Noise generation by instabilities in low Reynolds number supersonic jets

An experimental investigation of noise generation by instabilities in low Reynolds number supersonic air jets has been performed. Sound pressure levels, spectra and acoustic phase fronts were measured with a traversing condenser microphone in the acoustic field of axisymmetric, perfectly expanded, cold jets of Mach numbers 1·4, 2·1 and 2·5. Low Reynolds numbers in the range from Re = 3700 to Re = 8700 were obtained by exhausting the jets into an anechoic vacuum chamber test facility. This contrasts with Reynolds numbers of over 10⁶ for similar jets exhausting into atmospheric pressure. The flow fluctuations of the instability in all three jets have been measured with a hot-wire and the results are documented in a previous paper by Morrison and McLaughlin. Acoustic measurements show that the major portion of the sound radiated by all three jets is produced by the instability's rapid growth and decay that occurs near the end of the potential core. This takes place over a relatively short distance (less than two wavelengths of the instability) in the jet. In the lower two Mach number jets the instability has a phase velocity less than the ambient acoustic velocity. In the Mach number 2·5 jet the instability phase speed is 1·11 times the ambient acoustic velocity. In this case the acoustic phase fronts indicate the possibility of a Mach wave component. It was also determined that low level excitation at the dominant frequency of the instability actually decreased the radiated noise by suppressing the broad band component.     

Coiling, entrainment, and hydrodynamic coupling of decelerated fluid jets

From algal suspensions to magma upwellings, one finds jets which exhibit complex symmetry-breaking instabilities as they are decelerated by their surroundings. We consider here a model system--a saline jet descending through a salinity gradient--which produces dynamics unlike those of standard momentum jets or plumes. The jet coils like a corkscrew within a conduit of viscously entrained fluid, whose upward recirculation braids the jet, and nearly confines transverse mixing to the narrow conduit. We show that the underlying jet structure and certain scaling relations follow from similarity solutions to the fluid equations and the physics of Kelvin-Helmholtz instabilities.     

Turbulent structure in supersonic jets with a high Reynolds number

The turbulent properties of a supersonic jet were studied related to a high level of pressure pulsation found in model jets of a reentry flight vehicle approaching the landing ground. This study comprised measurements of total pressure at a small-size target using a dynamic pressure probe placed in a free jet. The most comprehensive data about jet turbulence can be obtained by direct transformation of the pressure reading at the stagnation point near the target into the normalized velocity. The oscillogram of normalized velocity produces the velocity average value, root-mean-square value as well as turbulence intensity and turbulence spectrum. It was demonstrated that a high level of turbulence for a high-head jet retains along the supersonic core length and at the beginning of subsonic interval.     

PIV measurements of turbulent jets issuing from triangular and circular orifice plates

The present study experimentally investigated the near-field flow mixing characteristics of two turbulent jets issuing from equilateral triangular and circular orifice plates into effectively unbounded surroundings,respectively.Planar particle image velocimetry(PIV) was applied to measure the velocity field at the same Reynolds number of Re=50,000,where Re = UeDe /with Ue being the exit bulk velocity and the kinematic viscosity of fluid,D e the equivalent diameters.The instantaneous velocity,mean velocity,Reynolds stresses were obtained.From the mean velocity field,the centreline velocity decay rate and half-velocity width were derived.Comparing the mixing characteristics of the two jets,it is found that the triangular jet has a faster mixing rate than the circular counterpart.The triangular jet entrainments with the ambient fluid at a higher rate in the near field.This is evidenced by a shorter unmixed core,faster Reynolds stress and centreline turbulence intensity growth.The primary coherent structures in the near field are found to break down more rapidly in the triangular jet as compared to the circular jet.Over the entire measurement region,the triangular jet maintained a higher rate of decay and spread.Moreover,all components of Reynolds stress of the triangular jet appear to reach their peaks earlier,and then decay more rapidly than those of the circular jet.In addition,the axis-switching phenomenon is observed in the triangular jet.     

Vortex dynamics in oscillatory chemical systems

Vortex core dynamics is studied in the Brusselator both near to and far from the Hopf bifurcation line for random and pair initial conditions. Extensive simulations are carried out for a pair of counter-rotating vortices close to the Hopf bifurcation line. Provided the vortices are not so far apart that wave-front annihilation produces strong gradients between their centers, the simulation results compare favorably with theories based on the complex Ginzburg-Landau equation. Far from the Hopf line the vortex core dynamics changes character and phenomena such as periodic motion of the vortex centers arise.     

Vortex dynamics in superfluids and the Berry phase

There is a close analogy between the dynamics of electrons in a strong magnetic field and the dynamics of quantized vortices in superfluids and superconductors. In both systems an important part is played by a term in the Lagrangian linear in velocity that corresponds to a Berry phase in the quantum theory. This Berry phase can be calculated from the usual trial wave function for a vortex. This has important consequences for quantum tunneling of vortices, and leads unambiguously to the form of the Magnus force in a superconductor.     

