Unstable Waves Research Articles

Controllable nonautonomous localized waves and dynamics for a quasi-1D Gross-Pitaevskii equation in Bose-Einstein condensations with attractive interaction.

This paper investigates dynamical behaviors and controllability of some nonautonomous localized waves based on the Gross-Pitaevskii equation with attractive interatomic interactions. Our approach is a relation constructed between the Gross-Pitaevskii equation and the standard nonlinear Schrödinger equation through a new self-similarity transformation which is to convert the exact solutions of the latter to the former's. Subsequently, one can obtain the nonautonomous breather solutions and higher-order rogue wave solutions of the Gross-Pitaevskii equation. It has been shown that the nonautonomous localized waves can be controlled by the parameters within the self-similarity transformation, rather than relying solely on the nonlinear intensity, spectral parameters, and external potential. The control mechanism can induce an unusual number of loosely bound higher-order rogue waves. The asymptotic analysis of unusual loosely bound rogue waves shows that their essence is energy transfer among rogue waves. Numerical simulations test the dynamical stability of obtained localized wave solutions, which indicate that modifying the parameters in the self-similarity transformation can improve the stability of unstable localized waves and prolong their lifespan. We numerically confirm that the rogue wave controlled by the self-similarity transformation can be reproduced from a chaotic initial background field, hence anticipating the feasibility of its experimental observation, and propose an experimental method for observing these phenomena in Bose-Einstein condensates. The method presented in this paper can help to induce and observe new stable localized waves in some physical systems.

Experimental study of swirling flow pattern at the swirler outlet using a Wire-Mesh sensor

Entrained droplets and flow pattern change adversely affects separation performance of swirl-vane separators. Investigating gas–liquid distribution at swirler outlet, an experiment was conducted using a wire-mesh sensor positioned. Air and liquid superficial velocities ranged from 8.3 to 25.6 m/s and 0.1 to 1.4 m/s, respectively, covering swirling annular and swirling churn flow at swirler outlet. In swirling annular flow, liquid phase primarily exists as a stable thin film which facilitates efficient separation. In swirling churn flow, wall liquid film has unstable large amplitude disturbance waves. Disrupting liquid film leads to entrained droplets forming in gas center, increasing separation distance and hindering gas–liquid separation. The transition boundary from swirling churn to swirling annular is crucial. Increasing swirler angle shifts the transition boundary towards higher gas velocity at the same liquid velocity. A theoretical model based on interfacial shear stress and gas core blockage predicts the flow pattern transition at swirler outlet.

Absolute instability of moisture‐coupled waves on the equatorial beta‐plane

AbstractThe instabilities produced by a linear model of the tropical atmosphere coupled to a prognostic equation for water vapour are investigated. The basic model with no meridional wind supports unstable eastward‐propagating waves. For parameter regimes relevant to the Indo‐Pacific warm pool, the long‐time asymptotic behaviour of the unstable waves is found to be absolutely unstable, so that the amplitude of disturbances will grow in time at every point in the domain. The absolute instability of the system is realized at planetary length‐scales and intraseasonal frequencies. Other parameter choices for the system do not produce this same behaviour at these length‐ and time‐scales. It is shown that the resultant long‐time behaviour of the instability is characterized by roughly equal roles for temperature and moisture fluctuations in setting the thermodynamic tendency of the waves. With the inclusion of momentum damping, the phase speed of the absolutely unstable solution is about 7 ms. Addition of a strong background meridional moisture gradient, as in recent studies on the Madden–Julian Oscillation (MJO), appears to remove the absolute instability from the system. In a background state that varies slowly in the zonal direction, it is shown analytically that localized regions of instability may be formed, again using parameter choices relevant to the warm pool. The dynamics and thermodynamics of these local instabilities show some correspondence with the observed development of the MJO as it propagates through the warm pool.

