Global mode analysis of ideal magnetohydrodynamic modes in a heliotron/torsatron system: I. Mercier-unstable equilibria

1999 ◽  
Vol 6 (5) ◽  
pp. 1562-1574 ◽  
Author(s):  
J. Chen ◽  
N. Nakajima ◽  
M. Okamoto
Keyword(s):  
Mode Analysis ◽  
Global Mode ◽  
Ideal Magnetohydrodynamic

Wall stabilization in a collisionless bumpy theta-pinch

1977 ◽  
Vol 18 (2) ◽  
pp. 317-337 ◽  
Author(s):  
George Vahala ◽  
Linda Vahala
Keyword(s):  
Growth Rates ◽  
Normal Mode Analysis ◽  
Upper And Lower Bounds ◽  
Mode Analysis ◽  
Well Posedness ◽  
Theta Pinch ◽  
Pressure Anisotropy ◽  
Special Cases ◽  
Ideal Magnetohydrodynamic ◽  
The Ideal

Finite wavelength guiding centre plasma stability of the bumpy θ-pinch is examined by a normal mode analysis. It is shown that previous bumpy θ-pinch calculations are recoverable as special cases of this analysis. The ideal magnetohydrodynamic and guiding centre plasma growth rates are compared for various pressure anisotropies and for various wavenumbers of the field line bumpiness. The well-posedness conditions on the guiding centre plasma equations are shown to give upper and lower bounds on the permissible pressure anisotropy which corresponds to the Aifvén continuum staying on the stable side of the spectrum and to the particle mirror force not having a singularity. It is also found that the higher azimuthal m ≥ 2 modes have growth rates larger than the m = 1 mode.

Global mode analysis of a pipe flow through a 1:2 axisymmetric sudden expansion

2010 ◽  
Vol 22 (7) ◽  
pp. 071702 ◽  
Author(s):  
E. Sanmiguel-Rojas ◽  
C. del Pino ◽  
C. Gutiérrez-Montes
Keyword(s):  
Pipe Flow ◽  
Mode Analysis ◽  
Sudden Expansion ◽  
Global Mode ◽  
Flow Through

scholarly journals Improvements in global mode analysis

2008 ◽  
Vol 118 ◽  
pp. 012083 ◽  
Author(s):  
T P Larson ◽  
J Schou
Keyword(s):  
Mode Analysis ◽  
Global Mode

scholarly journals Global mode analysis of axisymmetric bluff-body wakes: Stabilization by base bleed

2009 ◽  
Vol 21 (11) ◽  
pp. 114102 ◽  
Author(s):  
E. Sanmiguel-Rojas ◽  
A. Sevilla ◽  
C. Martínez-Bazán ◽  
J.-M. Chomaz
Keyword(s):  
Bluff Body ◽  
Mode Analysis ◽  
Global Mode ◽  
Base Bleed

Boussinesq global modes and stability sensitivity, with applications to stratified wakes

2017 ◽  
Vol 812 ◽  
pp. 1146-1188
Author(s):  
Kevin K. Chen ◽  
Geoffrey R. Spedding
Keyword(s):  
Bluff Body ◽  
Boussinesq Equations ◽  
Base Flow ◽  
Mode Analysis ◽  
Flow Density ◽  
Global Mode ◽  
Multiple Production ◽  
Small Density ◽  
Global Modes ◽  
The Stability

For the Boussinesq equations, we present a theory of linear stability sensitivity to base flow density and velocity modifications. Given a steady-state flow with small density variations, the sensitivity of the stability eigenvalues is computed from the direct and adjoint global modes of the linearised Boussinesq equations, similarly to Marquetet al.(J. Fluid Mech., vol. 615, 2008, pp. 221–252). Combinations of the density and velocity components of these modes reveal multiple production and transport mechanisms that contribute to the eigenvalue sensitivity. We present an application of the sensitivity theory to a stably linearly density-stratified flow around a thin plate at a$90^{\circ }$angle of attack, a Reynolds number of 30 and Froude numbers of 1, 8 and$\infty$. The global mode analysis reveals lightly damped undulations pervading through the entire domain, which are predicted by both inviscid uniform base flow theory and Orr–Sommerfeld theory. The sensitivity to base flow velocity modifications is primarily concentrated just downstream of the bluff body. On the other hand, the sensitivity to base flow density modifications is concentrated in regions both immediately upstream and immediately downstream of the plate. Both sensitivities have a greater upstream presence for lower Froude numbers.

