Cyclone–anticyclone vortex asymmetry mechanism and linear Ekman friction

Allowance for the linear Ekman friction has been found to ensure a threshold (in rotation frequency) realization of the linear dissipative–centrifugal instability and the related chiral symmetry breaking in the dynamics of Lagrangian particles, which leads to the cyclone–anticyclone vortex asymmetry. An excess of the fluid rotation rate ω₀ over some threshold value determined by the fluid eigenfrequency ω (i.e., ω₀ > ω) is shown to be a condition for the realization of such an instability. A new generalization of the solution of the Karman problem to determine the steady-state velocity field in a viscous incompressible fluid above a rotating solid disk of large radius, in which the linear Ekman friction was additionally taken into account, has been obtained. A correspondence of this solution and the conditions for the realization of the dissipative–centrifugal instability of a chiral-symmetric vortex state and the corresponding cyclone–anticyclone vortex asymmetry has been shown. A generalization of the well-known spiral velocity distribution in an “Ekman layer” near a solid surface has been established for the case where the fluid rotation frequency far from the disk ω differs from the disk rotation frequency ω₀.     

Development of instability in the problem of flow around a sphere

Multimoment hydrodynamics equations are used to solve the problem of flow around a quiescent solid sphere. The solutions to the multimoment hydrodynamics equations are found, which enable to interpret of the phenomenon of vortex shedding. The solutions give a pattern of instability development that qualitatively reproduces experimental data over a wide range of Reynolds numbers. The replacement of one unstable flow mode by another unstable mode is governed the tendency of the system to find the fastest way to depart from the state of statistical equilibrium. After stability loss, the system does not reach a new stable state. Such a scenario is at odds with the ideas of classical hydrodynamics, which interprets the development of instability in terms of a bifurcation transition from one stable state to another. This picture presented shows the direction of solving the problems faced by classical hydrodynamics in the interpretation of the phenomenon of vortex shedding.     

Essence of Inviscid Shear Instability: a Point View of Vortex Dynamics

The essence of shear instability is reviewed both mathematically and physically, which extends the instability theory of a sheet vortex from the viewpoint of vortex dynamics. For this, the Kelvin-Arnol＇d theorem is retrieved in linear context, i.e., the stable flow minimizes the kinetic energy associated with vorticity. Then the mechanism of shear instability is explored by combining the mechanisms of both Kelvin Helmholtz instability （K-H instability） and resonance of waves. The waves, which have the same phase speed with the concentrated vortex, have interactions with the vortex to trigger the instability. The physical explanation of shear instability is also sketched by extending Batchelor＇s theory. These results should lead to a more comprehensive understanding on shear instabilities.     

Nonequilibrium quasiparticle relaxation in the vortex state of La2-xSrxCuO4

We have measured the charge dynamics in the vortex state of La(2-x)Sr(x)CuO(4) by femtosecond time-resolved reflectance, which we demonstrate to be a direct probe of low-energy quasiparticle states. Application of a c-axis magnetic field induces regions surrounding vortex cores that display pseudogap charge dynamics. We determine the characteristic width approximately 130 A in optimally doped material and we show that it increases with decreasing doping. These results confirm a new experimental method of probing the microscopic properties of vortices in the cuprates.     

Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates

We have theoretically investigated Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates. Counterrotating perturbation induces an elliptical instability to the initially straight vortex line, driven by a parametric resonance between a quadrupole mode and a pair of Kelvin modes of opposite momenta. Subsequently, Kelvin waves rapidly decay to longer wavelengths emitting sound waves in the process. We present a modified Kelvin wave dispersion relation for trapped superfluids and propose a simple method to excite Kelvin waves of specific wave number.     

Breakdown of the superheated Meissner state and spontaneous vortex nucleation in type II superconductors

The theory of local stability of the superheated Meissner state presented in an earlier paper is supplemented by an investigation of global stability in two dimensions. We conclude that flux penetration cannot be delayed beyond the fieldH _s1 where local instability sets in. Various new two-dimensional Ginzburg-Landau solutions, obtained numerically, are discussed. These include the lowest saddle point separating the Meissner from the normal and vortex state and a solution resembling the “nascent vortex state” whose existence was postulated recently by Walton and Rosenblum. Using these solutions the process of spontaneous vortex nucleation is discussed.     

