Theoretical analysis of the elastic Kelvin-Helmholtz instability in explosive weldings

By considering the joint effects of the Kelvin-Helmholtz(KH) and Rayleigh-Taylor(RT) instabilities, this paper presents an interpretation of the wavy patterns that occur in explosive welding. It is assumed that the elasticity of the material at the interface effectively determines the wavelength, because explosive welding is basically a solid-state welding process. To this end, an analytical model of elastic hydrodynamic instabilities is proposed, and the most unstable mode is selected in the solid phase. Similar approaches have been widely used to study the interfacial behavior of solid metals in high-energy-density physics. By comparing the experimental and theoretical results, it is concluded that thermal softening,which significantly reduces the shear modulus, is necessary and sufficient for successful welding. The thermal softening is verified by theoretical analysis of the increase in temperature due to the impacting and sliding of the flyer and base plates, and some experimental observations are qualitatively validated.In summary, the combined effect of the KH and RT instabilities in solids determines the wavy morphology, and our theoretical results are in good qualitative agreement with experimental and numerical observations.

Mode coupling in nonlinear Kelvin-Helmholtz instability

This paper investigates the interaction of a small number of modes in the two-fluid Kelvin-Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be relatively long range in wave-number space and also it acts in both directions, i.e. short wavelengths affect long wavelengths and vice versa. There is no simple equivalent transformation from a band of similar modes to one mode representing their effective amplitude. Three distinct stages of interaction have been identified.

Magnetohydrodynamic Kelvin-Helmholtz instability for finite-thickness fluid layers

We have derived the analytical formulas for the Kelvin-Helmholtz instability(KHI)of two superposed finite-thickness fluid layers with the magnetic field effect into consideration.The linear growth rate of KHI will be reduced when the thickness of the fluid with large density is decreased or the thickness of fluid with small density is increased.When the thickness and the magnetic field act together on the KHI,the effect of thickness is more obvious when the magnetic field intensity is weak.The magnetic field transition layer destabilizes(enforces)the KHI,especially in the case of small thickness of the magnetic field transition layer.When considering the effect of magnetic field,the linear growth rate of KHI always decreases after reaching the maximum with the increase of total thickness.The stronger the magnetic field intensity is,the more obvious the growth rate decreases with the total thickness.Thus,it should be included in applications where the effect of fluid thickness on the KHI cannot be ignored,such as in double-cone ignition scheme for inertial confinement fusion.

NONLINEAR MHD KELVIN-HELMHOLTZ INSTABILITY IN A PIPE

Nonlinear MHD Kelvin-Helmholtz(K-H)instability in a pipe is treated with the deriva- tive expansion method in the present paper The linear stability problem was discussed in the past by Chandrasekhar(1961)and Xu et al.(1981).Nagano(1979)discussed the nonlinear MHD K-H instability with infinite depth.He used the singular perturbation method and extrapolated the ob- tained second order modifier of amplitude vs.frequency to seek the nonlinear effect on the instability growth rate γ.However,in our view,such an extrapolation is inappropriate.Because when the instabili- ty sets in,the growth rates of higher,order terms on the right hand side of equations will exceed the cor- responding secular producing terms,so the expansion will still become meaningless even if the secular producing terms are eliminated.Mathematically speaking,it's impossible to derive formula(39) when γ_0~2 is negative in Nagano's paper.Moreover,even as early as γ_0~2→O^+,the expansion be- comes invalid because the 2nd order modifier γ_2(in his formula(56))tends to infinity.This weak- ness is removed in this paper,and the result is extended to the case of a pipe with finite depth.

Influence of interlayer on characteristics of Kelvin-Helmholtz instability

Characteristics of the Kelvin-Helmholtz （KH） instability of the interfaces formed by two semi-infinitely distributed fluids and one interlayer were studied. It was found that the coupling effects between theinterfaces should be considered if the interlayer thickness was less than 0. 5 times of the disturbation wave-length. And the degenerate modes could be produced in the situation with proper parameters.

Simulation of Kelvin-Helmholtz Instability with Flux-Corrected Transport Method

The sixth-order accurate phase error flux-corrected transport numerical algorithm is introduced, and used to simulate Kelvin-Helmholtz instability. Linear growth rates of the simulation agree with the linear theories of Kelvin Helmholtz instability. It indicates the validity and accuracy of this simulation method. The method also has good capturing ability of the instability interface deformation.

