Excitation Of Instability Research Articles

Coal‐wall spalling prevention mechanism using advance‐grooving pressure relief in the large‐mining‐height working face of a shallow coal seam

AbstractIn mining, the roof structure of a working face with a large mining height in a shallow‐buried coal seam is prone to cutting instability in front of the support, which causes support crushing and coal‐wall spalling. This study analyzes 2201 working faces with large mining heights in the Haiwan No. 3 Mine by investigating the mechanical response law of coal walls under the transient excitation of roof structure instability. A mechanical model of coal walls under dynamic and static load coupling is established, revealing the formation mechanism of coal wall spalling and its main influencing factors. Prevention and control technologies of advanced grooving and pressure relief are proposed, and grooving parameters are determined. The results show that: During the mining process of large mining height working face in shallow buried coal seam, the step change of static response of coal wall is induced by the transient instability of roof structure, and the high abutment pressure is formed on the coal wall. At the same time, the strain energy and gravitational potential energy of roof cutting instability are released to form a dynamic load. Under the action of dynamic and static load, the plastic failure dissipation power of the coal wall is greater than the critical power, and the coal wall spalling occurs. The main influencing factors are mining load, mining height, and internal friction angle of the coal wall. The method of advanced grooving pressure relief can change the roof structure and coal force mechanism, by cutting off the connection between the coal wall and immediate roof, reducing the height of the coal wall force, effectively controlling the position of the roof cut off break line, reducing the static load effect of the roof on the coal, and transferring the position of the dynamic load response to the depth of the coal wall. When the grooving height‐depth ratio k is 0.75, the peak value of the abutment pressure moves 5.57 m to the front of the working face, and the pressure relief effect is the best. The above research results provide an effective active protection method for controlling coal wall spalling in fully mechanised working face with large mining height.

Role of nonthermal solar wind protons in the excitation of electromagnetic proton-cyclotron instability: a kinetic theory based exact numerical investigation

Free transverse kinetic energy i.e. perpendicular temperature anisotropy of protons excite the electromagnetic ion/proton cyclotron instability which is pertained to waves associated with prevalent electromagnetic ion/proton cyclotron emissions in various natural regions of plasmas. The transverse dielectric response function of left hand circularly polarized electromagnetic proton cyclotron (EPC) instability is calculated for two models of nonthermal Cairns distributed plasmas. These models are distinguished according to the effective thermal velocities of protons. For the energetic nonthermal protons populations, nonthermality dependent effective temperature model is proposed which significantly contributes in the excitation of aforementioned plasma mode and cause an appreciable enhancement in the instability growth rate. Exact numerical solution of dispersion relation yields oscillatory real frequency and growth rate of instability. A comparative analysis is also carried out to examine the instability behavior in distinct nonthermal and thermal plasma models. Contemporary numerical investigations are highly beneficial to understand the intricate dynamics of space plasmas.

The effect of Lévy index coefficient on modulational instability and rogue wave excitation in nonlocal media with cubic–quintic nonlinearities

This paper explores the modulational instability (MI) of a plane wave and its behavior in the nonlinear Schrödinger equation (NLSE) with a fractional diffraction term quantified by its Lévy index coefficient and nonlocal cubic–quintic nonlinearities. First, we analyze the stability of the plane wave solution and examine how nonlocal nonlinearities and the Lévy index coefficient affect the MI gain. We observe that the stability in the fractional NLSE exhibits new features that differ from those in the standard NLSE. Specifically, when dealing with competing cubic and quintic nonlinearities, the interaction between nonlocality and the Lévy index coefficient α can eliminate MI for low values of α, unlike the classical NLSE with α=2, where we find the plane wave to be unstable. Besides the linear stability analysis, numerical simulations are performed to understand further the plane wave dynamics from its nonlinear stage in this model. The results reveal the generation of periodic chains of localized peaks. Guided by analytical predictions and using the plane wave solution subject to Gaussian perturbation, we numerically investigate the possibility of exciting rogue waves in the parameter spaces where MI exists. We find that the different combinations of signs of the cubic and quintic nonlinearities (focusing and defocusing) and the fractional diffraction term significantly impact the formation of rogue waves. These results may pave the way for the theoretical and experimental study of nonlinear phenomena in physical models with fractional derivatives and nonlocal nonlinearities.