Study on the extension mechanism of hydraulic fractures in bedding coal

This study is aimed at investigating the formation process and extension mechanism of hydraulic fractures (HFs) in bedding coal. To achieve this aim, a numerical model of hydraulic fracturing of bedding coal was established based on the cohesive element. Furthermore, the influences of stress field, bedding dip angle and fracturing fluid displacement on the extension law of HFs in bedding coal were studied, and the formation process and extension mechanism of HFs in bedding coal were analyzed. The following beneficial results were obtained. HFs prefer penetrating the bedding plane when extending towards it at a large angle, while they tend to extend along the bedding plane when the angle is small. Under certain stress field conditions, during hydraulic fracturing, changing the extension direction of original HFs enables HFs to develop into a complex fracture network under the combined effect of bedding structure and stress field. Meanwhile, altering injection displacement can enlarge the extension range of HFs on the bedding plane. The principle can be explained as follows: under the action of continuous unstable pressure waves caused by fluctuant injection displacement, coal is likely to undergo fatigue damage, which further promotes the generation of micro cracks within coal and facilitates the opening and extension of HFs. The pore pressure near HFs increases linearly with the rise of fluid pressure in HFs, decreases linearly with the growth of distance from HFs, and is inversely proportional to the square root of the fracturing fluid’s filtration time. After HFs penetrate the bedding plane, coal is prone to shear failure and further generates secondary fractures under the filtration effect of fracturing fluid. Under the joint effect of fracturing parameters such as bedding, ground stress and displacement, main HFs and secondary HFs can intersect to form a complex fracture network when penetrating the bedding plane.

Evolution of the electron phase space of the two-stream and bump-on-tail instabilities in collisional plasma

Particle collisions can have significant effects on plasma instabilities, especially in dense and/or low temperature plasmas. To understand the influence of collisional effects on the plasma waves, the Vlasov–Poisson system with Krook collisions is applied to study the long-term evolution of the two-stream (TS) and bump-on-tail (BOT) instabilities. The system is solved numerically with the fourth-order Runge–Kutta scheme and the Thomas algorithm. It is found that collisions can enhance the wave damping and mitigate the energy of the characteristic slow evolving nonlinear Landau damping oscillations associated with the wave-trapped electrons, especially if the collision rate ν is higher than 0.01ωp, where ωp is the plasma frequency of the background plasma. Collisions can also decrease the growth rate and saturation level of the TS and BOT unstable waves and tend to shrink the phase space vortex and narrow the phase-mixed region of the trapped electrons. However, our simulations show that collisions cannot readily prevent the nonlinear Landau damping oscillations. In fact, only with ν>0.001ωp for the TS instability and ν>0.01ωp for the BOT instability, as well as evolution times greater than several hundred ωp−1, the vortex structure of the wave-trapped electrons can be undetectable. The corresponding growth rates also drop dramatically, and the maximum wave energy can be one or two orders lower than that of the collisionless limits.

Long-wave instabilities of sloping stratified exchange flows

We investigate the linear instability of two-layer stratified shear flows in a sloping two-dimensional channel, subject to non-zero longitudinal gravitational forces. We reveal three previously unknown instabilities, distinct from the well-known Kelvin–Helmholtz instability and Holmboe wave instability, in that they have longer wavelengths (of the order of 10 to $10^3$ shear-layer depths) and often slower growth rates. Importantly, they can grow in background flows with gradient Richardson number $\gg 1$ , which offers a new mechanism to sustain turbulence and mixing in strongly stratified flows. These instabilities are shown to be generic and relatively insensitive to Reynolds number, Prandtl number, base flow profile and boundary conditions. The nonlinear evolution of these instabilities is investigated through a forced direct numerical simulation, in which the background momentum and density are sustained. The growth of long unstable waves in background flows initially stable to short wave causes a decrease in the local gradient Richardson number. This leads to local nonlinear processes that result in small-scale overturns resembling Kelvin–Helmholtz billows. Our results establish a new energy exchange pathway, where the mean kinetic energy of a strongly stratified flow is extracted by primary unstable long waves and secondary short waves, and subsequently dissipated into internal energy.

