Absolute Instability Threshold Research Articles

The effect of local thermal non-equilibrium on the onset of thermal instability for a metallic foam

Mixed convection in metallic foams modeled with Darcy's law under local thermal non-equilibrium conditions is investigated, where the solid phase thermal conductivity is assumed to be infinitely larger than its fluid phase counterpart. A linear and modal stability analysis was employed to evaluate the convective and absolute instability thresholds as well as their respective cell patterns. This analysis indicates that local thermal non-equilibrium always has a stabilizing effect and the spanwise uniform mode is always the most unstable. At the onset of convective instability, however, the number of equally unstable cell patterns increases with both the aspect ratio and the local thermal non-equilibrium strength.

Predominance of pressure transport in spatial energy budget for a mixing layer approaching absolute instability

In this letter, we report the outcome of a spatial energy budget performed for the linear convective instability of the plane incompressible mixing layer within the inviscid framework. We find that, as the critical condition for the onset of absolute instability is approached, the integrated pressure-transport term becomes increasingly more prominent as compared to the integrated production term and it dominates the energy budget completely at the critical condition. This implies that, near the threshold of absolute instability, the growth of disturbances is almost entirely due to the pressure transport mechanism (rather than the production mechanism), which is a striking result. The part of the pressure-transport term that represents the work done by the fluctuating pressure forces is seen to be primarily responsible for the observed shift in the energy balance. These results can help us better understand the physical processes causing absolute instability in a mixing layer. In particular, the redistribution of disturbance energy in streamwise direction by fluctuating pressure, which is "non-local" in character for incompressible flows, seems to play a key role in this respect.

Multibeam absolute stimulated Raman scattering and two-plasmon decay.

Multibeam absolute instability thresholds for stimulated Raman scattering (SRS) and two-plasmon decay (TPD) are calculated in three dimensions for conditions relevant to direct-drive inertial confinement fusion experiments on the OMEGA laser and at the National Ignition Facility (NIF). Although multibeam effects are found to be significant for both instabilities, SRS is found to have less efficient multibeam coupling than TPD. The results are consistent with the observation of a TPD-dominated regime on the OMEGA laser and a SRS-dominated regime on the NIF despite the single-beam SRS threshold being lower than the single-beam TPD threshold on both facilities. The minimum instability threshold for NIF plasma parameters occurs for SRS near quarter-critical densities with a shared electromagnetic wave propagating along the beam axis.

Thresholds of absolute instabilities driven by a broadband laser

Absolute instability thresholds for stimulated Raman scattering (SRS) and two-plasmon decay (TPD) driven by a broadband laser pulse are evaluated numerically. The scalings of the calculated thresholds with the density scale length, temperature, and central wavelength are qualitatively similar to the existing analytical results. The threshold values, however, exhibit significant quantitative differences. Comparisons between the thresholds calculated for various broadband power spectra indicate a universal scaling of the threshold intensity with laser coherence time (τc). For SRS, Ithr∝τc−1/3, and for TPD, Ithr∝τc−1/2.

Theory and measurements of convective Raman side scatter in inertial confinement fusion experiments.

Raman side scatter, whereby scattered light is resonant while propagating perpendicularly to a density gradient in a plasma, was identified experimentally in planar-target experiments at the National Ignition Facility at intensities orders of magnitudes below the threshold for absolute instability. We have derived a new theoretical description of convective Raman side scatter below the absolute threshold, validated by numerical simulations. We show that inertial confinement fusion experiments at full ignition scale, i.e., with mm-scale spot sizes and density scale lengths, are prone to increased coupling losses from Raman side scatter as the instability can extend from the absolute regime near the quarter-critical density to the convective regime at lower electron densities.

Buckling of a compliant hollow cylinder attached to a rotating rigid shaft

Bifurcations in the equilibrium shape of a thick elastic layer attached to a circular rigid cylinder rotating about its axis are investigated analytically and numerically. The centrifugal force breaks the symmetry of the system leading to deformations invariant along the axis as the result of an instability. The instability threshold depends at linear order on the relative thickness of the compliant layer, and on a dimensionless control parameter based on the elastic modulus, the angular velocity and the outer radius. A weakly non linear analysis, carried out for layers following the Mooney–Rivlin constitutive law, points out the discontinuous (sub-critical) features of the bifurcation, except for relative thickness laying in a very narrow range in which the bifurcation is super-critical. Numerical simulations in the fully post-buckled regime yield the absolute instability threshold, and the order in the rotational symmetry of the developed equilibrium shape.