Effect of temperature anisotropy formed by fast electron beams moving in the flare loop on its excited electron-cyclotron maser instability

Context. The electron-cyclotron maser instability (ECMI) is a significant coherent radio emission mechanism widely utilized in various astrophysical radio phenomena. It is well known that the velocity anisotropic distribution of energetic electrons, which leads to an inverted perpendicular population in the vertical direction with ∂fb/∂v⊥ > 0, can provide the free energy necessary for the ECMI. Aims. The initial velocity distribution of energetic electrons leaving the acceleration region is typically isotropic or beam-like. However, as these energetic electrons travel along the magnetic field as fast electron beams (FEBs) in magnetic plasma, various velocity anisotropic distributions can emerge. In this paper, we examine the impact of temperature anisotropy formed by beam electrons traveling along a flare loop on the ECMI. Methods. By neglecting the energy loss of energetic electrons as they traverse the corona and invoking the conservation of energy and magnetic moments, we established the relationship between momentum dispersion and the magnetic field. Utilizing the magnetic field model of the flare loop, we calculated the evolution of momentum dispersion and the growth rates of the ECMI as FEBs precipitate along the flare loop. Results. The results demonstrate that the temperature anisotropy arising as FEBs descend along the flare loop significantly impacts the ECMI. The maximum growth rates of the excited modes exhibit a gradual increase initially and then decline rapidly after reaching a critical height for β0 = 0.2c and 0.15c. The results also show that the growth rates of the O2 mode are one order of magnitude smaller than those of the O1 and X2 modes. This indicates that the harmonic radiation is X-mode polarized. Notably, the temperature anisotropy of FEBs as they precipitate along the flare loop with different magnetic field models or at different heights has similar effects on the ECMI.

Enhanced energy deposition of laser-produced proton beams in high-density plasmas due to beam density self-steepening

The energy deposition of laser-accelerated proton beams in solid-density plasmas with different ion charge numbers is studied with detailed one-dimensional particle-in-cell simulations. In the plasma with a high ion charge number, in which the plasma collision frequency approaches electron oscillation frequency, the beam protons are strongly decelerated by the electric field induced by the plasma return current. The energy deposition is further enhanced as the beam travel distance increases due to beam density self-steeping, which is also confirmed by multi-dimensional particle-in-cell simulation. A simple analytical model is proposed to estimate the characteristic travel distance for significant density self-steeping, showing agreement with the simulation results. While in the plasma with a low ion charge number, in which the plasma collision frequency is much smaller than the electron oscillation frequency, the proton beam is modulated significantly by the excited two-stream instability.

Kinematic Stability Analysis of Anchor Cable Structures in Submerged Floating Tunnel under Combined Parametric–Vortex Excitation

The submerged floating tunnel is a marine transportation infrastructure that links two shorelines. The tunnel tube body’s buoyancy exceeds gravity, with anchoring ensuring equilibrium. Anchoring reliability is crucial. This study presents a three-way coupled kinematic model for the mooring structure, formulated on Hamilton’s principle and Kirchhoff’s assumption. It explores the impact of the tube body’s buoyancy-to-weight ratio and the sea current’s angle of incidence on mooring motion response. By solving the motion analysis model, Hill’s equation system is derived to assess the parameter instability of the anchor cable structure. The coefficient of excitation instability intervals for the submerged floating tunnel is determined and validated. The findings indicate the following: (1) Increasing the float-weight ratio reduces displacement response amplitudes in all directions, bringing downstream and transverse currents closer to their initial positions; (2) Changes in current direction angles result in decreased downstream excitation strength and increased transverse displacement response with the same excitation direction; (3) The instability interval visualization effectively predicts anchor cable structure instability under parametric excitation. Structures within the instability region are deemed unstable, while those outside are considered stable.