Modulated dust-ion-acoustic waves result from Earth's magnetosphere and lunar ionosphere interactions

The Earth's magnetosphere's modulational amplitude dust-ion-acoustic waves are studied. When the moon passes through the Earth's magnetotail, its dust grains may interact, causing these waves. The theoretical plasma model for this study includes positive ionospheric ion fluids, isothermal electrons, and fluid-negative dust grains on the moon. A perturbation technique derived the nonlinear Schrödinger equation, which exhibited dispersion and nonlinear effects. The nonlinear and dispersion term coefficients' polarity may predict stable and unstable pulse domains. A numerical study was performed to identify unstable pulse domains and their connections with bright and rogue unstable modes. The effects of critical plasma conditions on these pulses' basic features have been studied. This study showed that increasing the ratio of ions to electrons temperature and density reduces system nonlinearity. Consequently, shorter unstable pulses are formed. Amplification of plasma unstable waves results in an increase in their intensity and energy, potentially impacting any device traveling through the area of impact.

Proton- and Alpha-driven Instabilities in an Ion Cyclotron Wave Event

Ion-scale wave events or wave storms in the solar wind are characterized by enhancements in magnetic field fluctuations as well as coherent magnetic field polarization signatures at or around the local ion cyclotron frequencies. In this paper, we study in detail one such wave event from Parker Solar Probe's (PSP) fourth encounter, consisting of an initial period of left-handed (LH) polarization abruptly transitioning to a strong period of right-handed (RH) polarization, accompanied by a clear core beam structure in both the alpha and proton velocity distribution functions. A linear stability analysis shows that the LH-polarized waves are anti-sunward propagating Alfvén/ion cyclotron waves primarily driven by a proton cyclotron instability in the proton core population, and the RH polarized waves are anti-sunward propagating fast magnetosonic/whistler waves driven by a firehose-like instability in the secondary alpha beam population. The abrupt transition from LH to RH is caused by a drop in the proton core temperature anisotropy. We find very good agreement between the frequencies and polarizations of the unstable wave modes as predicted by linear theory and those observed in the magnetic field spectra. Given the ubiquity of ion-scale wave signatures observed by PSP, this work gives insight into which exact instabilities may be active and mediating energy transfer in wave–particle interactions in the inner heliosphere, as well as highlighting the role a secondary alpha population may play as a rarely considered source of free energy available for producing wave activity.

Response of second-mode instability to backward-facing steps in a high-speed flow

Stability in a Mach 4.5 boundary layer over backward-facing steps (BFSs) is investigated using numerical methods. Two types of cases are considered with different laminar inflow conditions, imposed with single-frequency or broadband-frequency modes, respectively. Compared with the typical K-type transition over a flat plate, the boundary layer transition initiated by 90 kHz-frequency second mode appears to follow the same pattern but with a noticeable delay over the step. A larger step height leads to a better inhibition of the downstream Λ-vortices and thus a later transition, providing the step height is smaller than the local boundary layer thickness. Moreover, both the frequency weighted power spectral density and the root mean square of the streamwise velocity indicate the presence of Kelvin–Helmholtz (K–H) instability when the step height is equivalent to the thickness of the nearby boundary layer. There may exist an optimal step height for suppressing single-frequency (90 kHz) mode without exciting significant K–H modes. Similar to the previous studies on roughness, BFS can act as an amplifier for the low-frequency second modes and a suppressor for the high-frequency second modes. The critical frequency is equal to that of the unstable mode whose synchronization point is exactly located at the step corner. Additionally, the correction effects of the step induce the change of the phase speed of the fast mode, which correspondingly results in the movement of the synchronization point. Generally, the BFS is not able to completely alleviate the transition initiated by the broadband-frequency second modes but can still delay the boundary layer transition in a certain degree by suppressing the high-frequency unstable waves.

