scholarly journals Stability of three-dimensional Gaussian vortices in an unbounded, rotating, vertically stratified, Boussinesq flow: linear analysis

2017 ◽  
Vol 824 ◽  
pp. 97-134 ◽  
Author(s):  
Mani Mahdinia ◽  
Pedram Hassanzadeh ◽  
Philip S. Marcus ◽  
Chung-Hsiang Jiang
Keyword(s):  
Growth Rate ◽  
Parameter Space ◽  
Accretion Disks ◽  
Growth Rates ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Small Region ◽  
Giant Planets ◽  
Ocean Eddies ◽  
The Stability

The linear stability of three-dimensional vortices in rotating, stratified flows has been studied by analysing the non-hydrostatic inviscid Boussinesq equations. We have focused on a widely used model of geophysical and astrophysical vortices, which assumes an axisymmetric Gaussian structure for pressure anomalies in the horizontal and vertical directions. For a range of Rossby numbers ($-0.5<Ro<0.5$) and Burger numbers ($0.02<Bu<2.3$) relevant to observed long-lived vortices, the growth rate and spatial structure of the most unstable eigenmodes have been numerically calculated and presented as a function of $Ro{-}Bu$. We have found neutrally stable vortices only over a small region of the $Ro{-}Bu$ parameter space: cyclones with $Ro\sim 0.02{-}0.05$ and $Bu\sim 0.85{-}0.95$. However, we have also found that anticyclones in general have slower growth rates compared to cyclones. In particular, the growth rate of the most unstable eigenmode for anticyclones in a large region of the parameter space (e.g. $Ro<0$ and $0.5\lesssim Bu\lesssim 1.3$) is slower than 50 turnaround times of the vortex (which often corresponds to several years for ocean eddies). For cyclones, the region with such slow growth rates is confined to $0<Ro<0.1$ and $0.5\lesssim Bu\lesssim 1.3$. While most calculations have been done for $f/\bar{N}=0.1$ (where $f$ and $\bar{N}$ are the Coriolis and background Brunt–Väisälä frequencies), we have numerically verified and explained analytically, using non-dimensionalized equations, the insensitivity of the results to reducing $f/\bar{N}$ to the more ocean-relevant value of 0.01. The results of our stability analysis of Gaussian vortices both support and contradict the findings of earlier studies with QG or multilayer models or with other families of vortices. The results of this paper provide a stepping stone to study the more complicated problems of the stability of geophysical (e.g. those in the atmospheres of giant planets) and astrophysical vortices (in accretion disks).

scholarly journals Instability Through Anisotropy in Spherical Stellar Systems

1987 ◽  
Vol 127 ◽  
pp. 515-516
Author(s):  
P.L. Palmer ◽  
J. Papaloizou
Keyword(s):  
Growth Rate ◽  
Eigenvalue Problem ◽  
Growth Rates ◽  
Stellar Systems ◽  
Matrix Eigenvalue Problem ◽  
Simple Method ◽  
Anisotropic Models ◽  
Poisson Equations ◽  
Degree Of Anisotropy ◽  
The Stability

We consider the linear stability of spherical stellar systems by solving the Vlasov and Poisson equations which yield a matrix eigenvalue problem to determine the growth rate. We consider this for purely growing modes in the limit of vanishing growth rate. We show that a large class of anisotropic models are unstable and derive growth rates for the particular example of generalized polytropic models. We present a simple method for testing the stability of general anisotropic models. Our anlysis shows that instability occurs even when the degree of anisotropy is very slight.

Resistive Ballooning Modes in Three-Dimensional Configurations

1982 ◽  
Vol 37 (8) ◽  
pp. 848-858 ◽  
Author(s):  
D. Correa-Restrepo
Keyword(s):  
Growth Rates ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Coupled System ◽  
Small Constant ◽  
Ballooning Mode ◽  
The Stability ◽  
The Magnetic Field ◽  
Symmetric Systems ◽  
The Ideal

Resistive ballooning modes in general three-dimensional configurations are studied on the basis of the equations of motion of resistive MHD. Assuming small, constant resistivity and perturbations localized transversally to the magnetic field, a stability criterion is derived in the form of a coupled system of two second-order differential equations. This criterion contains several limiting cases, in particular the ideal ballooning mode criterion and criteria for the stability of symmetric systems. Assuming small growth rates, analytical results are derived by multiple-length-scale expansion techniques. Instabilities are found, their growth rates scaling as fractional powers of the resistivity

On Estimates for Growth Rates of Unstable Azimuthal Disturbances in the Stability Problem of Swirling Flows with Radius- Dependent Density

2017 ◽  
Vol 13 (3) ◽  
pp. 1-12
Author(s):  
Halle Dattu Malai Subbiah
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Stability Problem ◽  
Variable Density ◽  
Swirling Flows ◽  
Wave Number ◽  
Two Dimensional ◽  
Azimuthal Wave Number ◽  
The Stability ◽  
Dependent Density

Estimates for the growth rate of unstable two-dimensional disturbances to swirling flows with variable density are obtained and as a consequence it is proved that the growth rate tends to zero as the azimuthal wave number tends to infinity for two classes of basic flows.