NUMERICAL MODELING OF KELVIN-HELMHOLTZ INSTABILITY AND RAYLEIGH-TAYLOR INSTABILITY AT LARGE DEFORMATION STAGE——(Ⅰ) NUMERICAL METHOD AND NUMERICAL RESULTS OF RAYLEIGHTAYLOR INSTABILITY

This paper improves the discrete vortex method for modeling Kelvin-Helmholtz instability and Rayleigh-Tay- lor instability by proper choice of velocity weighted average coefficients, redistribution of markers and successive adding of computational points with the increase of interfacial deformation and gives the numerical results of Rayleigh-Taylor instability. The numerical results show that the first two techniques greatly enhance the ability of the discrete vortex method for modeling large interracial deformations and the last technique greatly reduces the computational amounts of the numerical modeling at large deformation stage. The numerical modeling of Rayleigh- Taylor instability not only reproduces some phenomena such as the roll up at the end part of the spike observed in experiments but also finds some new phenomena such as the splashes at the roll up parts which needs to be tested by experiment.

Kinetic Simulation of Nonequilibrium Kelvin-Helmholtz Instability

The recently developed discrete Boltzmann method(DBM), which is based on a set of uniform linear evolution equations and has high parallel efficiency, is employed to investigate the dynamic nonequilibrium process of Kelvin-Helmholtz instability(KHI). It is found that, the relaxation time always strengthens the global nonequilibrium(GNE), entropy of mixing, and free enthalpy of mixing. Specifically, as a combined effect of physical gradients and nonequilibrium area, the GNE intensity first increases but decreases during the whole life-cycle of KHI. The growth rate of entropy of mixing shows firstly reducing, then increasing, and finally decreasing trends during the KHI process. The trend of the free enthalpy of mixing is opposite to that of the entropy of mixing. Detailed explanations are:(i) Initially,binary diffusion smooths quickly the sharp gradient in the mole fraction, which results in a steeply decreasing mixing rate.(ii) Afterwards, the mixing process is significantly promoted by the increasing length of material interface in the evolution of the KHI.(iii) As physical gradients are smoothed due to the binary diffusion and dissipation, the mixing rate reduces and approaches zero in the final stage. Moreover, with the increasing Atwood number, the global strength of viscous stresses on the heavy(light) medium reduces(increases), because the heavy(light) medium has a relatively small(large) velocity change. Furthermore, for a smaller Atwood number, the peaks of nonequilibrium manifestations emerge earlier, the entropy of mixing and free enthalpy of mixing change faster, because the KHI initiates a higher growth rate.

Nonequilibrium and morphological characterizations of Kelvin-Helmholtz instability in compressible flows

We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann model.Technically,two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic processes.One is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures;the other is to evaluate the growth rate of KHI from the slopes of morphological functionals.Physically,it is found that the time histories of width of mixing layer,TNE intensity,and boundary length show high correlation and attain their maxima simultaneously.The viscosity effects are twofold,stabilize the KHI,and enhance both the local and global TNE intensities.Contrary to the monotonically inhibiting effects of viscosity,the heat conduction effects firstly refrain then enhance the evolution afterwards.The physical reasons are analyzed and presented.

复合坐标系跨临界液滴表面Kelvin-Helmholtz不稳定增长高效预测方法

针对混合动力专用内燃机实际运行的跨临界条件,传统方法对于主导可燃混合气形成质量的液滴表面Kelvin-Helmholtz不稳定性分析方法难以实现跨临界宽范围的有效预测。采用复合坐标系方法,建立跨临界强对流环境的等效液滴不稳定性高效预测模型,分别采用全局扩散动力学模型、热力学控制模型及局部液滴表面切向不稳定模型。在全局坐标系模型可以通过模态坐标变换求得解析解,局部坐标系引入势函数等,提高求解速度。而对于可实用性流体计算仿真模型,可通过无量纲物理参数描述不同跨临界条件下空气动力、惯性力、黏性力、表面张力、加速度等控制因素的变化规律,以及其对液滴表面切向和法向不稳定波增长的影响规律。结果表明:液滴表面的空气动力仍然支配着跨临界条件液滴表面切向不稳定波的发展;压力增大时,液相雷诺数控制的流动特性减小与欧尼索控制的液滴黏性力减弱基本抵消;环境温度增加时,雷诺数表征的流动特性对Kelvin-Helmholtz波增长的贡献越来越小,液滴的惯性力影响也越来越弱。

Applications of Non-Classical Equations and Their Approaches to the Solution of Some of Classes Equations Arise in the Kelvin-Helmholtz Mechanism and Instability