Prediction of sodium leakage droplet size distribution in sodium-cooled fast reactor loop

Sodium spray fire is a significant containment-related safety concern in sodium-cooled fast reactors (SFRs). The droplet size distribution of sodium spray is an important factor affecting the combustion intensity of sodium spray fire. Due to the unstable chemical properties of sodium, water is usually used to simulate sodium to carry out spray experiments, and the droplet size relationship between them needs to be obtained. Based on the unstable wave theory, the droplet size similarity model characterized by liquid physical property parameters and atomization pressure difference is developed and verified from the two aspects of pressure and physical property parameters, and compared with existing models. Furthermore, an experimental facility of water atomization using a nozzle to simulate a break is built and the droplet size of water atomization under the differential pressure range of 1.0 bar–6.0 bar is obtained. The droplet size similarity model is used to predict the sodium atomization droplet size at 300–600 °C under different pressures based on these experimental data.

Pengaruh Koreksi Ionosfer Terhadap Pergeseran Vertikal Pada Citra Satelit ALOS-PALSAR

Interferometric Synthetic Aperture Radar (InSAR) is an effective technique for changing the earth's surface with wide coverage and high accuracy. However, the accuracy of InSAR can be affected by wave propagation activity in the atmosphere. The ionospheric medium in the atmosphere contains free electrons which cause unstable waves to produce bias. Therefore, it is necessary to correct the ionosphere in SAR image processing so that it does not contain bias. This study examines the effect of ionospheric correction on vertical deformation in ALOS-PALSAR satellite imagery. The data used includes satellite image data and GNSS. Image data is processed by considering the presence or absence of ionospheric correction so that the results can be analyzed to determine the effect of the ionosphere on SAR images. GNSS data is processed by a static method to produce coordinates that can be used as a reference for validating the results of SAR image processing. The results of SAR and GNSS image processing are then visualized in the form of a vertical deformation map to facilitate the analysis of the results. The results showed that the direction of the vertical deformation in the ionospheric corrected satellite image was consistent with the direction of the vertical deformation in the GNSS. This indicates that the ionospheric correction affects the vertical deformation in the satellite image. In the process of vertical changes, there are obstacles, namely the vertical point reference has not been used as a validation of the results. In addition, there are no other satellite image references to compare the results of the ALOS-PALSAR satellite image processing.

Experimental Study of the Interaction of Controlled Disturbances from Two Sources in the Supersonic Boundary Layer of a Swept Wing

Experimental results of the interaction of disturbances from two point sources of periodic controlled pulsations in the supersonic boundary layer of a swept wing at a Mach number of 2 are presented. It is shown that as a result of the summation of disturbances, an interference pattern is formed and, for certain values of the wave numbers, it is possible to suppress the corresponding components of unstable waves.

Instability of Ion Cyclotron Waves (ICWS) at the Expense of Lower Hybrid Drift Waves (LHDWS) Turbulence Energy

Instability of ion cyclotron waves(ICWs) is investigated in presence of lower hybrid drift waves(LHDWs) turbulence. Plasma inhomogeneity in the Earth’s magnetopause region supports a range of low frequency drift wave turbulent fields due to gradients in density in different regions of the media. One of these drift phenomena is identified as lower hybrid drift waves (LHDWs) which satisfies resonant conditions ω − k · v = 0. We have considered a nonlinear wave-particle interaction model where the resonant wave that accelerates the particle in magnetopause may transfer its energy to ion cyclotron waves through a modulated field. In spite of the frequency gaps between the two waves, energy can be transferred nonlinearly to generate unstable ion cyclotron waves which always do not satisfy the resonant condition Ω−K · v ≠ 0 and the nonlinear scattering condition Ω − ω − (K − k) · v ̸= 0. Here, ω and Ω are frequencies of the resonant and the nonresonant waves respectively and k and K are the corresponding wave numbers. We have obtained a nonlinear dispersion relation for ion cyclotron waves(ICWs) in presence of lower hybrid drift waves(LHDWs)turbulence. The growth rate of the ion cyclotron waves using space observational data in the magnetopause region has been estimated.