Nonlinear transition from convective to absolute Raman instability with trapped electrons and inflationary growth of reflectivity

We propose a nonlinear mechanism for transition from convective to absolute in stimulated Raman backscattering instability due to the effect of trapped particles in the plasma wave. Convective instability saturates at the low level, yet it is sufficient to trap electrons near the plasma phase velocity. The trapped electrons tend to flatten the distribution function. With spatial averaging over the trapped region, we find that the flattened distribution function reduces the damping rate due to bounce resonance of the plasma wave and then decreases the threshold for absolute instability. So the transition from a weak, convective instability to a strong, absolute instability can occur, leading to exponential growth everywhere and inflation of reflectivity of several orders of magnitude as observed in the experiment, once the threshold is exceeded.

Threshold fields for stimulated Brillouin scattering in spatially limited plasma

Brillouin scattering in an infinite medium is anisotropic, in this case the threshold of absolute instability is caused by attenuation of scattered waves. If the collision attenuation mechanism prevails, the minimum threshold value is observed during backward scattering. For a scattering region limited in the longitudinal direction (parallel to the direction of pumping wave propagation), the backward scattering threshold will be greater than for an infinite medium due to convective loss associated with energy removal by scattered waves. In this paper, the scattering of a wide wave beam in plasma is considered, whose dimension in the transverse direction to the pumping wave propagation substantially exceeds the dimension in the longitudinal direction. It was revealed that in this case, during angle scattering the instability threshold can be less than the threshold for backward scattering due to the increased time of radiation removal from the interaction region. This effect was not taken into account previously. In turn, the decrease of the threshold leads to increasing the radiation loss, which is important in plasma heating problems. The results can also be used for plasma diagnostics.

Linear Stability Analysis of Mixed Convection Under Soret Effect in Bounded Horizontal Fluid Layer with Slip Conditions

The aim of this study is to analyze the mixed convection under Soret effect in a liquid layer subjected to adverse temperature and concentration gradients and slip conditions. Theoretical linear stability analysis and numerical methods were performed to study the convective and absolute instabilities of the transverse rolls. It is found that, for convective instabilities, the problem has analytical solution and is a Galilean transformation of natural convection. The throughflow makes the rolls to propagate and the frequency shift is proportional to Reynolds number. For higher Rayleigh numbers, advection breaks Galilean invariance, and absolute instabilities settle. At the threshold of absolute instability, the presence of throughflow breaks the symmetry by the rotational invariance, and the system selects among an infinite number of unstable modes, the progressive waves, in the direction of the flow.

Secondary instabilities in all fiber ring cavities

We study secondary instabilities in a coherently driven passive optical fiber cavity. We show that time-modulated solutions which are generated at the onset of instability experience convective and absolute Eckhaus instabilities. The splitting of the secondary instabilities into convective and absolute instabilities drastically impacts the instability boundaries. As a consequence, the stability range of time-modulated waves is enlarged. More importantly, the threshold of absolute instability determines the transition from time-periodic wave trains to a chaotic regime. In the latter the wave trains are composed of irregular oscillations embedded in regular ones. The predictions are in excellent agreement with numerical simulations.

Convective Raman amplification of light pulses causing kinetic inflation in inertial fusion plasmas