On the stability of nonlinear waves coexisting with plasma beams

1975 ◽  
Vol 13 (1) ◽  
pp. 173-187 ◽  
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Nonlinear Wave ◽  
Growth Rates ◽  
Three Dimensional ◽  
Stationary Waves ◽  
One Dimensional ◽  
Long Wavelength ◽  
Long Wave ◽  
Set Up ◽  
The Stability ◽  
The One

In this paper we consider the stability of one-dimensional stationary waves set up by two counter-streaming beams of electrons in a background of stationary ions. The perturbations considered are long-wave in a direction perpendicular to the wave. The presence of a uniform magnetic field in the direction of the wave and the effect of a perpendicular pressure are taken into account. In the long-wavelength limit growth rates are diminished by the nonlinear wave. When the amplitude of this wave tends to its maximum value, the growth rates tend to zero. Thus the wave has a stabilizing effect for long-wave perturbations. Three- dimensional effects lead to additional instabilities which are also quenched by the nonlinear wave, but not as fast as the one-dimensional calculation indicates.

scholarly journals The htrA Gene Plays an Important role During Yersinia Pseudotuberculosis Growth at High Temperature

2020 ◽  
Author(s):  
Elena Escobar Garduño ◽  
Lucia Soto Urzua ◽  
Rogelio Rodriguez Sotres ◽  
Luis Javier Martinez Morales
Keyword(s):  
Growth Rate ◽  
Mutant Strain ◽  
Growth Rates ◽  
Yersinia Pseudotuberculosis ◽  
Wild Strain ◽  
Three Dimensional ◽  
Data Bank ◽  
Immunoblot Analysis ◽  
Dimensional Structure ◽  
Bacteria Growth

Abstract htrA is a gene coding for the stress inducible HtrA protein, identified as a temperature stress response protein in several Gram positive and Gram negative bacteria. Growth rates at several temperatures (30ºC, 37ºC and 42ºC) were compared for Yersinia pseudotuberculosis YPIII wild strain and the isogenic mutant 1YPIII (htrA::Km), which was obtained by insertion of a kanamycin resistance cassette into the htrA gene.Y. pseudotuberculosis 1YPIII growth rates did not differ from the Y. pseudotuberculosis wild strain growth rates when cultivated at 30°C, which is consistent with a non-essential role for the HtrA protein at this temperature. However, 1YPIII mutant strain growth rate decreased by 18.73% at 37°C, and by 60.14% at 42°C, as compared to the Y. pseudotuberculosis YPIII wild strain growth rate. HtrA complementation in the strain 1YPIII/pAHTRA46 suppressed the differences in growth rates. Immunoblot analysis confirmed the absence of the HtrA protein in the 1YPIII mutant strain at any of the growth temperatures under analysis. In silico predictions were obtained for the three-dimensional structure of amino acid sequence belonging to HtrA from Y. pseudotuberculosis YPIII, Yersinia pestis CO92, using the protein data bank structure 1KY9:B from Escherichia coli, as template. The model's quality was found to be acceptable. Southern blot analysis shows a single htrA gene signal. These data indicate that the unique htrA gene in Y. pseudotuberculosis YPIII is required for the adaptive response of this species to high temperatures and although it is not a pathogenicity factor, it can be targeted by antibiotics.

scholarly journals The Growth and Saturation of Submesoscale Instabilities in the Presence of a Barotropic Jet

2018 ◽  
Vol 48 (11) ◽  
pp. 2779-2797 ◽  
Author(s):  
Megan A. Stamper ◽  
John R. Taylor ◽  
Baylor Fox-Kemper
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Initial Conditions ◽  
Boussinesq Equations ◽  
Small Region ◽  
Computational Domain ◽  
Mean Flow ◽  
The Mean

AbstractMotivated by recent observations of submesoscales in the Southern Ocean, we use nonlinear numerical simulations and a linear stability analysis to examine the influence of a barotropic jet on submesoscale instabilities at an isolated front. Simulations of the nonhydrostatic Boussinesq equations with a strong barotropic jet (approximately matching the observed conditions) show that submesoscale disturbances and strong vertical velocities are confined to a small region near the initial frontal location. In contrast, without a barotropic jet, submesoscale eddies propagate to the edges of the computational domain and smear the mean frontal structure. Several intermediate jet strengths are also considered. A linear stability analysis reveals that the barotropic jet has a modest influence on the growth rate of linear disturbances to the initial conditions, with at most a ~20% reduction in the growth rate of the most unstable mode. On the other hand, a basic state formed by averaging the flow at the end of the simulation with a strong barotropic jet is linearly stable, suggesting that nonlinear processes modify the mean flow and stabilize the front.