Vibrations and vortices in combustion chambers

Computational and experimental studies have been made of large-scale vortex structures as sources of acoustic vibrations. Low-frequency sources of vibration in combustion chambers of solid propellant jet engines have been shown to be due to the hydrodynamic instability of large-scale vortex structures in the main gas flow.M. A. Lavrent'ev Institute of Hydrodynamics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 111–118, April, 1994.     

Emergence and decay of turbulence in stirred atomic Bose-Einstein condensates

We show that "weak" elliptical deformation of an atomic Bose-Einstein condensate rotating at close to the quadrupole instability frequency leads to turbulence with a Kolmogorov energy spectrum. The turbulent state is produced by energy transfer to condensate fragments that are ejected by the quadrupole instability. This energy transfer is driven by breaking the twofold rotational symmetry of the condensate. Subsequently, vortex-sound interactions damp the turbulent state leading to the crystallization of a vortex lattice.     

Vortex liquid crystals in anisotropic type II superconductors

In an isotropic type II superconductor in a moderate magnetic field, the transition to the normal state occurs by vortex lattice melting. In certain anisotropic cases, the vortices acquire elongated cross sections and interactions. Systems of anisotropic, interacting constituents generally exhibit liquid crystalline phases. We examine the possibility of a two step melting in homogeneous type II superconductors with anisotropic superfluid stiffness from a vortex lattice into first a vortex smectic and then a vortex nematic at high temperature and magnetic field. We find that fluctuations of the ordered phase favor an instability to an intermediate smectic-A in the absence of intrinsic pinning.     

Spontaneous splitting of a quadruply charged vortex

We studied the splitting instability of a quadruply charged vortex both experimentally and theoretically. The density defect, which is a signature of the vortex core, is experimentally observed to deform into a linear shape. The deformed defect is theoretically confirmed to be an array of four linearly aligned singly charged vortices. The array of vortices rotates and precesses simultaneously with different angular velocities. The initial state of the system is not rotationally symmetric, which enables spontaneous splitting without external perturbations.     

关于转捩边界层中流向涡的产生

给出了转捩边界中流向涡产生的物理过程,这个过程是A－涡和二次涡环相互作用产生旋涡轴向失稳断裂造成的。     

Development of diocotron instability in the squeezed state of a relativistic electron beam

Nonlinear nonstationary processes in a beam-plasma system containing a hollow intense relativistic electron beam with an overcritical current in the squeezed state are studied numerically. The emergence and development of diocotron instability in the squeezed state, which leads to formation of vortex structures, is analyzed in detail, and the effect the magnitude of the external magnetic field has on the processes of structure formation in the beam is investigated.     

Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.     

Whistler instability in an electron-magnetohydrodynamic spheromak

A three-dimensional magnetic vortex, propagating in the whistler mode, has been produced in a laboratory plasma. Its magnetic energy is converted into electron kinetic energy. Non-Maxwellian electron distributions are formed which give rise to kinetic whistler instabilities. The propagating vortex radiates whistler modes along the ambient magnetic field. A new instability mechanism is proposed.     

Centrifugal-dissipative instability of Rossby vortices and their cyclonic-anticyclonic asymmetry

A new linear centrifugal-dissipative mechanism is proposed that explains the vortex asymmetry observed, in particular, in the structure of low-frequency anticyclonic Rossby vortices. It is shown that the relevant centrifugal-dissipative instability, which spontaneously breaks the chiral symmetry of the vortices, takes place only in the range ω<Ω, where ω is the frequency of small oscillations corresponding to the effective solid-body rotation of a vortex and Ω is the rotation rate of a noninertial frame of reference. The onset of the instability is associated with the existence of an optimum magnitude of the frictional force. In the vortex model based on a two-dimensional oscillator with the natural frequency ω in a noninertial reference frame rotating at the rate Ω, the instability shows up as an exponential increase in the total angular momentum. It is noted that the centrifugal dissipative instability may also manifest itself in the seismically active regions of the world.     