We perform 1D particle-in-cell (PIC) simulations using OSIRIS, which model a short-duration (∼500ω0−1 FWHM) scattered light seed pulse in the presence of a constant counter-propagating pump laser with an intensity far below the absolute instability threshold. The seed undergoes linear convective Raman amplification and dominates over fluctuations due to particle discreteness. Our simulation results are in good agreement with results from a coupled-mode solver when we take into account special relativity and the use of finite size PIC simulation particles. We present linear gain spectra including both effects. Extending the PIC simulations past when the seed exits the simulation domain reveals bursts of large-amplitude scattering in many cases, which does not occur in simulations without the seed pulse. These bursts can have amplitudes several times greater than the amplified seed pulse, and we demonstrate that this large-amplitude scattering is the result of kinetic inflation by examining trapped particle orbits. This large-amplitude scattering is caused by the seed modifying the distribution function earlier in the simulation. We perform some simulations with longer duration seeds, which lead to parts of the seeds undergoing kinetic inflation and reaching amplitudes several times more than the steady-state linear theory results. Simulations with continuous seeds demonstrate that the onset of inflation depends on seed wavelength and incident intensity, and we observe oscillations in the reflectivity at a frequency equal to the difference between the seed frequency and the frequency at which the inflationary stimulated Raman scattering grows.

Inviscid helical magnetorotational instability in cylindrical Taylor-Couette flow

This paper presents the analysis of axisymmetric helical magnetorotational instability (HMRI) in the inviscid limit, which is relevant for astrophysical conditions. The inductionless approximation defined by zero magnetic Prandtl number is adopted to distinguish the HMRI from the standard MRI in the cylindrical Taylor-Couette flow subject to a helical magnetic field. Using a Chebyshev collocation method convective and absolute instability thresholds are computed in terms of the Elsasser number for a fixed ratio of inner and outer radii λ = 2 and various ratios of rotation rates and helicities of the magnetic field. It is found that the extension of self-sustained HMRI modes beyond the Rayleigh limit does not reach the astrophysically relevant Keplerian rotation profile not only in the narrow- but also in the finite-gap approximation. The Keppler limit can be attained only by the convective HMRI mode provided that the boundaries are perfectly conducting. However, this mode requires not only a permanent external excitation to be observable but also has a long axial wavelength, which is not compatible with limited thickness of astrophysical accretion disks.

Low-threshold absolute parametric decay instabilities in experiments on electron cyclotron resonance heating in tokamaks

We have analyzed experimental conditions for the excitation of absolute parametric decay instabilities accompanying the electron cyclotron resonance heating (ECRH) of plasma at the second harmonic of resonance in tokamaks. It has been shown that, in the case of a nonmonotonic radial profile of the plasma density, when a heating beam passes near the equatorial plane of a tokamak, the parametric excitation of resonances of ion Bernstein waves accompanied by the generation of the backscattered microwave radiation can occur. The threshold of absolute instability thus developed is determined by the dissipation of an ion Bernstein wave and can be exceeded in current experiments on the ECRH of a plasma in tokamaks.

Absolute instability in backward wave four-wave mixing: spatial effects

The spatial distribution of new beams generated above the threshold of absolute instability of two counterpropagating incoherent light waves is studied and compared with the results of calculation.

Three-dimensional absolute and convective instabilities in mixed convection of a viscoelastic fluid through a porous medium

By using the mathematical formalism of absolute and convective instabilities we study the nature of unstable three-dimensional disturbances of viscoelastic flow convection in a porous medium with horizontal through-flow and vertical temperature gradient. Temporal stability analysis reveals that among three-dimensional (3 D) modes the pure down-stream transverse rolls are favored for the onset of convection. In addition, by considering a spatiotemporal stability approach we found that all unstable 3 D modes are convectively unstable except the transverse rolls which may experience a transition to absolute instability. The combined influence of through-flow and elastic parameters on the absolute instability threshold, wave number and frequency is then determined, and results are compared to those of a Newtonian fluid.

Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow

We analyze numerically the magnetorotational instability of a Taylor-Couette flow in a helical magnetic field [helical magnetorotational instability (HMRI)] using the inductionless approximation defined by a zero magnetic Prandtl number (Pr_{m}=0) . The Chebyshev collocation method is used to calculate the eigenvalue spectrum for small-amplitude perturbations. First, we carry out a detailed conventional linear stability analysis with respect to perturbations in the form of Fourier modes that corresponds to the convective instability which is not in general self-sustained. The helical magnetic field is found to extend the instability to a relatively narrow range beyond its purely hydrodynamic limit defined by the Rayleigh line. There is not only a lower critical threshold at which HMRI appears but also an upper one at which it disappears again. The latter distinguishes the HMRI from a magnetically modified Taylor vortex flow. Second, we find an absolute instability threshold as well. In the hydrodynamically unstable regime before the Rayleigh line, the threshold of absolute instability is just slightly above the convective one although the critical wavelength of the former is noticeably shorter than that of the latter. Beyond the Rayleigh line the lower threshold of absolute instability rises significantly above the corresponding convective one while the upper one descends significantly below its convective counterpart. As a result, the extension of the absolute HMRI beyond the Rayleigh line is considerably shorter than that of the convective instability. The absolute HMRI is supposed to be self-sustained and, thus, experimentally observable without any external excitation in a system of sufficiently large axial extension.

