The effect of trapped particles on the linear stability of long wavelength resistive modes

We have investigated the linear stability of plane Couette-Poiseuille flow in the presence of a cross-flow. The base flow is characterised by the cross flow Reynolds number, Ri and the dimensionless wall velocity, k. Corresponding to each k ∈ [0,1], we have observed two ranges of Ri for which the flow is unconditionally linearly stable. In the lower range, we have a stabilisation of long wavelengths leading to a cut-off Ri. In this range, cross-flow stabilisation and Couette stabilisation appear to act via very similar mechanisms in this range, leading to the potential for robust compensatory design of flow stabilisation using either mechanism. As Ri is increased, we see first destabilisation and then stabilisation at very large Ri. The instability is again a long wavelength mechanism. A linear energy analysis reveals that in this range the Reynolds stress becomes amplified, the critical layer is irrelevant and viscous dissipation is completely dominated by the energy production/negation, which approximately balances at criticality.

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Instabilities at a sheared interface over a liquid laden with soluble surfactant

Journal of Engineering Mathematics ◽

10.1007/s10665-021-10140-4 ◽

2021 ◽

Vol 129 (1) ◽

Author(s):

A. Kalogirou ◽

M. G. Blyth

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Fluid Layer ◽

Threshold Value ◽

Long Wavelength ◽

Budget Analysis ◽

Insoluble Surfactant ◽

Bounded Below ◽

Soluble Surfactant

AbstractThe linear stability of a semi-infinite fluid undergoing a shearing motion over a fluid layer that is laden with soluble surfactant and that is bounded below by a plane wall is investigated under conditions of Stokes flow. While it is known that this configuration is unstable in the presence of an insoluble surfactant, it is shown via a linear stability analysis that surfactant solubility has a stabilising effect on the flow. As the solubility increases, large-wavelength perturbations are stabilised first, leaving open the possibility of mid-wave instability for moderate surfactant solubilities, and the flow is fully stabilised when the solubility exceeds a threshold value. The predictions of the linear stability analysis are supported by an energy budget analysis which is also used to determine the key physical effects responsible for the (de)stabilisation. Asymptotic expansions performed for long-wavelength perturbations turn out to be non-uniform in the insoluble surfactant limit. In keeping with the findings for insoluble surfactant obtained by Pozrikidis & Hill (IMA J Appl Math 76:859–875, 2011), the presence of the wall is found to be a crucial factor in the instability.

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Stability Analysis of Collisional Granular Flow on a Slope

International Journal of Modern Physics B ◽

10.1142/s0217979203022337 ◽

2003 ◽

Vol 17 (22n24) ◽

pp. 4290-4294

Author(s):

Namiko Mitarai ◽

Hiizu Nakanishi

Keyword(s):

Stability Analysis ◽

Kinetic Theory ◽

Numerical Simulations ◽

Linear Stability ◽

Granular Flow ◽

Granular Flows ◽

Uniform Flow ◽

Density Region ◽

Long Wavelength

We analyze the linear stability of a collisional granular flow on a slope under gravity using hydrodynamical equations based on kinetic theory of inelastic particles. It is shown that the steady, uniform flow is unstable against longitudinal long-wavelength perturbations in lower density region. The results are compared with the instabilities found in numerical simulations of granular flows.

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Activated Prominences; Mechanisms for Activation and Eruption

International Astronomical Union Colloquium ◽

10.1017/s0252921100065714 ◽

1979 ◽

Vol 44 ◽

pp. 307-313

Author(s):

D.S. Spicer

Keyword(s):

Pressure Gradient ◽

Density Gradient ◽

Current Density ◽

Convective Instability ◽

Tearing Mode ◽

Magnetic Shear ◽

Long Wavelength ◽

Ideal Mhd ◽

Gradient Change ◽

Accelerated Particles

A possible relationship between the hot prominence transition sheath, increased internal turbulent and/or helical motion prior to prominence eruption and the prominence eruption (“disparition brusque”) is discussed. The associated darkening of the filament or brightening of the prominence is interpreted as a change in the prominence’s internal pressure gradient which, if of the correct sign, can lead to short wavelength turbulent convection within the prominence. Associated with such a pressure gradient change may be the alteration of the current density gradient within the prominence. Such a change in the current density gradient may also be due to the relative motion of the neighbouring plages thereby increasing the magnetic shear within the prominence, i.e., steepening the current density gradient. Depending on the magnitude of the current density gradient, i.e., magnetic shear, disruption of the prominence can occur by either a long wavelength ideal MHD helical (“kink”) convective instability and/or a long wavelength resistive helical (“kink”) convective instability (tearing mode). The long wavelength ideal MHD helical instability will lead to helical rotation and thus unwinding due to diamagnetic effects and plasma ejections due to convection. The long wavelength resistive helical instability will lead to both unwinding and plasma ejections, but also to accelerated plasma flow, long wavelength magnetic field filamentation, accelerated particles and long wavelength heating internal to the prominence.

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