Three-dimensional stability of solitary shear kinetic Alfvén waves in a low-beta plasma

1989 ◽  
Vol 41 (1) ◽  
pp. 171-184 ◽  
Author(s):  
K. P. Das ◽  
L. P. J. Kamp ◽  
F. W. Sluijter
Keyword(s):  
Growth Rate ◽  
Dimensional Stability ◽  
Three Dimensional ◽  
Alfven Waves ◽  
Magnetized Plasma ◽  
Alfvén Waves ◽  
Ion Acoustic Solitons ◽  
The Stability ◽  
External Uniform Magnetic Field ◽  
Kinetic Alfvén Waves

The three-dimensional stability of solitary shear kinetic Alfvén waves in a low-β plasma is investigated by the method of Zakharov & Rubenchik (1974). It is found that there is no instability if the direction of perturbation falls within a certain region of space. The growth rate of the instability for the unstable region is determined. This growth rate is found to decrease with increasing angle between the direction of propagation of the solitary wave and the direction of the external uniform magnetic field. A particular case of the present analysis gives results on the stability of ion-acoustic solitons in a magnetized plasma.

The Effect of Phosphine Pressure on the Band Gap of Ga0.5In0.5P

1994 ◽  
Vol 340 ◽  
Author(s):  
Sarah R. Kurtz ◽  
D. J. Arent ◽  
K. A. Bertness ◽  
J. M. Olson
Keyword(s):  
Growth Rate ◽  
Surface Structure ◽  
Band Gap ◽  
Surface Diffusion ◽  
Parameter Space ◽  
Growth Temperature ◽  
Growth Rates ◽  
Diffusion Length ◽  
Group V ◽  
Group Iii

ABSTRACTThe band gap of Ga0.51n0.5P is studied as a function of phosphine pressure, B-type substrate misorientation, growth rate, and growth temperature, with emphasis placed on the effect of the phosphine pressure. Over most of the parameter space explored (high temperatures, large substrate misorientations, and low growth rates), the band gap increases with decreasing phosphine. This increase is proposed to be caused by lower phosphorus coverage of the surface, resulting in a different surface structure that doesn't promote ordering. The implications of this effect on the observed variations of band gap with growth temperature, substrate misorientation, and growth rate are discussed. For regions of parameter space in which the ordering appears to be kinetically limited by surface diffusion, the band gap increases slightly with phosphine pressure, consistent with observations that increased group-V pressure decreases the group-III surface diffusion length.

Thermoacoustic Instability Model With Porous Media: Linear Stability Analysis and the Impact of Porous Media

2018 ◽  
Author(s):  
Cody S. Dowd ◽  
Joseph W. Meadows
Keyword(s):  
Growth Rate ◽  
Porous Media ◽  
Stability Analysis ◽  
Frequency Shift ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Growth Rates ◽  
Thermoacoustic Instability ◽  
The Stability ◽  
The Impact

Lean premixed (LPM) combustion systems are susceptible to thermoacoustic instability, which occurs when acoustic pressure oscillations are in phase with the unsteady heat release rates. Porous media has inherent acoustic damping properties, and has been shown to mitigate thermoacoustic instability; however, theoretical models for predicting thermoacoustic instability with porous media do not exist. In the present study, a 1-D model has been developed for the linear stability analysis of the longitudinal modes for a series of constant cross-sectional area ducts with porous media using a n-Tau flame transfer function. By studying the linear regime, the prediction of acoustic growth rates and subsequently the stability of the system is possible. A transfer matrix approach is used to solve for acoustic perturbations of pressure and velocity, stability growth rate, and frequency shift without and with porous media. The Galerkin approximation is used to approximate the stability growth rate and frequency shift, and it is compared to the numerical solution of the governing equations. Porous media is modeled using the following properties: porosity, flow resistivity, effective bulk modulus, and structure factor. The properties of porous media are systematically varied to determine the impact on the eigenfrequencies and stability growth rates. Porous media is shown to increase the stability domain for a range of time delays (Tau) compared to similar cases without porous media.

The three-dimensional stability of finite-amplitude convection in a layered porous medium heated from below

1990 ◽  
Vol 211 ◽  
pp. 437-461 ◽  
Author(s):  
D. A. S. Rees ◽  
D. S. Riley
Keyword(s):  
Porous Medium ◽  
Parameter Space ◽  
Dimensional Stability ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Neutral Curve ◽  
Horizontal Extent ◽  
Square Cells ◽  
The Stability

Landau–Ginzburg equations are derived and used to study the three-dimensional stability of convection in a layered porous medium of infinite horizontal extent. Criteria for the stability of convection with banded or square planform are determined and results are presented for two-layer and symmetric three-layer systems. In general the neutral curve is uni-modal and parameter space is divided into regions where either rolls or square cells are stable. For certain ranges of parameters, however, the neutral curve is bimodal and there exists a locus of parameters where two modes with different wavenumbers have simultaneous onset.

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