Linear Stability of Jet Flows

1977 ◽  
Vol 44 (3) ◽  
pp. 378-384 ◽  
Author(s):  
A. K. Bajaj ◽  
V. K. Garg
Keyword(s):  
Stability Theory ◽  
Outer Region ◽  
Parallel Flow ◽  
Jet Flows ◽  
Complex Eigenvalue ◽  
Spatial Stability ◽  
Laminar Jets ◽  
Flow Approximation ◽  
The Stability ◽  
Asymptotic Forms

A theoretical investigation into the linear, spatial stability of plane laminar jets is presented. The three cases studied are: 1. Inviscid stability of Sato’s velocity profile. 2. Viscous stability of the Bickley’s jet using parallel-flow stability theory. 3. Viscous stability of the Bickley’s jet using a theory modified to account for the inflow terms. The integration of stability equations is started from the outer region of the jet toward the jet axis using the solution of the asymptotic forms of the governing equations. An eigenvalue search technique is employed to find the number of eigenvalues and their approximate location in a closed region of the complex eigenvalue plane. The accurate eigenvalues are obtained using secant method. The inviscid spatial stability theory is found to give results that are in better agreement with Sato’s experimental results than those obtained by him after transformation of the temporal theory results. For the viscous case the critical Reynolds number found by using the theory accounting for inflow is in better agreement with the experimental value than that given by the parallel-flow theory, implying thereby that the parallel-flow approximation for a jet is erroneous for the stability analysis.

Nonparallel Effects on the Stability of Jet Flows

1978 ◽  
Vol 45 (4) ◽  
pp. 717-722 ◽  
Author(s):  
V. K. Garg ◽  
G. F. Round
Keyword(s):  
Transverse Velocity ◽  
Outer Region ◽  
Wave Number ◽  
Jet Flows ◽  
Frequency Range ◽  
Governing Equations ◽  
Low Frequencies ◽  
High Frequencies ◽  
The Stability ◽  
Asymptotic Forms

A theoretical analysis of the linear, spatial stability of Bickley’s jet is presented. The analysis takes into account the effects of transverse velocity component and the axial variations of the basic flow and of the disturbance amplitude, wavenumber and spatial growth rate. The integration of stability equations is started from the outer region of the jet toward the jet axis using the solution of the asymptotic forms of the governing equations. Results are compared with those for the parallel-flow stability analysis. It is found that the nonparallel effects decrease the wave number at low frequencies but increase it at high frequencies. Thus the nonparallel effects make Bickley’s jet unstable over a wider frequency range.

Basic Concepts in the Stability Theory of Thin-walled Structures

2010 ◽  
Author(s):  
A. Guran ◽  
L. Lebedev ◽  
Michail D. Todorov ◽  
Christo I. Christov
Keyword(s):  
Stability Theory ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Basic Concepts ◽  
The Stability

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

On the Non-Uniqueness of the Parallel-Flow Approximation

1992 ◽  
pp. 344-355 ◽  
Author(s):  
C. David Pruett ◽  
Lian L. Ng ◽  
Gordon Erlebacher
Keyword(s):  
Parallel Flow ◽  
Flow Approximation

Stability of parallel flow of a multi-component cylindrical plasma to electrostatic perturbations

1981 ◽  
Vol 26 (2) ◽  
pp. 369-383
Author(s):  
R. Lucas
Keyword(s):  
Normal Mode ◽  
Axial Velocity ◽  
Sufficient Conditions ◽  
Parallel Flow ◽  
Zeroth Order ◽  
Unperturbed State ◽  
Plasma Component ◽  
Cylindrical Plasma ◽  
The Stability ◽  
System Variables

Sufficient conditions for the stability of parallel flow of a warm N-component cylindrical plasma to electrostatic perturbations are obtained. In the unperturbed state the jth plasma component is assumed to have axial velocity Vj0(r), r being the radial co-ordinate, and the equilibrium quantities are permitted to be arbitrary functions of r consistent with the zeroth-order equations. The L2-norms of certain system variables are shown to be bounded uniformly in time. Circle theorems are obtained for the complex eigenfrequencies of any normal mode.

scholarly journals SYMPLECTIC STABILITY, ANALYTIC STABILITY IN NON-ALGEBRAIC COMPLEX GEOMETRY

2004 ◽  
Vol 15 (02) ◽  
pp. 183-209 ◽  
Author(s):  
ANDREI TELEMAN
Keyword(s):  
Weight Function ◽  
Complex Manifold ◽  
Stability Theory ◽  
Complex Geometry ◽  
Reductive Group ◽  
Hamiltonian Action ◽  
Maximal Weight ◽  
Analytic Stability ◽  
The Stability

We give a systematic presentation of the stability theory in the non-algebraic Kählerian geometry. We introduce the concept of "energy complete Hamiltonian action". To an energy complete Hamiltonian action of a reductive group G on a complex manifold one can associate a G-equivariant maximal weight function and prove a Hilbert criterion for semistability. In other words, for such actions, the symplectic semistability and analytic semistability conditions are equivalent.

scholarly journals Inviscid spatial stability of a compressible mixing layer. Part 3. Effect of thermodynamics

1991 ◽  
Vol 224 ◽  
pp. 159-175 ◽  
Author(s):  
T. L. Jackson ◽  
C. E. Grosch
Keyword(s):  
Prandtl Number ◽  
Mixing Layer ◽  
Mean Flow ◽  
Temperature Relation ◽  
Compressible Mixing Layer ◽  
Spatial Stability ◽  
Mean Temperature ◽  
The Mean ◽  
The Difference ◽  
The Stability

We report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

Sign in / Sign up

Export Citation Format

Share Document