弱相互作用玻色-爱因斯坦凝聚体中涡旋动力学与量子混沌轨道简

利用变分法和数值模拟方法,我们分别从解析上和数值上研究了弱相互作用玻色-爱因斯坦凝聚体中不同涡旋蔟的动力学性质.借助玻姆量子力学中的方法,我们定义了相应量子流体中的量子轨道,并且研究了由于不同涡旋结构的存在而导致量子轨道出现混沌的性质.当存在一单涡旋,我们发现混沌轨道出现与否和涡旋轨道的形状紧密相关.此外,玻色凝聚体原子中的两体相互作用对各向异性谐振子势下涡旋对出现时量子轨道混沌的发生也具有重要的作用.因为这一非线性相互作用会破坏相应速度场的时间周期性.最后,在涡旋极子情形下,我们还讨论了由于涡旋相互激发或淹没的作用而导致规则岛膨胀的性质.这些规则区域镶嵌在一定的混沌海中.     

Vortex dynamics in classical non-Abelian spin models

We discuss the Abelian vortex dynamics in the Abelian projection approach to non-Abelian spin models. We show numerically that in the three-dimensional SU(2) spin model in the maximal Abelian projection the Abelian off-diagonal vortices, unlike the diagonal vortices, are not responsible for the phase transition. A generalization of the Abelian projection approach to SU(N) spin models is briefly discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 526–530 (25 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Vortex dynamics in single crystal Hg-1201

Anisotropic superconducting materials often show an enhanced pinning along their crystallographic ab-planes. To obtain information about such a behavior of the high-T_c system Hg-1201 (HgBa₂CuO₄) magnetic investigations on a single crystal are performed for the two field orientations, parallel to the c-axis and parallel to the ab-planes. The dependence of the ac magnetization on temperature, magnetic field and frequency is determined. Compared to former results on powder samples of this system no indication of a second peak in the imaginary part of the susceptibility χ′′ is found. It seems to be shifted to higher temperatures overlapping now with the first peak. The corresponding irreversibility lines for both orientations, parallel to c and parallel to ab, are determined and discussed within the framework of a “diffusion” model.     

Effective swimming strategies in low Reynolds number flows

The optimal strategy for a microscopic swimmer to migrate across a linear shear flow is discussed. The two cases, in which the swimmer is located at large distance, and in the proximity of a solid wall, are taken into account. It is shown that migration can be achieved by means of a combination of sailing through the flow and swimming, where the swimming strokes are induced by the external flow without need of internal energy sources or external drives. The structural dynamics required for the swimmer to move in the desired direction is discussed and two simple models, based respectively on the presence of an elastic structure, and on an orientation dependent friction, to control the deformations induced by the external flow, are analyzed. In all cases, the deformation sequence is a generalization of the tank-treading motion regimes observed in vesicles in shear flows. Analytic expressions for the migration velocity as a function of the deformation pattern and amplitude are provided. The effects of thermal fluctuations on propulsion have been discussed and the possibility that noise be exploited to overcome the limitations imposed on the microswimmer by the scallop theorem have been discussed.     

Vortex phases and dynamics in high-temperature and conventional amorphous superconductors

The vortex phases and dynamics of high-temperature and conventional amorphous superconductors are investigated over a broad frequency range. A second-order vortex-solid melting transition in both YBa₂Cu₃O₇ single crystals with random point defects and amorphous Mo₃Si films is manifested by a set of universal critical exponents (ν≈2/3 and z≈3) from both ac and dc transport as well as ac magnetic susceptibility measurements. In contrast, the melting transition in YBa₂Cu₃O₇ single crystals with correlated columnar defects is found to be consistent with a Bose-glass phase transition characterized by a different set of critical exponents (ν≈1/2 and z′≈4).     

Level-crossing statistics and production in low Reynolds number wall turbulence

Statistical properties at velocity level crossings are analysed in a low Reynolds number fully developed turbulent channel flow. Emphasis is placed on local production statistics conditioned by fixed amplitudes of the streamwise u and wall-normal v velocity components. Direct numerical simulations performed in large computational domains are used for this purpose. The Reynolds number based on the channel half width and the shear velocity varies from 180 to 1100. Particular attention is paid to correctly determine the conditional quantities at level crossings of u and v velocity fluctuations, to prevent biasing effects. Level crossings along the longitudinal x and spanwise z directions in homogeneous planes are introduced together with different characterisations, such as directional and contour crossings. The frequency of events detected at fixed thresholds follows a Gaussian model acceptably well. There is more level-crossing activity in the spanwise direction than in the streamwise. The mean conditional production distributions are dissymmetrical with respect to the level-crossing thresholds in the low buffer and viscous sublayers. These statistics differ significantly from a statistical model that assumes joint normality between u and v. There is a clear but relatively mild Reynolds number dependence of the conditional expected means of u and v that do not scale with inner, outer or mixed variables. The Reynolds number sensitivity of these statistics increases towards the edge of the wall layer.     

Vortex dynamics in Bose-Einstein condensates: Numerical calculations

We numerically study properties of the dynamics of vortices in nonrotating Bose-Einstein condensates in the Thomas-Fermi regime. On the one hand, we compute the vortex energy as a function of its position and we predict, using the expression of the Magnus force, the vortex precession velocity. On the other hand, we calculate the temporal evolution of the vortex-state and test the accuracy of the previous prediction. We also investigate the validity of analytical formulae of this velocity involving the healing length. In addition, we analyze the velocity field and the angular momentum and we compare them to available analytical expressions.