Dynamics, stability and bifurcations of a planar three-link swimmer with passive visco-elastic joint using “ideal fluid” model

Articulated swimming robots have a promising potential for various marine applications. A common theoretical model assumes ideal fluid, where the viscosity is negligible and the swimmer–fluid interaction is induced by reactive forces originating from added mass effect. Some previous works used this model to study planar multi-link swimmers under kinematic input prescribing all joint angles. Inspired by biological swimmers in nature that utilize body flexibility, in this work we consider an underactuated three-link swimmer where one joint is periodically actuated while the other joint is passive and viscoelastic. Analysis of the swimmer’s nonlinear dynamics reveals that its motion depends significantly on the amplitude and frequency of the actuated joint angle. Optimal frequency is found where the swimmer’s net displacement per cycle is maximized, under symmetric periodic oscillations of the passive joint. In addition, upon crossing critical values of amplitude or frequency, the system undergoes a bifurcation where the symmetric periodic solution loses stability and asymmetric solutions evolve, for which the swimmer moves along an arc. We analyze these phenomena using numerical simulations and analytical methods of perturbation expansion, harmonic balance, Floquet theory, and Hill’s determinant. The results demonstrate the important role of parametric excitation in stability and bifurcations of motion for flexible underactuated locomotion.

Large-scale semi-organized rolls in a sheared convective turbulence: Mean-field simulations

Based on a mean-field theory of a non-rotating turbulent convection [T. Elperin et al., Phys. Rev. E 66, 066305, (2002)], we perform mean-field simulations (MFS) of sheared convection that takes into account an effect of modification of the turbulent heat flux by the non-uniform large-scale motions. This effect is caused by the production of additional essentially anisotropic velocity fluctuations generated by tangling of the mean-velocity gradients by small-scale turbulent motions due to the influence of the inertial forces during the lifetime of turbulent eddies. These anisotropic velocity fluctuations contribute to the turbulent heat flux. As the result of this effect, there is an excitation of large-scale convective-shear instability, which causes the formation of large-scale semi-organized structures in the form of rolls. The lifetimes and spatial scales of these structures are much larger compared to the turbulent scales. By means of MFS performed for stress-free and no-slip vertical boundary conditions, we determine the spatial and temporal characteristics of these structures. Our study demonstrates that the modification of the turbulent heat flux by non-uniform flows leads to a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale rolls. During the nonlinear stage of the convective-shear instability, there is a transition from a two-layer vertical structure with two rolls in the vertical direction before the system reaches steady-state to a one-layer vertical structure with one roll after the system reaches steady state. This effect is observed for all effective Rayleigh numbers. We find that inside the convective rolls, the spatial distribution of the mean potential temperature includes regions with a positive vertical gradient of the potential temperature caused by the mean heat flux of the convective rolls. This study might be useful for understanding the origin of large-scale rolls observed in atmospheric convective boundary layers, as well as in numerical simulations and laboratory experiments.

Parametrically excited shape distortion of a submillimeter bubble

The existence of finite amplitude shape distortion caused by parametrically excited surface instabilities for a gas bubble in water driven by a temporally periodic, spatially uniform pressure field in an axisymmetric geometry is investigated. Employing a nonlinear coupled system of equations which includes shape mode interactions to third order, the resultant spherical oscillations, translation, and shape distortion of the bubble are modelled, placing no restriction on the size of the spherical oscillations. The model accounts for viscous and thermal damping with compressibility effects. The existence of synchronous and higher order parametrically induced sustained, finite amplitude, periodic shape deformation is demonstrated. The excitement of an odd shape mode via the synchronous mechanism is shown to give rise to linear bubble self-propulsion. For larger driving amplitudes, it is shown that more than one shape mode can be parametrically excited at the same driving frequency but by different resonance mechanisms, leading to more involved shape deformation and the increased possibility of bubble self-propulsion.

