Strato-hyperbolic instability: a new mechanism of instability in stably stratified vortices

2018 ◽  
Vol 854 ◽  
pp. 293-323
Author(s):  
Shota Suzuki ◽  
Makoto Hirota ◽  
Yuji Hattori
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Local Stability ◽  
Underlying Mechanism ◽  
Internal Gravity Waves ◽  
Stagnation Points ◽  
Local Stability Analysis ◽  
The Stability ◽  
Parameter Values ◽  
Stuart Vortices

The stability of stably stratified vortices is studied by local stability analysis. Three base flows that possess hyperbolic stagnation points are considered: the two-dimensional (2-D) Taylor–Green vortices, the Stuart vortices and the Lamb–Chaplygin dipole. It is shown that the elliptic instability is stabilized by stratification; it is completely stabilized for the 2-D Taylor–Green vortices, while it remains and merges into hyperbolic instability near the boundary or the heteroclinic streamlines connecting the hyperbolic stagnation points for the Stuart vortices and the Lamb–Chaplygin dipole. More importantly, a new instability caused by hyperbolic instability near the hyperbolic stagnation points and phase shift by the internal gravity waves is found; it is named the strato-hyperbolic instability; the underlying mechanism is parametric resonance as unstable band structures appear in contours of the growth rate. A simplified model explains the mechanism and the resonance curves. The growth rate of the strato-hyperbolic instability is comparable to that of the elliptic instability for the 2-D Taylor–Green vortices, while it is smaller for the Stuart vortices and the Lamb–Chaplygin dipole. For the Lamb–Chaplygin dipole, the tripolar instability is found to merge with the strato-hyperbolic instability as stratification becomes strong. The modal stability analysis is also performed for the 2-D Taylor–Green vortices. It is shown that global modes of the strato-hyperbolic instability exist; the structure of an unstable eigenmode is in good agreement with the results obtained by local stability analysis. The strato-hyperbolic mode becomes dominant depending on the parameter values.

scholarly journals Local stability analysis and eigenvalue sensitivity of reacting bluff-body wakes

2016 ◽  
Vol 788 ◽  
pp. 549-575 ◽  
Author(s):  
Benjamin Emerson ◽  
Tim Lieuwen ◽  
Matthew P. Juniper
Keyword(s):  
Stability Analysis ◽  
Acoustic Waves ◽  
Local Stability ◽  
Bluff Body ◽  
Density Ratio ◽  
Global Mode ◽  
Eigenvalue Sensitivity ◽  
Local Stability Analysis ◽  
Measured Time ◽  
The Stability

This paper presents an experimental and theoretical investigation of high-Reynolds-number low-density reacting wakes near a hydrodynamic Hopf bifurcation. This configuration is applicable to the wake flows that are commonly used to stabilize flames in high-velocity flows. First, an experimental study is conducted to measure the limit-cycle oscillation of this reacting bluff-body wake. The experiment is repeated while independently varying the bluff-body lip velocity and the density ratio across the flame. In all cases, the wake exhibits a sinuous oscillation. Linear stability analysis is performed on the measured time-averaged velocity and density fields. In the first stage of this analysis, a local spatiotemporal stability analysis is performed on the measured time-averaged velocity and density fields. The stability analysis results are compared to the experimental measurement and demonstrate that the local stability analysis correctly captures the influence of the lip-velocity and density-ratio parameters on the sinuous mode. In the second stage of the analysis, the linear direct and adjoint global modes are estimated by combining the local results. The sensitivity of the eigenvalue to changes in intrinsic feedback mechanisms is found by combining the direct and adjoint global modes. This is referred to as the eigenvalue sensitivity throughout the paper for reasons of brevity. The predicted global mode frequency is consistently within 10 % of the measured value, and the linear global mode shape closely resembles the measured nonlinear oscillations. The adjoint global mode reveals that the oscillation is strongly sensitive to open-loop forcing in the shear layers. The eigenvalue sensitivity identifies a wavemaker in the recirculation zone of the wake. A parametric study shows that these regions change little when the density ratio and lip velocity change. In the third stage of the analysis, the stability analysis is repeated for the varicose hydrodynamic mode. Although not physically observed in this unforced flow, the varicose mode can lock into longitudinal acoustic waves and cause thermoacoustic oscillations to occur. The paper shows that the local stability analysis successfully predicts the global hydrodynamic stability characteristics of this flow and shows that experimental data can be post-processed with this method in order to identify the wavemaker regions and the regions that are most sensitive to external forcing, for example from acoustic waves.

scholarly journals The effect of a lifted flame on the stability of round fuel jets

2008 ◽  
Vol 609 ◽  
pp. 275-284 ◽  
Author(s):  
JOSEPH W. NICHOLS ◽  
PETER J. SCHMID
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Local Stability ◽  
Premixed Flame ◽  
Absolute Instability ◽  
Low Mach Number ◽  
Lifted Flame ◽  
Local Stability Analysis ◽  
The Stability ◽  
Globally Stable

The stability and dynamics of an axisymmetric lifted flame are studied by means of direct numerical simulation (DNS) and linear stability analysis of the reacting low-Mach-number equations. For light fuels (such as non-premixed methane/air flames), the non-reacting premixing zone upstream of the lifted flame base contains a pocket of absolute instability supporting self-sustaining oscillations, causing flame flicker even in the absence of gravity. The liftoff heights of the unsteady flames are lower than their steady counterparts (obtained by the method of selective frequency damping (SFD)), owing to premixed flame propagation during a portion of each cycle. From local stability analysis, the lifted flame is found to have a significant stabilizing influence at and just upstream of the flame base, which can truncate the pocket of absolute instability. For sufficiently low liftoff heights, the truncated pocket of absolute instability can no longer support self-sustaining oscillations, and the flow is rendered globally stable.

