Destabilizing effect of plane Couette flow

Tatsuno, T.; Yoshida, Zensho; Mahajan, S. M.

doi:10.1063/1.1573211

Cited by 6 publications

(12 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, Tatsuno et al (2003) studied how a shear flow can destabilize a homogeneous magnetic field in the presence of an unstable density gradient. They found that a linear (Couette) velocity profile can be destabilizing when the velocity shear was not too strong.…”

Section: Introduction To Shear Flow Instabilitiesmentioning

confidence: 99%

Violation of Richardson's Criterion via Introduction of a Magnetic Field

Lecoanet

Zweibel

Townsend

et al. 2010

ApJ

View full text Add to dashboard Cite

Shear flow instabilities can profoundly affect the diffusion of momentum in jets, stars, and disks. The Richardson criterion gives a sufficient condition for instability of a shear flow in a stratified medium. The velocity gradient V ′ can only destabilize a stably stratified medium with squared Brunt-Väisälä frequency N 2 if V ′2 /4 > N 2 . We find this is no longer true when the medium is a magnetized plasma. We investigate the effect of stable stratification on magnetic field and velocity profiles unstable to magneto-shear instabilities, i.e., instabilities which require the presence of both magnetic field and shear flow. We show that a family of profiles originally studied by Tatsuno & Dorland (2006) remain unstable even when V ′2 /4 < N 2 , violating the Richardson criterion. However, not all magnetic fields can result in a violation of the Richardson criterion. We consider a class of flows originally considered by Kent (1968), which are destabilized by a constant magnetic field, and show that they become stable when V ′2 /4 < N 2 , as predicted by the Richardson criterion. This suggests that magnetic free energy is required to violate the Richardson criterion. This work implies that the Richardson criterion cannot be used when evaluating the ideal stability of a sheared, stably stratified, and magnetized plasma. We briefly discuss the implications for astrophysical systems.

show abstract

Section: Introduction To Shear Flow Instabilitiesmentioning

confidence: 99%

Violation of Richardson's Criterion via Introduction of a Magnetic Field

Lecoanet

Zweibel

Townsend

et al. 2010

ApJ

View full text Add to dashboard Cite

show abstract

“…The sufficiency of the condition (13) immediately follows from the conservation law (10). The necessity is drawn from Eq.…”

Section: Reduced Magnetohydrodynamics and Its Basic Properties 21 Fomentioning

confidence: 99%

“…5, we discuss the destabilizing effect of shear flow [13]. In contrast to its well-known stabilization of the low-frequency plasma motions, a shear flow may equally effectively destabilize a class of plasma modes.…”

Section: Introductionmentioning

confidence: 99%

“…KH instability is one of the most famous instabilities in parallel shear flow systems, in which the background flow is stable unless its curvature changes sign in the domain. However, even the background shear flow having a linear profile (free from KH instability) can make the equilibrium more unstable when combined with an Alfvén wave [13]. While the stabilizing mechanisms of shear flow have been stressed, relatively little attention has been paid to its destabilizing effect.…”

Section: Introductionmentioning

confidence: 99%

“…Equations (10) and (12) lead to the energy principle [5][6][7], which states that the equilibrium is linearly stable if and only if δW ≥ 0 ( Ψ) (13) is satisfied. The sufficiency of the condition (13) immediately follows from the conservation law (10).…”

Section: Reduced Magnetohydrodynamics and Its Basic Properties 21 Fomentioning

confidence: 99%

See 2 more Smart Citations

Stabilizing and Destabilizing Effect of Shear Flow -Beyond Kelvin-Helmholtz Instability-

Tatsuno

2003

J. Plasma Fusion Res.

View full text Add to dashboard Cite

Recent progress in linear spectral studies of incompressible plasma (fluid) with flows is reviewed. Mathematically, non-Hermiticity of the generating operator brings about incompleteness of the eigenvalue analysis and unremovable coupling between modes. This may lead to secular growth (algebraic in time) even if all eigenvalues exhibit stable oscillations. Physically, the stretching effect of shear flow is considered a stabilizing mechanism for various plasma instabilities; however, shear flow may equally effectively destabilize a class of plasma modes. The condition for stabilization/ destabilization is discussed as well as its physical mechanisms.

show abstract