Secondary Whistler and Ion-cyclotron Instabilities Driven by Mirror Modes in Galaxy Clusters

Electron cyclotron waves (whistlers) are commonly observed in plasmas near Earth and the solar wind. In the presence of nonlinear mirror modes, bursts of whistlers, usually called lion roars, have been observed within low magnetic field regions associated with these modes. In the intracluster medium (ICM) of galaxy clusters, the excitation of the mirror instability is expected, but it is not yet clear whether electron and ion cyclotron (IC) waves can also be present under conditions where gas pressure dominates over magnetic pressure (high β). In this work, we perform fully kinetic particle-in-cell simulations of a plasma subject to a continuous amplification of the mean magnetic field B (t) to study the nonlinear stages of the mirror instability and the ensuing excitation of whistler and IC waves under ICM conditions. Once mirror modes reach nonlinear amplitudes, both whistler and IC waves start to emerge simultaneously, with subdominant amplitudes, propagating in low- B regions, quasi-parallel to B (t). We show that the underlying source of excitation is the pressure anisotropy of electrons and ions trapped in mirror modes with loss-cone-type distributions. We also observe that IC waves play an essential role in regulating the ion pressure anisotropy at nonlinear stages. We argue that whistler and IC waves are a concomitant feature at late stages of the mirror instability even at high β, and therefore, expected to be present in astrophysical environments like the ICM. We discuss the implications of our results for collisionless heating and dissipation of turbulence in the ICM.

Destratifying and Restratifying Instabilities During Down‐Front Wind Events: A Case Study in the Irminger Sea

AbstractObservations indicate that symmetric instability is active in the East Greenland Current during strong northerly wind events. Theoretical considerations suggest that mesoscale baroclinic instability may also be enhanced during these events. An ensemble of idealized numerical ocean models forced with northerly winds shows that the short time‐scale response (from 10 days to 3 weeks) to the increased baroclinicity of the flow is the excitation of symmetric instability, which sets the potential vorticity of the flow to zero. The high latitude of the current means that the zero potential vorticity state has low stratification, and symmetric instability destratifies the water column. On longer time scales (greater than 4 weeks), baroclinic instability is excited and the associated slumping of isopycnals restratifies the water column. Eddy‐resolving models that fail to resolve the submesoscale should consider using submesoscale parameterizations to prevent the formation of overly stratified frontal systems following down‐front wind events. The mixed layer in the current deepens at a rate proportional to the square root of the time‐integrated wind stress. Peak water mass transformation rates vary linearly with the time‐integrated wind stress. Mixing rates saturate at high wind stresses during wind events of a fixed duration which means increasing the peak wind stress in an event leads to no extra mixing. Using ERA5 reanalysis data we estimate that between 0.9 Sv and 1.0 Sv of East Greenland Coastal Current Waters are produced by mixing with lighter surface waters during wintertime due to down‐front wind events. Similar amounts of East Greenland‐Irminger Current water are produced.

Electromagnetic Ion Beam Instability in the Solar Corona

Remote-sensing measurements indicate that heavy ions in the corona undergo an anisotropic and mass-charge dependent energization. A popular explanation to this phenomenon is the damping of the Alfvén/ion cyclotron waves. In this paper, we propose that the ion beam instability can be an important source of the Alfvén/ion cyclotron waves, and we study the excitation of the ion beam instability in the corona at the heliocentric distance ∼3R ⊙ and the corresponding energy transfer process therein based on plasma kinetic theory. The results indicate that the existence of the motionless heavy ions inhibits the ion beam instability. However, the anisotropic beams of heavy ions promote the excitation of the ion beam instability. Besides, the existence of α beams can provide a second energy source for exciting beam instability. However, when both the proton beam and the α beam reach the instability excitation threshold, the proton beam driven instability excites preferentially. Moreover, the excitation threshold of the Alfvén/ion cyclotron instability driven by ion beam is of the local Alfvén speed or even less in the corona.