scholarly journals Direct and adjoint global modes of a recirculation bubble: lift-up and convective non-normalities

2009 ◽  
Vol 622 ◽  
pp. 1-21 ◽  
Author(s):  
OLIVIER MARQUET ◽  
MATTEO LOMBARDI ◽  
JEAN-MARC CHOMAZ ◽  
DENIS SIPP ◽  
LAURENT JACQUIN
Keyword(s):  
High Speed ◽  
Passive Control ◽  
Three Dimensional ◽  
Adjoint Problem ◽  
Base Flow ◽  
Mode Analysis ◽  
Global Mode ◽  
Recirculation Bubble ◽  
Global Modes ◽  
The Stability

The stability of the recirculation bubble behind a smoothed backward-facing step is numerically computed. Destabilization occurs first through a stationary three-dimensional mode. Analysis of the direct global mode shows that the instability corresponds to a deformation of the recirculation bubble in which streamwise vortices induce low- and high-speed streaks as in the classical lift-up mechanism. Formulation of the adjoint problem and computation of the adjoint global mode show that both the lift-up mechanism associated with the transport of the base flow by the perturbation and the convective non-normality associated with the transport of the perturbation by the base flow explain the properties of the flow. The lift-up non-normality differentiates the direct and adjoint modes by their component: the direct is dominated by the streamwise component and the adjoint by the cross-stream component. The convective non-normality results in a different localization of the direct and adjoint global modes, respectively downstream and upstream. The implications of these properties for the control problem are considered. Passive control, to be most efficient, should modify the flow inside the recirculation bubble where direct and adjoint global modes overlap, whereas active control, by for example blowing and suction at the wall, should be placed just upstream of the separation point where the pressure of the adjoint global mode is maximum.

scholarly journals Global Mode Analysis of Ion-Temperature-Gradient Instabilities Using the Gyro-Fluid Model in Linear Devices

2018 ◽  
Vol 13 (0) ◽  
pp. 1401081-1401081 ◽  
Author(s):  
Tomotsugu OHNO ◽  
Naohiro KASUYA ◽  
Makoto SASAKI ◽  
Masatoshi YAGI
Keyword(s):  
Temperature Gradient ◽  
Fluid Model ◽  
Mode Analysis ◽  
Ion Temperature ◽  
Ion Temperature Gradient ◽  
Global Mode

Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows

2007 ◽  
Vol 593 ◽  
pp. 333-358 ◽  
Author(s):  
DENIS SIPP ◽  
ANTON LEBEDEV
Keyword(s):  
Reynolds Numbers ◽  
Cavity Flow ◽  
Open Cavity ◽  
Mode Analysis ◽  
Mean Flow ◽  
Global Mode ◽  
Weakly Nonlinear ◽  
Experimental Function ◽  
The Mean ◽  
Cylinder Flow

This article deals with the first Hopf bifurcation of a cylinder flow, and more particularly with the properties of the unsteady periodic Kármán vortex street regime that sets in for supercritical Reynolds numbers Re > 46. Barkley (Europhys. Lett. vol.75, 2006, p. 750) has recently studied the linear properties of the associated mean flow, i.e. the flow which is obtained by a time average of this unsteady periodic flow. He observed, thanks to a global mode analysis, that the mean flow is marginally stable and that the eigenfrequencies associated with the global modes of the mean flow fit the Strouhal to Reynolds experimental function well in the range 46 < Re < 180. The aim of this article is to give a theoretical proof of this result near the bifurcation. For this, we do a global weakly nonlinear analysis valid in the vicinity of the critical Reynolds number Rec based on the small parameter ε = Rec−1 − Re−1 ≪ 1. We compute numerically the complex constants λ and μ′ which appear in the Stuart-Landau amplitude equation: dA/dt = ε λA − εμ′ A|A|2. Here A is the scalar complex amplitude of the critical global mode. By analysing carefully the nonlinear interactions yielding the term μ′, we show for the cylinder flow that the mean flow is approximately marginally stable and that the linear dynamics of the mean flow yields the frequency of the saturated Stuart-Landau limit cycle. We will finally show that these results are not general, by studying the case of the bifurcation of an open cavity flow. In particular, we show that the mean flow in this case remains strongly unstable and that the frequencies associated with the eigenmodes do not exactly match those of the nonlinear unsteady periodic cavity flow. It will be demonstrated that two precise conditions must hold for a linear stability analysis of a mean flow to be relevant and useful.

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