Deciphering the physical basis of the intermediate-scale instability

We study the underlying physics of cosmic ray (CR)-driven instabilities that play a crucial role for CR transport across a wide range of scales, from interstellar to galaxy cluster environments. By examining the linear dispersion relation of CR-driven instabilities in a magnetised electron–ion background plasma, we establish that both the intermediate and gyroscale instabilities have a resonant origin, and show that these resonances can be understood via a simple graphical interpretation. These instabilities destabilise wave modes parallel to the large-scale background magnetic field at significantly distinct scales and with very different phase speeds. Furthermore, we show that approximating the electron–ion background plasma with either magnetohydrodynamics (MHD) or Hall-MHD fails to capture the fastest-growing instability in the linear regime, namely the intermediate-scale instability. This finding highlights the importance of accurately characterising the background plasma for resolving the most unstable wave modes. Finally, we discuss the implications of the different phase speeds of unstable modes on particle–wave scattering. Further work is needed to investigate the relative importance of these two instabilities in the nonlinear, saturated regime and to develop a physical understanding of the effective CR transport coefficients in large-scale CR hydrodynamics theories.

Cavitation in Internal Flows of Liquid Jet Through a Throat

The interaction of a liquid with the surrounding air produces unstable waves that disintegrate the liquid into droplets, which is known as liquid atomization. The common internal flow of a liquid atomization nozzle experiences a single-phase flow but might turn into a multiphase flow with the existence of cavitation. Cavitation in internal flow has gotten a lot of attention because of the positive and negative consequences it can have depending on the application. One such advantageous result is that cavitation has been used to promote the atomization of liquid jets by causing gas bubbles in the atmosphere to collapse. Most of the past research on cavitation has focused on the exit orifice’s constant cross-section area. The current study investigates the effect of throat location and geometry on cavitation characteristics. Filtered water was used as the simulation fluid. The high-speed shadowgraph technique was applied to record the images of the internal flow patterns. The placement of the throat was discovered to have a substantial impact on the status of the cavitation. Cavitation began at the inlet of the throat when the throat was placed at the uppermost part of the exit orifice. However, when the throat is placed in the middle of the exit orifice, the cavitation begins at the end of the throat. Four cavitation regimes were identified, namely developing, mixed, super and sudden expansion cavitation. Furthermore, it was found that the discharge coefficient depends on the cavitation’s state and length, except when the cavitation is in the supercavitation regime.

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.

A special phenomenon of wave interactions: An application of nonlinear evolution equation in (3+1)-dimension

The Lie group transformation approach can be used in the reduction of the generalized (3+1)-dimensional nonlinear evolution equation to ordinary differential equations (ODEs). In this work, infinitesimal generators, commutator table of Lie algebra, adjoint representation of subalgebras, symmetry group, and similarity reduction for (3+1)-dimensional shallow-water-like (gSWL) equation are obtained. Interactions of soliton solutions of a gSWL equation are evaluated that depict how near-inertial waves affect the dynamics of barotropic and baroclinic balanced flows. It is shown that the temporo-spatial localization of multi-soliton complexes (MSCs), gradually escalating incoherent interactivity amidst multi parameter group of MSCs along with spatial inhomogeneity alter the shape of quasi-periodic MSCs. The interactions among bright and dark solitons are shown. The increased number of solitons and increased self-interactions among solitary waves contribute to an unstable wave field. Breathers have a well-separating and initial localized energy domain. A limiting case of breather solutions is the peregrine soliton. Thus, interactions among these soliton structures show that multiple breathers retain their wave characteristic.

