The role of negative energy waves in some instabilities of parallel flows

Cairns, R. A.

doi:10.1017/s0022112079000495

Cited by 264 publications

(220 citation statements)

References 14 publications

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“…to a situation where the amplitude of waves propagating along the interface grows as exp(ω i t). Following the method developed by Cairns (1979) we write the dispersion relation as…”

Section: Instability Conditionsmentioning

confidence: 99%

“…In this case the energy of the wave is the phase-averaged difference between the energy of the system when the wave is present, and its energy when the wave is absent. A criterion that can be used to determine the nature of waves is the formula suggested by Cairns (1979) where a wave is considered to have negative energy if the quantity…”

Section: Instability Conditionsmentioning

confidence: 99%

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Dissipative instability in partially ionised prominence plasmas

Ballai

Oliver

Alexandrou

2015

A&A

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Aims. We investigate the nature of dissipative instability at the boundary (seen here as tangential discontinuity) between the viscous corona and the partially ionised prominence plasma in the incompressible limit. The importance of the partial ionisation is investigated in terms of the ionisation fraction. Methods. Matching the solutions for the transversal component of the velocity and total pressure at the interface between the prominence and coronal plasmas, we derive a dispersion relation whose imaginary part describes the evolution of the instability. Results are obtained in the limit of weak dissipation. Results. Using simple analytical methods, we show that dissipative instabilities appear for flow speeds that are lower than the Kelvin-Helmholtz instability threshold. While viscosity tends to destabilise the plasma, the effect of partial ionisation (through the Cowling resistivity) will act towards stabilising the interface. For ionisation degrees closer to a neutral gas the interface will be unstable for larger values of equilibrium flow. The same principle is assumed when studying the appearance of instability at the interface between prominences and dark plumes. The unstable mode appearing in this case has a very small growth rate and dissipative instability cannot explain the appearance of flows in plumes.Conclusions. The present study improves our understanding of the complexity of dynamical processes at the interface of solar prominences and solar corona, and the role partial ionisation can have on the stability of the plasma. Our results clearly show that the problem of partial ionisation introduces new aspects of plasma stability with consequences on the evolution of solar prominences.

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“…to a situation where the amplitude of waves propagating along the interface grows as exp(ω i t). Following the method developed by Cairns (1979) we write the dispersion relation as…”

Section: Instability Conditionsmentioning

confidence: 99%

Section: Instability Conditionsmentioning

confidence: 99%

Dissipative instability in partially ionised prominence plasmas

Ballai

Oliver

Alexandrou

2015

A&A

View full text Add to dashboard Cite

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“…The various eigenmodes (when distinct) can be classified as either positive-or negative-energy waves (PEW or NEW); see e.g. Cairns (1979). Irreversible energy transfer has a stabilizing effect on the PEW but a destabilizing effect on the NEW.…”

Section: Referred To As I)mentioning

confidence: 99%

Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer

2003

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A study is carried out of the linear global behaviour corresponding to the absolute instability of the rotating-disc boundary layer. It is based on direct numerical simulations of the complete linearized Navier–Stokes equations obtained with the novel velocity–vorticity method described in Davies & Carpenter (2001). As the equations are linear, they become separable with respect to the azimuthal coordinate, $\theta$. This permits us to simulate a single azimuthal mode. Impulse-like excitation is used throughout. This creates disturbances that take the form of wavepackets, initially containing a wide range of frequencies. When the real spatially inhomogeneous flow is approximated by a spatially homogeneous flow (the so-called parallel-flow approximation) the results ofthe simulations are fully in accordance with the theory of Lingwood (1995). If the flow parameters are such that her theory indicates convective behaviour the simulations clearly exhibit the same behaviour. And behaviour fully consistent with absolute instability is always found when the flow parameters lie within the theoretical absolutely unstable region. The numerical simulations of the actual inhomogeneous flow reproduce the behaviour seen in the experimental study of Lingwood (1996). In particular, there is close agreement between simulation and experiment for the ray paths traced out by the leading and trailing edges of the wavepackets. In absolutely unstable regions the short-term behaviour of the simulated disturbances exhibits strong temporal growth and upstream propagation. This is not sustained for longer times, however. The study suggests that convective behaviour eventually dominates at all the Reynolds numbers investigated, even for strongly absolutely unstable regions. Thus the absolute instability of the rotating-disc boundary layer does not produce a linear amplified global mode as observed in many other flows. Instead the absolute instability seems to be associated with transient temporal growth, much like an algebraically growing disturbance. There is no evidence of the absolute instability giving rise to a global oscillator. The maximum growth rates found for the simulated disturbances in the spatially inhomogeneous flow are determined by the convective components and are little different in the absolutely unstable cases from the purely convectively unstable ones. In addition to the study of the global behaviour for the usual rigid-walled rotating disc, we also investigated the effect of replacing an annular region of the disc surface with a compliant wall. It was found that the compliant annulus had the effect of suppressing the transient temporal growth in the inboard (i.e. upstream) absolutely unstable region. As time progressed the upstream influence of the compliant region became more extensive.

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“…For a wave triplet, all the three waves grow simultaneously. This phenomenon was first described by Cairns [10] using the kinetic equation which takes into account the interactions of waves with random phases and different signs of energy. Fainshtein and Chernova [11] have investigated the high power electromagnetic radiation from the development of explosive and high-frequency instabilities in a system consisting of a relativistic ion beam and a nonisothermal plasma.…”

Section: Introductionmentioning

confidence: 99%

Low and high frequency instabilities in an explosion-generated-plasma and possibility of wave triplet

Malik¹,

Singh

Malik

et al. 2015

J Theor Appl Phys

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An explosion-generated-plasma is explored for low and high frequency instabilities by taking into account the drift of all the plasma species together with the dust particles which are charged. The possibility of wave triplet is also discussed based on the solution of dispersion equation and synchronism conditions. High frequency instability (HFI) and low frequency instability (LFI) are found to occur in this system. LFI grows faster with the higher concentration of dust particles, whereas its growth rate goes down if the mass of the dust is higher. The ion and electron temperatures affect its growth in opposite manner and the electron temperature causes this instability to grow. In addition to the instabilities, a simple wave is also observed to propagate, whose velocity is larger for larger wave number, smaller mass of the dust and higher ion temperature.

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The role of negative energy waves in some instabilities of parallel flows

Cited by 264 publications

References 14 publications

Dissipative instability in partially ionised prominence plasmas

Dissipative instability in partially ionised prominence plasmas

Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer

Low and high frequency instabilities in an explosion-generated-plasma and possibility of wave triplet

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