Oscillations of Accretion Disks and Boundary Layers in Cataclysmic Variables. II. A Local, Linear Stability Analysis of Accretion Disk Boundary Layers

2000 ◽  
Vol 534 (2) ◽  
pp. 944-966 ◽  
Author(s):  
T. J. B. Collins ◽  
H. L. Helfer ◽  
H. M. Van Horn
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Boundary Layers ◽  
Accretion Disk ◽  
Accretion Disks ◽  
Linear Stability Analysis ◽  
Cataclysmic Variables ◽  
Local Linear

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.

scholarly journals Stability of a Double-Diffusive Interface in the Diffusive Convection Regime

2012 ◽  
Vol 42 (5) ◽  
pp. 840-854 ◽  
Author(s):  
J. R. Carpenter ◽  
T. Sommer ◽  
A. Wüest
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Boundary Layers ◽  
Linear Stability Analysis ◽  
Direct Numerical Simulations ◽  
Diffusive Convection ◽  
Diffusive Interface ◽  
Double Diffusive

Abstract In this paper, the authors explore the conditions under which a double-diffusive interface may become unstable. Focus is placed on the case of a cold, freshwater layer above a warm, salty layer [i.e., the diffusive convection (DC) regime]. The “diffusive interface” between these layers will develop gravitationally unstable boundary layers due to the more rapid diffusion of heat (the destabilizing component) relative to salt. Previous studies have assumed that a purely convective-type instability of these boundary layers is what drives convection in this system and that this may be parameterized by a boundary layer Rayleigh number. The authors test this theory by conducting both a linear stability analysis and direct numerical simulations of a diffusive interface. Their linear stability analysis reveals that the transition to instability always occurs as an oscillating diffusive convection mode and at boundary layer Rayleigh numbers much smaller than previously thought. However, these findings are based on making a quasi-steady assumption for the growth of the interfaces by molecular diffusion. When diffusing interfaces are modeled (using direct numerical simulations), the authors observe that the time dependence is significant in determining the instability of the boundary layers and that the breakdown is due to a purely convective-type instability. Their findings therefore demonstrate that the relevant instability in a DC staircase is purely convective.

scholarly journals Linear stability analysis of oscillating Ekman boundary layers

PAMM ◽  
2009 ◽  
Vol 9 (1) ◽  
pp. 489-490
Author(s):  
Martin Withalm ◽  
Jasmin Röper ◽  
Norbert P. Hoffmann
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Boundary Layers ◽  
Linear Stability Analysis
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