The Impact of Pickup Ion Thermal Spread on Pickup Ion Ring-beam-driven Instabilities and Scattering in the Outer Heliosheath

The present study investigates the unstable waves driven by the pickup ions of ring-beam distributions with various pickup angles and pickup ion temperatures in the outer heliosheath, using both linear instability analysis and hybrid simulations. While previous papers have generally assumed specific pickup ion temperatures, this study takes a more comprehensive approach by examining a wide range of pickup ion temperatures that may occur in the outer heliosheath. Our one-dimensional simulations demonstrate that regardless of the initial pickup ion temperature, the pitch-angle scattering of the pickup ions at small pickup angles saturates before the pickup ions can reach the hemisphere of negative parallel velocities with respect to the background magnetic field in velocity space, while at a 90° pickup angle, the pickup ions of ring distributions attain a significant level of isotropy. In contrast, the two-dimensional simulation results show that at all pickup angles, increasing the pickup ion temperature only slightly reduces the pickup ion scattering rate, but does not prevent the pickup ions from reaching the hemisphere of negative parallel velocities. Overall, the results do not align with the requirements of the earlier proposed scenarios for the secondary energetic neutral atom (ENA) mechanism of the Interstellar Boundary Explorer ENA ribbon, which demand either weak pickup ion scattering in the outer heliosheath or at least incomplete pickup ion scattering in the off-ribbon directions.

Numerical simulation of laminar-turbulent transition in a supersonic boundary layer under the action of acoustic disturbances

In low disturbance environment, laminar-turbulent transition (LTT) is associated with excitation of unstable normal modes of small initial amplitudes (receptivity problem). These modes grow exponentially to a critical amplitude in accord with the linear stability theory (LST) and trigger the nonlinear breakdown. In the current study numerical simulation of laminar-turbulent transition (LTT) in the boundary layer on the upper surface of a flat plate in a supersonic free stream of Mach number M∞=3 and Reynolds number Re∞=2 × 107 is carried out. The flow is perturbed by fast or slow acoustic waves of low intensity, which excite unstable waves of the first mode. The latter have frequencies corresponding to the integral amplification N ≈ 9.16 typical for flight conditions. Two cases are considered: the angle of attack AoA=0° at which acoustic waves pass through a weak shock induced by viscous-inviscid interaction; AoA=5° at which acoustic waves pass through the expansion fan emanating from the plate leading edge. A holistic modeling of all stages of the transition from receptivity to the birth of turbulent spots is performed using direct numerical simulations. Linear stability theory is used to interpret the results. Feasibility of practical implementation of the amplitude method for predictions of the LTT onset in the considered and similar cases is discussed. It has been shown that to realize the amplitude method in the considered and similar cases, it is sufficient: to calculate the initial amplitudes of instability in a small vicinity of the leading edge and the propagation of instability from the leading edge to the station where the instability reaches the critical amplitude u′max≈4%. Analysis of known numerical and experimental data showed that this criterion weakly depends on the local Mach number in the range 0<Me<7, and it is acceptable for practical predictions of the transition onset points.

Stabilization for the Klein–Gordon–Zakharov system

This paper deals with global stability dynamics for the Klein–Gordon–Zakharov system in R 2 . We first establish that this system admits a family of linear mode unstable explicit quasi-periodic wave solutions. Next, we prove that the Kelvin–Voigt damping can help to stabilize those linear mode unstable explicit quasi-periodic wave solutions for the Klein–Gordon–Zakharov system in the Sobolev space H s + 1 ( R 2 ) × H s + 1 ( R 2 ) × H s + 1 ( R 2 ) for any s ⩾ 1. Moreover, the Kelvin–Voigt damped Klein–Gordon–Zakharov system admits a unique Sobolev regular solution exponentially convergent to some special solutions (including quasi-periodic wave solutions) of it. Our result can be extended to the n-dimension dissipative Klein–Gordon–Zakharov system for any n ⩾ 1.