Estimation of dynamic parameters of overthreshold parametric phase conjugation of ultrasound in magnetostrictive ferrites according to data of quasi-static measurements

A simple method for testing ferrite samples intended to be active elements of parametric phase conjugator of ultrasound was proposed and experimentally approved. The method allows one to estimate such dynamic parameters of parametric phase conjugator of ultrasound as the parametric amplification increment, threshold of absolute parametric instability, and optimum operating point position for a particular sample using results of measurements in a dc magnetic field. Results for two ferrite samples of different compositions and properties were compared to direct measurement data; their satisfactory agreement was obtained.

Flow behavior and blockage effects in stenosed arteries

Flows, both steady and pulsatile, through a circular tube with an axisymmetricblockage of varying size are studied experimentally and numerically. Selectedas an idealized model of a stenosed artery at various points in its development,the geometry consists of a long straight tube and a blockage, semi-circular incross-section. The stenosis has been simplified to a single-parameter blockagein order to highlight fundamental behaviors of constricted flows. Experimentally,a water flow is considered inside a tube of 19mm diameter, which has anunblocked length of 2 m both upstream and downstream of the blockage. Theflow is characterized using dye visualisations and Particle Image Velocimetry. These results are complemented by spectral-element numerical simulations.The study initially looks at steady inlet flows, using them as a limiting case forpulsatile flow. At low Reynolds numbers, the flow is characterized by a jet emanatingfrom the constriction, surrounded by an axisymmetric recirculation zone,the length of which increases linearly with Reynolds number. Our numericalresults indicate a critical Reynolds number threshold for absolute instability,while our experiments point to the existence of convective instabilities at lowerReynolds numbers.Flows subject to a pulsatile inlet condition, which more closely describe thetype of flow found in the cardio-vascular system are also investigated. With aparticular focus on the effects of the blockage size, we investigate the stabilityof such flows, transition to turbulent flow and also other physical properties pertinent to cardiovascular fluid mechanics, such as wall shear stress.

Absolute and convective nature of Raman instability in relativistic hot plasmas

The modulational and Raman instabilities are investigated in the relativistic regime, for a large amplitude electromagnetic wave propagating in a hot plasma of arbitrary density. Temporal growth rates and the number of unstable branches are determined when the plasma temperature, density, and the amplitude of the wave vary. The convective or absolute nature of the Raman instabilities is then determined. The present paper extends previous results by Guérin et al. [Phys. Plasmas 2, 2807 (1995)] and Couairon and Mora [Phys. Plasmas 8, 3434 (2001)]. It is shown that for any temperature, the Raman instability is convectively unstable at low density and low intensity, and absolutely unstable when the intensity or the density exceeds a threshold that we determine as a function of the temperature. In contrast with the cold plasma case, the threshold for absolute instability does not coincide with the merging of branches found by a classical temporal stability analysis.

Dynamic instability of speckle patterns in nonlinear random media

Linear stability analysis is performed of speckle pattern resulting from multiple, diffuse scattering of coherent light waves in random media with intensity-dependent refractive index (noninstantaneous Kerr nonlinearity). The speckle pattern is shown to become unstable with respect to dynamic perturbations within a certain frequency band, provided that the nonlinearity exceeds some frequency-dependent threshold. Although the absolute instability threshold is independent of the response time of the nonlinearity, the latter significantly affects speckle dynamics (in particular, its spectral content) beyond the threshold. Our results suggest that speckle dynamics becomes chaotic immediately beyond the threshold.