The gap-size influence on the excitation of magnetorotational instability in cylindricTaylor–Couette flows

The excitation conditions of the magnetorotational instability (MRI) are studied for axially unbounded Taylor–Couette (TC) flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wavenumber and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes, we find the critical Lundquist number of the applied axial magnetic field: the lower, the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap, the more spherical the cells are. The marginal rotation rate of the inner cylinder – for a fixed size of the outer cylinder – always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at $r_{{\rm in}}\simeq 0.4$ , where $r_{{\rm in}}$ is the ratio of the radii of the two rotating cylinders. The lowest magnetic field amplitudes to excite the instability are required for TC flows between perfect-conducting cylinders with gaps corresponding to $r_{{\rm in}}\simeq ~0.2$ . For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the non-axisymmetric modes with $|m|=1$ have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison with those for the axisymmetric modes. If TC experiments with too slow rotation for the applied magnetic fields yield unstable modes of any azimuthal symmetry, such as the currently reported Princeton experiment (Wang et al., Phys. Rev. Lett., vol. 129, 115001), then also other players, including axial boundary effects, than the MRI-typical linear combination of current-free fields and differential rotation should be in the game.

Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media

We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, α 1 α 2 ∈ ( 1 , 2 ] , and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic FNLS equation with only one Lévy index (LI) α = 1 , can be suppressed in the two-LI FNLS system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability (MI) of continuous waves is investigated in the two-LI system too. In particular, the MI may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the MI, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.

Solitonic rogue waves induced by the modulation instability in a split-ring-resonator-based left-handed coplanar waveguide

Modulation instability and nonlinear excitation modes in lower and upper frequency bands are investigated in the nonlinear left-handed coplanar waveguide, where nonlinear capacitance (voltage-dependent) is used. The multi-scale method is employed to derive a system of two coupled nonlinear Schödinger equations governing the evolution of the kink and bright solitons of these modes. A modulation instability is investigated to show the effects of the left-handed and right-handed influences on the modulation instability gain and the intensity of the plane wave. In the lower and upper frequency modes, the breathing structures have strong values for the left-handed component. At the end, the numerical simulation of the continuous wave is used to show the development of the modulated waves and localized objects. Another relevant localized structure has been obtained to display the second-order breathers and Akhmediev breathers of types A and B under the variation of the perturbed wave number. Both linear inductances and perturbed wave numbers are tools for controlling the amplitude of the localized structures, and modulation instability is sensitive to these parameters.

Excitation of proton firehose instability in magnetospheric cold and hot proton plasma: a quasilinear approach

Abstract Unstable states of different charged species in the solar wind and Earth’s magnetosphere are governed with the collective and collisional processes. For these dilute plasmas, the contribution of microinstabilities driven by the anisotropic particle distribution and heat flux becomes important in defining the stable/equilibrium states of electrons and ions/protons. The present paper highlights the key role of proton firehose instability to regulate an unchecked rise in the temperature anisotropy in these solar wind and magnetospheric environments. Right-handed circularly polarized proton firehose mode becomes unstable when the temperature condition of T ‖p > T ⊥p is satisfied, where the directional subscripts denote directions with respect to the ambient magnetic field. Based on the observations of magnetospheric multi-scale (MMS) space mission, we assume the bi-Maxwellian nature of the model distribution for the multi-component proton plasma. To study the time evolution of the unstable mode, we further allow the time variation in the cold and hot proton temperatures. For the choice of the initial conditions related with observations, we unveil the wave properties (growth and unstable wave number domain) corresponding to the cold/hot proton temperature anisotropy and the plasma betas of constituents proton components. In the back action of proton firehose instability, we highlight the time-scale modifications and saturation of initial bi-Maxwellian distributions and resulting wave-energy densities for various choices of initial cold-hot temperature anisotropy and plasma betas.