In the presented work, we consider applications of non-classical equations and their approaches to the solution of some classes of equations that arise in the Kelvin-Helmholtz Mechanism (KHM) and instability. In all areas where the Kelvin-Helmholtz instability (KHI) problem is investigated with the corresponding data unchanged, the solution can be taken directly in a specific form (for example, to determine the horizontal structure of a perturbation in a barotropic rotational flow, which is a boundary condition taken, as well as other types of Kelvin-Helmholtz instability problems). In another example, the shear flow along the magnetic field in the Z direction, which is the width of the contact layer between fast and slow flows, has a velocity gradient along the X axis with wind shear. The most difficult problems arise when the above unmentioned equation has singularities simultaneously at points and in this case, our results also remain valid. In the case of linear wave analysis of Kelvin-Helmholtz instability (KHI) at a tangential discontinuity (TD) of ideal magneto-hydro-dynamic (MHD) plasma, it can be attributed to the presented class, and in this case, as far as we know, solutions for eigen modes of instability KH in MHD plasma that satisfy suitable homogeneous boundary conditions. Based on the above mentioned area of application for degenerating ordinary differential equations in this work, the method of functional analysis in order to prove the generalized solution is used. The investigated equation covers a class of a number of difficult-to-solve problems, namely, generalized solutions are found for classes of problems that have analytical and mathematical descriptions. With the aid of lemmas and theorems, the existence and uniqueness of generalized solutions in the weight space are proved, and then general and particular exact solutions are found for the considered problems that are expressed analytically explicitly. Obtained our results may be used for all the difficult-to-solve processes of KHM and instabilities and instabilities, which cover widely studied areas like galaxies, Kelvin-Helmholtz instability in the atmospheres of planets, oceans, clouds and moons, for example, during the formation of the Earth or the Red Spot on Jupiter, as well as in the atmospheres of the Sun and other stars. In this paper, also, a fairly common class of equations and examples are indicated that can be used directly to enter data for the use of the studied suitable tasks.

Construction and validation of somatic mutation-derived long noncoding RNAs signatures of genomic instability to predict prognosis of hepatocellular carcinoma

BACKGROUND Long non-coding RNAs(LncRNAs)have been found to be a potential prognostic factor for cancers,including hepatocellular carcinoma(HCC).Some LncRNAs have been confirmed as potential indicators to quantify genomic instability(GI).Nevertheless,GI-LncRNAs remain largely unexplored.This study established a GI-derived LncRNA signature(GILncSig)that can predict the prognosis of HCC patients.AIM To establish a GILncSig that can predict the prognosis of HCC patients.METHODS Identification of GI-LncRNAs was conducted by combining LncRNA expression and somatic mutation profiles.The GI-LncRNAs were then analyzed for functional enrichment.The GILncSig was established in the training set by Cox regression analysis,and its predictive ability was verified in the testing set and TCGA set.In addition,we explored the effects of the GILncSig and TP53 on prognosis.RESULTS A total of 88 GI-LncRNAs were found,and functional enrichment analysis showed that their functions were mainly involved in small molecule metabolism and GI.The GILncSig was constructed by 5 LncRNAs(miR210HG,AC016735.1,AC116351.1,AC010643.1,LUCAT1).In the training set,the prognosis of high-risk patients was significantly worse than that of low-risk patients,and similar results were verified in the testing set and TCGA set.Multivariate Cox regression analysis and stratified analysis confirmed that the GILncSig could be used as an independent prognostic factor.Receiver operating characteristic curve analysis of the GILncSig showed that the area under the curve(0.773)was higher than the two LncRNA signatures published recently.Furthermore,the GILncSig may have a better predictive performance than TP53 mutation status alone.CONCLUSION We established a GILncSig that can predict the prognosis of HCC patients,which will help to guide prognostic evaluation and treatment decisions.

Kelvin-Helmholtz instability with mass transfer through porous media: Effect of irrotational viscous pressure

This paper studies the effect of the irrotational viscous pressure on Kelvin-Helmholtz instability of the plane interface of two viscous and incompressible fluids in a fully saturated porous media with mass and heat transfers across the interface. In the earlier work, the instability of the plane interface of two viscous and streaming miscible fluids through porous media was studied by assuming that the motion and the pressure are irrotational and the viscosity enters the normal stress balance. This theory is called the viscous potential flow theory. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by considering viscous contributions of the irrotational pressure. The Darcy-Brinkman model is used in the investigation and the stability criterion is formulated in terms of a critical value of the relative velocity. It is observed that the heat and mass transfer has a destabilizing effect on the stability of the system while the irrotational shearing stresses stabilize the system.

KELVIN-HELMHOLTZ INSTABILITY IN TOKAMAKS

<正> One of the main problems in Tokamaks is plasma heating. Neutral beam heating has made a considerable stride recently, the ion temperature T_i as high as 7.1 KeV has been obtained in PLT. But toroidal plasma rotational velocities up to 1×10~7 cm/sec due to an unbalanced injector system bas also been observed in the experiments. S.