A fractional-order toxin producing phytoplankton and zooplankton system

2014 ◽  
Vol 07 (04) ◽  
pp. 1450039 ◽  
Author(s):  
M. Javidi ◽  
N. Nyamoradi
Keyword(s):  
Stability Analysis ◽  
Nutrient Cycling ◽  
Fractional Order ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Stability Conditions ◽  
Hurwitz Stability ◽  
Local Stability Analysis ◽  
Mathematical System ◽  
Parameter Values

In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton–zooplankton (TPPZ) system with nutrient cycling. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the equilibriums are determined. Local stability analysis of the TPPZ is studied by using the fractional Routh–Hurwitz stability conditions. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.

scholarly journals Local linear stability analysis of cyclone separators

2017 ◽  
Vol 816 ◽  
pp. 507-538 ◽  
Author(s):  
T. A. Grimble ◽  
A. Agarwal ◽  
M. P. Juniper
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Local Stability ◽  
High Speed Photography ◽  
Unstable Flow ◽  
Local Stability Analysis ◽  
Local Linear ◽  
The Stability

Local linear stability analysis is applied to the flow inside a cyclone separator to investigate the unsteady precession of the vortex core. The results of the stability analysis are compared with experimental measurements of the vortex oscillations using high-speed photography with particle seeding and hot-wire anemometry. The experiments reveal distinct spatial variation in the oscillation behaviour within the cyclone. The unsteady motion is focused at each end of the device, at both the narrow cone tip and just below the exhaust duct at the top of the cone, which is known as a vortex finder. The local stability analysis shows that an absolute instability is present throughout the flow for some non-zero azimuthal wavenumbers. The unsteady flow is observed to be driven by coupling between the shear layer and inertial waves confined within the vortex core. Comparison of the stability analysis with experiments shows the same frequency and mode shape behaviour and suggests that the local analysis accurately predicts the unstable modes of the system. The precessing vortex core is responsible for a narrow-band acoustic noise. Comparisons are also drawn with acoustic measurements made on cyclones in which the system is defined by key non-dimensional parameters, such as the swirl number and outlet diameter ratio. The results in this study demonstrate the applicability of local stability analysis to a complex swirling system and yield credible details about the underlying mechanisms of the unstable flow inside the cyclone.

Stability Analysis of an Endoreversible Heat Engine with Stefan-Boltzmann Heat Transfer Law Working in Maximum-Power-Like Regime

2006 ◽  
Vol 13 (01) ◽  
pp. 43-53 ◽  
Author(s):  
J. C. Chimal-Eguía ◽  
M. A. Barranco-Jiménez ◽  
F. Angulo-Brown
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Local Stability ◽  
Heat Engine ◽  
Relaxation Times ◽  
Stability Study ◽  
Maximum Power ◽  
Working Fluid ◽  
Local Stability Analysis ◽  
The Stability

A local stability study of an endoreversible Stefan-Boltzmann (SB) engine, working in a maximum-power-like regime, is presented. This engine consists of a Carnot engine that exchanges heat with heat reservoirs T1 and T2, (T 1 > T2) through a couple of thermal links, both having the same conductance g. In addition, the working fluid has the same heat capacity C in the two isothermal branches of the cycle. From the local stability analysis we conclude that the SB engine is stable for every value of g, C and τ = T2/T1. After a small perturbation, the system decays to the steady state with either of two different relaxation times; both being proportional to C/g, and τ. Finally, when we plot some of the thermodynamic properties in the steady state versus τ, we find how an increment of τ can improve the stability of the system, at the same decreasing the efficiency and the power of the system. This suggests a compromise between the stability and the energetic properties of the engine driven by τ.

Local Stability of an Endoreversible Heat Engine Working in an Ecological Regime

2007 ◽  
Vol 14 (04) ◽  
pp. 411-424 ◽  
Author(s):  
J. C. Chimal-Eguía ◽  
I. Reyes-Ramírez ◽  
L. Guzmán-Vargas
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Stability Analysis ◽  
Local Stability ◽  
Heat Engine ◽  
Relaxation Times ◽  
Local Stability Analysis ◽  
The Stability ◽  
Qualitative Phase ◽  
Ecological Regime

We present a local stability analysis of an endoreversible engine working in an ecological regime, for three common heat transfer laws. From our local stability analysis we conclude that the system is stable for every value of the heat conductivity g, the heat capacity C and the ratio of temperatures τ = T2/T1 with T1 > T2. After a small perturbation the system decays exponentially to the steady state determined by two different relaxation times. We observe that the stability of the system improves as r increases whereas the steady-state energetic properties of the engine decline. Moreover, we compare the stability properties of the engine working in the ecological regime and under maximum power output. Finally, qualitative phase-space portraits for the evolution of the system are presented for representative cases.

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.

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