Effect mechanisms of leading-edge tubercle on blade cavitation control in a waterjet pump

The bio-inspired leading-edge tubercles (LET) are specifically designed and exploited to control the blade cavitation dynamics under the inlet guide vans (IGVs) wake impacts in a waterjet pump. The experiments, numerical simulation, and modal analysis are jointly carried out to elaborate on the effects mechanisms and cavitation oscillations of the LET pump. It is observed that the tubercle blade cavitation is stably confined in the troughs with a tubular-like pattern and the spanwise coherent development is broken. The tubercles drive the flow turbulent and then form low pressure in the troughs to give rise to cavities. Weak counter-rotating vortex pairs can be identified in the tubercle trough. The analysis of vortex transportation demonstrates that vortex stretching and dilatation would be induced by tubercle cavitation. The loading instabilities obtained by Dynamic Mode Decomposition (DMD) indicate that the dominant oscillations emerge around the tubercles in the blade middle part regarding heavy loading. Due to the large-scale cavities depression by the tubercles, the thrust extremes in some revolutions could be efficiently avoided. In comparison with smooth and tubercle pumps, the thrust energy regarding the tonal and broadband frequency for a single blade and impeller are closing, which need to be further studied to degrade excited force instabilities. This work fundamentally investigates the cavitation instabilities and mechanisms in a tubercle waterjet pump, which could provide a guide on pump design to stabilize cavitation oscillations under uncertain inflow perturbations.

Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics

This paper investigates a higher-order modified nonlinear Schrödinger equation with higher-order dispersion and self-steepening effects, which can be used to study the dynamics of asymmetric and steepened optical pulse transmission in optical fibres. The modulation instability of the plane-wave solution has been analysed, and the state transition of the rogue waves under the higher-order dispersion effect is presented. The findings demonstrate that the self-steepening effect may also produce an asymmetric unstable frequency band. Combined with the modulation instability, the rogue wave, rational soliton and mixed interaction of localized waves have a quantitative relationship with plane-wave parameters. Various exact solutions can be accurately located and obtained according to the generalized Darboux transformation. The asymptotic analysis of rational solutions demonstrates the state transition of higher-order rogue waves. This paper illustrates the significance of modulation instability for studying the integrable systems by the Darboux transformation. It is a new guidance to solve the difficulty of exact excitation of asymmetric localized waves in complex integrable systems. The results have prospective applications and references for the emergence, amplification and compression of asymmetric pulses in optical experiments.

Regulation of Proton–α Differential Flow by Compressive Fluctuations and Ion-scale Instabilities in the Solar Wind

Large-scale compressive slow-mode-like fluctuations can cause variations in the density, temperature, and magnetic-field magnitude in the solar wind. In addition, they also lead to fluctuations in the differential flow U pα between α-particles and protons (p), which is a common source of free energy for the driving of ion-scale instabilities. If the amplitude of the compressive fluctuations is sufficiently large, the fluctuating U pα intermittently drives the plasma across the instability threshold, leading to the excitation of ion-scale instabilities and thus the growth of corresponding ion-scale waves. The unstable waves scatter particles and reduce the average value of U pα . We propose that this “fluctuating-drift effect” maintains the average value of U pα well below the marginal instability threshold. We model the large-scale compressive fluctuations in the solar wind as long-wavelength slow-mode waves using a multi-fluid model. We numerically quantify the fluctuating-drift effect for the Alfvén/ion-cyclotron and fast-magnetosonic/whistler instabilities. We show that measurements of the proton–α differential flow and compressive fluctuations from the Wind spacecraft are consistent with our predictions for the fluctuating-drift effect. This effect creates a new channel for a direct cross-scale energy transfer from large-scale compressions to ion-scale fluctuations.

Modulation instability and nonlinear coupled-mode excitations in single-wall carbon nanotube

Modulation instability and nonlinear coupled-mode excitations in single-wall carbon nanotube