our theoretical results.

Stability and Bifurcation Analysis of a Prey–Predator Model

2021 ◽  
Vol 31 (04) ◽  
pp. 2150059
Author(s):  
T. N. Mishra ◽  
B. Tiwari
Keyword(s):  
Dynamical System ◽  
Linear Stability ◽  
Bifurcation Analysis ◽  
Finsler Space ◽  
Second Order ◽  
Critical Values ◽  
Numerical Examples ◽  
Stability And Bifurcation Analysis ◽  
Predator Model ◽  
The Stability

The purpose of the present paper is to study the stability of a prey–predator model using KCC theory. The KCC theory is based on the assumption that the second-order dynamical system and geodesics equation, in associated Finsler space, are topologically equivalent. The stability (Jacobi stability) based on KCC theory and linear stability of the model are discussed in detail. Further, the effect of parameters on stability and the presence of chaos in the model are investigated. The critical values of bifurcation parameters are found and their effects on the model are investigated. The numerical examples of particular interest are compared to the results of Jacobi stability and linear stability and it is found that Jacobi stability on the basis of KCC theory is global than the linear stability.

Channel formation by turbidity currents: Navier–Stokes-based linear stability analysis

2008 ◽  
Vol 615 ◽  
pp. 185-210 ◽  
Author(s):  
B. HALL ◽  
E. MEIBURG ◽  
B. KNELLER
Keyword(s):  
Shear Stress ◽  
Stability Analysis ◽  
Linear Stability ◽  
Suspended Sediment Concentration ◽  
Three Dimensional ◽  
Sediment Concentration ◽  
Base Flow ◽  
Navier Stokes ◽  
Streamwise Vortices ◽  
Sediment Bed

The linear stability of an erodible sediment bed beneath a turbidity current is analysed, in order to identify potential mechanisms responsible for the formation of longitudinal gullies and channels. On the basis of the three-dimensional Navier–Stokes equations, the stability analysis accounts for the coupled interaction of the three-dimensional fluid and particle motion inside the current with the erodible bed below it. For instability to occur, the suspended sediment concentration of the base flow needs to decay away from the sediment bed more slowly than does the shear stress inside the current. Under such conditions, an upward protrusion of the sediment bed will find itself in an environment where erosion decays more quickly than sedimentation, and so it will keep increasing. Conversely, a local valley in the sediment bed will see erosion increase more strongly than sedimentation, which again will amplify the initial perturbation.The destabilizing effect of the base flow is modulated by the stabilizing perturbation of the suspended sediment concentration and by the shear stress due to a secondary flow structure in the form of counter-rotating streamwise vortices. These streamwise vortices are stabilizing for small Reynolds and Péclet numbers and destabilizing for large values.For a representative current height of O(10–100m), the linear stability analysis provides the most amplified wavelength in the range of 250–2500m, which is consistent with field observations reported in the literature. In contrast to previous analyses based on depth-averaged equations, the instability mechanism identified here does not require any assumptions about sub- or supercritical flow, nor does it require the presence of a slope or a slope break.

Effect of confinement on three-dimensional stability in the wake of a circular cylinder

2009 ◽  
Vol 642 ◽  
pp. 477-487 ◽  
Author(s):  
SIMONE CAMARRI ◽  
FLAVIO GIANNETTI
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Dimensional Stability ◽  
Opposite Sign ◽  
Three Dimensional ◽  
The Body ◽  
Karman Street

This paper investigates the three-dimensional stability of the wake behind a symmetrically confined circular cylinder by a linear stability analysis. Emphasis has been placed on discussing analogies and differences with the unconfined case to highlight the role of the inversion of the von Kármán street in the nature of the three-dimensional transition. Indeed, in this flow, the vortices of opposite sign that are alternately shed from the body into the wake cross the symmetry line further downstream and they assume a final configuration which is inverted with respect to the unconfined case. It is shown that the transition to a three-dimensional state has the same space–time symmetries of the unconfined case, although the shape of the linearly unstable modes is affected by the inversion of the wake vortices. A possible interpretation of this result is given here.

Dynamics of Supply Chains: A Multilevel (Logistical–Informational–Financial) Network Perspective

2002 ◽  
Vol 29 (6) ◽  
pp. 795-818 ◽  
Author(s):  
Anna Nagurney ◽  
Ke Ke ◽  
Jose Cruz ◽  
Kitty Hancock ◽  
Frank Southworth
Keyword(s):  
Dynamical System ◽  
Stability Analysis ◽  
Supply Chains ◽  
Discrete Time ◽  
Equilibrium Solution ◽  
Adjustment Process ◽  
Financial Network ◽  
Numerical Examples ◽  
Space And Time

In this paper, we propose a multilevel network perspective for the conceptualization of the dynamics underlying supply chains in the presence of competition. The multilevel network consists of: the logistical network, the informational network, and the financial network. We describe the behavior of the network decisionmakers, which are spatially separated and which consist of the manufacturers and producing firms, the retailers, and the consumers located at the demand markets. We propose a projected dynamical system, along with stability analysis results, that captures the adjustments of the commodity shipments and the prices over space and time. A discrete-time adjustment process is described and implemented in order to illustrate in several numerical examples the evolution of the commodity shipments and prices to the equilibrium solution.

scholarly journals ON THE SENSITIVITY OF THE NONLINEAR TERM IN THE OUTFLOW BOUNDARY CONDITION

2021 ◽  
Vol 61 (SI) ◽  
pp. 117-121
Author(s):  
Tomáš Neustupa ◽  
Ondřej Winter
Keyword(s):  
Boundary Condition ◽  
Fluid Flow ◽  
Kinetic Energy ◽  
Stokes System ◽  
Nonlinear Term ◽  
Navier Stokes ◽  
Outflow Boundary Condition ◽  
Flow Through ◽  
Outflow Boundary

This paper studies the artificial outflow boundary condition for the Navier-Stokes system. This type of condition is widely used and it is therefore very important to study its influence on a numerical solution of the corresponding boundary-value problem. We particularly focus on the role of the coefficient in front of the nonlinear term in the boundary condition on the outflow. The influence of this term is examined numerically, comparing the obtained results in a close neighbourhood of the outflow. The numerical experiment is carried out for a fluid flow through the channel with so called sudden extension. Presented numerical results are obtained by means of the OpenFOAM toolbox. They confirm that the kinetic energy of the flow in the channel can be controlled by means of the proposed boundary condition.

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