scholarly journals Inertial instability of intense stratified anticyclones. Part 1. Generalized stability criterion

2013 ◽  
Vol 732 ◽  
pp. 457-484 ◽  
Author(s):  
Ayah Lazar ◽  
A. Stegner ◽  
E. Heifetz
Keyword(s):  
Stability Criterion ◽  
Finite Depth ◽  
Marginal Stability ◽  
Rayleigh Criterion ◽  
Rankine Vortex ◽  
Stability Diagrams ◽  
Suitable Parameter ◽  
Inertial Instability ◽  
The Stability ◽  
Vertical Eddy

AbstractThe stability of axisymmetric vortices to inertial perturbations is investigated by means of linear stability analysis, taking into account stratification, vertical eddy viscosity, as well as finite depth of the flow. We consider different types of circular barotropic vortices in a linearly stratified shallow layer confined with rigid lids. For the simplest case of the Rankine vortex we develop an asymptotic analytic dispersion relation and a marginal stability criterion, which compares well with numerical results. This is a further generalization to the well-known generalized Rayleigh criterion, which is only valid for non-dissipative and non-stratified eddies. Unlike the Rayleigh criterion, it predicts that intense anticyclones may be stable even with a core region of negative absolute vorticity, and that the dissipation and stratification work together to stabilize the flow. Numerical analysis reveals that the stability diagrams for various types of vortices are almost identical in the Rossby, Burger and Ekman parameter space. This allows extension of our analytical solutions for the Rankine vortex to a wide variety of vortices. Furthermore, we show that a more suitable parameter for the intensity of the vortex is the vortex Rossby number, while for the inviscid case it is the local normalized vorticity. These predictions are in agreement with laboratory experiments presented in part 2 (J. Fluid Mech., vol. 732, 2013, pp. 485–509).

scholarly journals Effects of the Control Parameters on the Stability of a Laminar Boundary Layer on a Porous Flat Plate

2021 ◽  
Vol 26 (4) ◽  
pp. 113-127
Author(s):  
T.F. Lihonou ◽  
A.V. Monwanou ◽  
C.H. Miwadinou ◽  
J.B. Chabi Orou
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Temporal Stability ◽  
Three Dimensional ◽  
Darcy Number ◽  
Basic Flow ◽  
Marginal Stability ◽  
Stability Diagrams ◽  
Plane Plate ◽  
The Stability

Abstract This work is devoted to the analysis of the linear temporal stability of a laminar dynamic boundary layer on a horizontal porous plane plate. The basic flow is assumed to be laminar and two-dimensional. The basic flow velocity profiles are obtained by numerically solving the Blasius equation using the Runge-Kutta method. The perturbations of these basic solutions are expressed in the form of three-dimensional Tollmien-Schlichting waves. The formulation of the stability problem leads to the Orr-Sommerfeld equation modified by the permeability parameter (Darcy number) and the small Reynolds number. This equation is given in a general form which can be applied to the Chebyshev domain and the boundary layer domain and solved numerically using the Chebyshev spectral collocation method. The marginal stability diagrams, the critical Reynolds numbers and the eigenvalue spectra are obtained for different values of the parameters which have modified the stability equation. Numerical solutions indicate the importance of the effect of these parameters on the flow stability characteristics.

The effect of magnetic fields on the nonlinear instability of two superposed magnetic streaming fluids, each of a finite depth

1995 ◽  
Vol 73 (3-4) ◽  
pp. 163-173 ◽  
Author(s):  
Abdel Raouf F. Elhefnawy
Keyword(s):  
Magnetic Field ◽  
Multiple Scale ◽  
Finite Depth ◽  
Nonlinear Instability ◽  
Helmholtz Instability ◽  
Perturbed System ◽  
Stability Diagrams ◽  
The Stability ◽  
Normal Magnetic Field ◽  
Horizontal Interface

The nonlinear Kelvin–Helmholtz instability of a horizontal interface separating two flowing superposed magnetic fluids of finite depths is described in the presence of a normal magnetic field. The fluids are taken to be incompressible and inviscid and the motion is assumed to be irrotational. The method of multiple-scale perturbations is used to obtain two nonlinear Schrödinger equations describing the behaviour of the perturbed system. The stability of the system is discussed both theoretically and numerically and the stability diagrams are obtained. The nonlinear cutoff magnetic field that separates the regions of instability from those of stability is also obtained.