磁控条件下激波冲击三角形气柱过程的数值研究

本文基于磁流体动力学方程组,在保证磁场散度为零的条件下,采用CTU+CT（corner transport upwind+constrained transport）算法,对有无磁场控制下激波与重质或轻质三角形气柱相互作用过程进行数值研究.结果表明：无论有无磁场,两气柱在激波冲击下均具有完全不同的波系结构和射流现象.其中,入射激波与重气柱发生常规折射,形成介质射流,而与轻气柱作用则发生非常规折射,形成反相空气射流.无磁场时,气柱在激波冲击下,产生Richtmyer-Meshkov和Kelvin-Helmholtz不稳定性,界面出现次级涡序列,重气柱上下角卷起形成主涡对,轻气柱空气射流穿过下游界面后形成偶极子涡.施加横向磁场后,次级涡序列、主涡对以及偶极子涡均消失.进一步研究表明,在磁场作用下,洛伦兹力将不稳定性诱导产生的涡量向界面两侧的Alfvén波上输运,减少界面涡量沉积,抑制界面卷起失稳.最终,涡量沿界面两侧形成相互远离的涡层,界面不稳定性得到控制.此外,定量分析表明磁场能加快两气柱上游界面的运动,抑制下游界面的运动,且对轻气柱的控制效果更好.     

Quantitative theory of thermal fluctuations and disorder in the vortex matter

A metastable supercooled homogeneous vortex liquid state exists down to zero fluctuation temperature in systems of mutually repelling objects. The zero temperature liquid state therefore serves as a (pseudo) ‘fixed point’ controlling the properties of vortex liquid below and even around the melting point. Based on this picture, a quantitative theory of vortex melting and glass transition in Type II superconductors in the framework of Ginzburg-Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps are calculated. The point-like disorder shifts the line downwards and joins the order-disorder transition line. On the other hand, the disorder induces irreversible effects via replica symmetry breaking. The irreversibility line can be calculated within the Gaussian variational method. Therefore, the generic phase diagram contains four phases divided by the irreversibility line and melting line: liquid, solid, vortex glass and Bragg glass. We compare various experimental results with the theoretical formula.     

三维边界层内诱导横流失稳模态的感受性机理

边界层感受性问题是层流向湍流转捩的初始阶段,在转捩过程中起关键性作用,尤其是三维边界层流动.因此,研究三维边界层感受性问题对进一步理解层流向湍流转捩机理以及湍流成因具有重要的理论意义.采用数值方法研究自由来流湍流与三维壁面局部粗糙相互作用下三维边界层的感受性问题,确定是否能在三维边界层内寻找一种新的横流失稳模态;确定在何种条件下三维边界层内能诱导出定常、非定常的横流失稳模态;探索自由来流湍流的强度、展向波数和法向波数以及三维壁面局部粗糙的大小和结构类型等因素在自由来流湍流与三维壁面局部粗糙作用下三维边界层内被激发出的感受性过程中有何影响,并确定何种横流失稳模态在三维边界层感受性过程中占据何种地位.对自由来流湍流与三维壁面局部粗糙作用激发三维边界层内感受性问题的深入研究,将有助于完善流动稳定性与湍流理论,为层流向湍流转捩过程的预测与控制提供合理的理论依据.     

Magnetized electron-whistler holes

Coherent magnetic structures comprising a magnetic vortex and an electron hole have been shown to be created by a Weibel-type, anisotropy driven instability. These structures arise from the electric and magnetic trapping of resonant electrons in the growing fields of the instability. The results of two dimensional Vlasov simulations of the nonlinear development of the instability are compared with a novel analytical model of a stationary propagating phase space structure which includes the depletion of the trapped electrons corresponding to the electron holes.