基于Kelvin-Helmholtz不稳定性和界面剪切作用的扰动波高预测模型

环雾状流广泛存在于天然气等工业环境中,深入探究扰动波特性对了解环雾状流的演化规律有着重要意义。本文在内径为15mm的垂直管路中进行了不同工况条件下的环雾状流实验,分别利用电导环传感器和液膜收集系统测量了液膜厚度和夹带率,并通过双阈值方法从液膜时序信号中提取了扰动波高数据。探究了扰动波高和夹带率随气、液相流量和工况压力的变化规律,发现两者均随着液相流量的增大而增大,而随着气相流量和工况压力的增大,扰动波高呈下降趋势,夹带率呈上升趋势,验证了两者之间存在密切关联。然后分析了影响扰动波高的尺度参数,建立了基于Kelvin-Helmholtz不稳定性和界面剪切作用的扰动波高预测模型,相对均方根误差rRMSE为4.05%,且98.7%的数据点都在±10.0%的误差以内,预测效果良好。最后,将新模型与现有的扰动波高关系式进行比较,预测精度和可扩展性都有了较大提高。

Wave nature of Rosensweig instability

The explicit analytical solution of Rosensweig instability spikes'shapes obtained by Navier-Stokes(NS)equation in diverse magnetic field H vertical to the flat free surface of ferrofluids are systematically studied experimentally and theoretically.After carefully analyzing and solving the NS equation in elliptic form,the force balanced surface equations of spikes in Rosensweig instability are expressed as cosine wave in perturbated magnetic field and hyperbolic tangent in large magnetic field,whose results both reveal the wave-like nature of Rosensweig instability.The results of hyperbolic tangent form are perfectly fitted to the experimental results in this paper,which indicates that the analytical solution is basically correct.Using the forementioned theoretical results,the total energy of the spike distribution pattern is calculated.By analyzing the energy components under different magnetic field intensities H,the hexagon-square transition of Rosensweig instability is systematically discussed and explained in an explicit way.

Tendoscopic Surgery for Peroneal Tendons Instability: A Literature Review

Introduction: There has been a surge in the use of tendoscopic surgery for treating peroneal tendons instability. The novelty of this approach demanded a literature review of its indications, limitations, and clinical outcomes. Aim: a literature review of the clinical studies reporting on tendoscopic peroneal tendon stabilisation surgery along with its outcomes and complications. Methods: We carried out a comprehensive review of the literature up until September 2022 with an extensive search of the MEDLINE, Embase and Cochrane library databases. Results: Initial search resulted in 66 articles. Four duplicate articles were removed. Further 30 articles were excluded after title and abstract screening. Eight studies satisfied the inclusion criteria and were included in this review. Articles were analysed for outcomes and complications. Conclusion: The tendoscopic technique for peroneal tendon instability is an effective and safe surgical technique with very low failure rate. Levels of Evidence: Level IV.

Transverse mode-coupling instability with longitudinal impedance

Transverse mode-coupling instability(TMCI)is a dangerous transverse single-bunch instability that can lead to severe par-ticle loss.The mechanism of TMCI can be explained by the coupling of transverse coherent oscillation modes owing to the transverse short-range wakefield(i.e.,the transverse broadband impedance).Recent studies on future circular colliders,e.g.,FCC-ee,showed that the threshold of TMCI decreased significantly when both longitudinal and transverse impedances were included.We performed computations for the circular electron-positron collider(CEPC)and observed a similar phenom-enon.Systematic studies on the influence of longitudinal impedance on the TMCI threshold were conducted.We concluded that the imaginary part of the longitudinal impedance,which caused a reduction in the incoherent synchrotron tune,was the primary reason for the reduction in the TMCI threshold.Additionally,the real part of the longitudinal impedance assists in increasing the TMCI threshold.

Chronic Ankle Instability: Therapeutic Exercise and Data Analysis

Background and Objectives: Ankle injuries are the most common type of injury in healthy active individuals. If not treated properly, recurrent sprains can lead to a condition of chronic ankle instability (CAI). The present paper examines some subjects with a previous history of acute inversion ankle sprain who have developed a subsequent condition of instability, grouping them according to inclusion criteria and analyzing them through four field tests considered objective by the scientific literature: SEBT test, BEES test, TIBT test, SHT test. The data obtained were stored in order to compare them following a re-education protocol aimed at improving proprioception, balance, walking and strengthening the extrinsic and intrinsic muscles of the foot. per year. The subjects were then divided into two categories: subjects with CAI > 1 year and subjects with CAI ≤ 1 year. A protocol lasting 6 weeks was administered to both groups, trying to work on improving balance in single stance, improving static and dynamic stability, strengthening the gluteus medius and maximus (pelvis stabilizers) and strengthening of the intrinsic muscles of the foot. At the end of the protocol the subjects were all re-evaluated with the same field tests used previously and the data obtained were compared both with the pre-protocol data and with the data measured by the control subjects.

Parametric instability in the pure-quartic nonlinear Schrödinger equation

We study the nonlinear stage of modulation instability(MI)in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically.Using the three-mode truncation,we reveal the complex recurrence of parametric resonance(PR)breathers,where each recurrence is associated with two oscillation periods(PR period and internal oscillation period).The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.