Stability of bounded rapid shear flows of a granular material

1996 ◽  
Vol 308 ◽  
pp. 31-62 ◽  
Author(s):  
Chi-Hwa Wang ◽  
R. Jackson ◽  
S. Sundaresan
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Granular Material ◽  
Bulk Density ◽  
Particulate Material ◽  
Dominant Mode ◽  
Marginal Stability ◽  
Sheared Layer ◽  
The Stability ◽  
Unusual Type

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

Intrinsic Thermal Stability of Anisotropic Thin-Film Superconductors

1990 ◽  
Vol 112 (1) ◽  
pp. 10-15 ◽  
Author(s):  
M. I. Flik ◽  
C. L. Tien
Keyword(s):  
Thin Film ◽  
Thermal Stability ◽  
Stability Criterion ◽  
High Temperature Superconductors ◽  
Stability Criteria ◽  
Anisotropic Thermal Conductivity ◽  
Operating Current ◽  
Released Energy ◽  
The Stability ◽  
Thermal Stability Of

Intrinsic thermal stability denotes a situation where a superconductor can carry the operating current without resistance at all times after the occurrence of a localized release of thermal energy. This novel stability criterion is different from the cryogenic stability criteria for magnets and has particular relevance to thin-film superconductors. Crystals of ceramic high-temperature superconductors are likely to exhibit anisotropic thermal conductivity. The resultant anisotropy of highly oriented films of superconductors greatly influences their thermal stability. This work presents an analysis for the maximum operating current density that ensures intrinsic stability. The stability criterion depends on the amount of released energy, the Biot number, the aspect ratio, and the ratio of the thermal conductivities in the plane of the film and normal to it.

The flow of a micropolar liquid layer down an inclined plane

1968 ◽  
Vol 64 (2) ◽  
pp. 513-526 ◽  
Author(s):  
A. J. Willson
Keyword(s):  
Thin Films ◽  
Steady State ◽  
Liquid Layer ◽  
Stability Criterion ◽  
Long Waves ◽  
Inclined Plane ◽  
The Stability ◽  
Micropolar Liquid

AbstractConsideration is given to the flow of a micropolar liquid down an inclined plane. The steady state is analysed and Yih's technique is employed in an investigation of the stability of this flow with respect to long waves. Detailed calculations are given for thin films and it is shown that the micropolar properties of the liquid play an important role in the stability criterion.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

The Meniscus Instability of a Thin Liquid Film

1988 ◽  
Vol 55 (4) ◽  
pp. 975-980 ◽  
Author(s):  
H. Koguchi ◽  
M. Okada ◽  
K. Tamura
Keyword(s):  
Thin Film ◽  
Analytical Solution ◽  
Liquid Film ◽  
Tilt Angle ◽  
Stability Criterion ◽  
Thin Liquid Film ◽  
Normal Direction ◽  
Wave Number ◽  
The Stability ◽  
Maximum Amplification

This paper reports on the instability for the meniscus of a thin film of a very viscous liquid between two tilted plates, which are separated at a constant speed with a tilt angle in the normal direction of the plates. The disturbances on the meniscus moving with movement of the plates are examined experimentally and theoretically. The disturbances are started when the velocity of movement of the plates exceeds a critical one. The wavelength of the disturbances is measured by using a VTR. The instability of the meniscus is studied theoretically using the linearized perturbation method. A simple and complete analytical solution yields both a stability criterion and the wave number for a linear thickness geometry. These results compared with experiments for the instability show the validity of the stability criterion and the best agreement is obtained with the wave number of maximum amplification.

scholarly journals Stability analysis of magnetic fluids in the presence of an oblique field and mass and heat transfer

2020 ◽  
Vol 330 ◽  
pp. 01035
Author(s):  
Rabah Djeghiour ◽  
Bachir Meziani
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Magnetic Fluids ◽  
Physical Parameters ◽  
Stability Diagrams ◽  
Stability And Instability ◽  
Mass And Heat Transfer ◽  
Model Equations ◽  
The Stability ◽  
Oblique Magnetic Field

In this paper, we investigate an analysis of the stability of a basic flow of streaming magnetic fluids in the presence of an oblique magnetic field is made. We have use the linear analysis of modified Kelvin-Helmholtz instability by the addition of the influence of mass transfer and heat across the interface. Problems equations model is presented where nonlinear terms are neglected in model equations as well as the boundary conditions. In the case of a oblique magnetic field, the dispersion relation is obtained and discussed both analytically and numerically and the stability diagrams are also obtained. It is found that the effect of the field depends strongly on the choice of some physical parameters of the system. Regions of stability and instability are identified. It is found that the mass and heat transfer parameter has a destabilizing influence regardless of the mechanism of the field.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

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