A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers

We present a validation study for the hybrid particle-mesh vortex method against a pseudo-spectral method for the Taylor–Green vortex at Re_Γ = 1600 as well as in the collision of two antiparallel vortex tubes at Re_Γ = 10,000. In this study we present diagnostics such as energy spectra and enstrophy as computed by both methods as well as point-wise comparisons of the vorticity field. Using a fourth order accurate kernel for interpolation between the particles and the mesh, the results of the hybrid vortex method and of the pseudo-spectral method agree well in both flow cases. For the Taylor–Green vortex, the vorticity contours computed by both methods around the time of the energy dissipation peak overlap. The energy spectrum shows that only the smallest length scales in the flow are not captured by the vortex method.In the second flow case, where we compute the collision of two anti-parallel vortex tubes at Reynolds number 10,000, the vortex method results and the pseudo-spectral method results are in very good agreement up to and including the first reconnection of the tubes. The maximum error in the effective viscosity is about 2.5% for the vortex method and about 1% for the pseudo-spectral method. At later times the flows computed with the different methods show the same qualitative features, but the quantitative agreement on vortical structures is lost.     

Site selection NMR study on electronic state in and near vortex core of YBa2Cu4O8

We report a site-selective ¹⁷O spin-lattice relaxation rate T₁⁻¹ in the vortex state of YBa₂Cu₄O₈. We found that T₁⁻¹ at the planar sites exhibits an unusual nonmonotonic NMR frequency dependence. Based on T₁⁻¹ in the vortex core region, we establish strong evidence that the local density of states within the vortex core is strongly reduced.     

Near-surface turbulence in the atmospheric boundary layer

Measurements of the near-surface turbulence in the atmospheric boundary layer have been made using hot-wire probes above the salt flats of northwestern Utah, where the momentum thickness Reynolds number, R_θ, is O(10⁶), and the surface is smooth and nearly devoid of flow obstructions. The measurements were made with arrays of up to 24 parallel straight sensors and with a modular 12-sensor probe capable of measuring all of the components of the instantaneous velocity vector and velocity gradient tensor. Measurements were also made in a laboratory wind tunnel at R_θ=1730 using 22 straight sensors. The data analysis focuses on the effects of the Reynolds number on turbulence properties and on the physics of the dissipation rate of turbulent kinetic energy.Some properties are found to be dependent on the Reynolds number when normalized with inner variables, while others are not. Among those that show the significant Reynolds number dependence are the rms and the skewness factor of the streamwise velocity fluctuations.Significant differences in flow structure, particularly those related to high rates of dissipation, are implied by the data. The joint PDF and covariance integrand of streamwise and wall normal vorticity fluctuations show less preferred orientation of the vorticity vector in the buffer layer at R_θ of O(10⁶) than at R_θ=1070. The largest contribution to the dissipation rate, at O(10⁶) is by the ∂w/∂z velocity gradient, while this term makes a quite small contribution to the dissipation rate at low R_θ. Here w and z are the spanwise velocity fluctuations and direction, respectively. Conditional analysis in the streamwise-wall normal (x−y) plane based on high instantaneous dissipation rate shows that the typical high dissipation rate events are generally similar at high and low Reynolds numbers, but display some significant differences.     

Asymptotics of unit Burger number rotating and stratified flows for small aspect ratio

Rotating and stably stratified Boussinesq flow is investigated for Burger number unity in domain aspect ratio (height/horizontal length) δ<1 and δ=1. To achieve Burger number unity, the non-dimensional rotation and stratification frequencies (Rossby and Froude numbers, respectively) are both set equal to a second small parameter ?<1. Non-dimensionalization of potential vorticity distinguishes contributions proportional to (?δ)⁻¹, δ⁻¹ and O(1). The (?δ)⁻¹ terms are the linear terms associated with the pseudo-potential vorticity of the quasi-geostrophic limit. For fixed δ=1/4 and a series of decreasing ?, numerical simulations are used to assess the importance of the δ⁻¹ contribution of potential vorticity to the potential enstrophy. The change in the energy spectral scalings is studied as ? is decreased. For intermediate values of ?, as the flow transitions to the (δ?)⁻¹ regime in potential vorticity, both the wave and vortical components of the energy spectrum undergo changes in their scaling behavior. For sufficiently small ?, the (δ?)⁻¹ contributions dominate the potential vorticity, and the vortical mode spectrum recovers k⁻³ quasi-geostrophic scaling. However, the wave mode spectrum shows scaling that is very different from the well-known k⁻¹ scaling observed for the same asymptotics at δ=1. Visualization of the wave component of the horizontal velocity at δ=1/4 reveals a tendency toward a layered structure while there is no evidence of layering in the δ=1 case. The investigation makes progress toward quantifying the effects of aspect ratio δ on the ?→0 asymptotics for the wave component of unit Burger number flows. At the lowest value of ?=0.002, it is shown that the horizontal kinetic energy spectral scalings are consistent with phenomenology that explains how linear potential vorticity constrains energy in the limit ?→0 for fixed δ.     

Scaling analysis of phase transition in Hg-based superconductor

With the vibrating-reed technique, the internal friction (IF) Q⁻¹ is measured for sing-phase (Hg_0.66Pb_0.34)Ba₂Ca₂Cu₃O_8+x superconductor as a function of temperature at low applied magnetic field up to 0.5 T and as a function of frequency at normal state temperatures. An IF peak associated with flux motion can be found below T_C. The IF peak becomes higher and shifts towards lower temperature with increasing magnetic field. In addition an IF peak is found near 200 K. By scaling analysis we have demonstrated that the internal friction around the peak temperature can be collapsed into a single curve, indicating that the IF peak below T_C is originated from a phase transition associated with a vortex glass transition and a structural phase transition occurs at around 200 K in the superconductor.     

Effective temperature and scaling laws of polarized quantum vortex bundles

An effective non-equilibrium temperature is defined for (locally) polarized and dense turbulent superfluid vortex bundles, related to the average energy of the excitations (Kelvin waves) of vortex lines. In the quadratic approximation of the excitation energy in terms of the wave amplitude A, a previously known scaling relation between amplitude and wavelength k of Kelvin waves in polarized bundles, namely A∝k−1/2, follows from the homogeneity of the effective temperature. This result is analogous to that of the well-known equipartition result in equilibrium systems.     

Energy dissipation in the deterministic and nondeterministic Nagel-Schreckenberg models

In this paper, we numerically study energy dissipation per unit time per car E_d in the Nagel-Schreckenberg (NS) model. Numerical results show that there is a critical density over which energy dissipation occurs, but below which no energy loss happens in the deterministic NS model. Energy dissipation depends on both the car density and initial configuration in the deterministic case. The energy dissipation rate, E_d, calculated starting from a completely jammed state whose value is minimum, decreases monotonously with the increase of car density above the critical density. In the nondeterministic case, however, there is no critical density and energy dissipation happens in the whole density region, and initial configuration has no effects on energy dissipation. The dissipated energy has two different contributions: one coming from the interactions and another from the braking noise in the stochastic case. The relative contributions of the two dissipation mechanisms are presented. In the free-flow state, E_d is proportional to p(1−p) where p is the stochastic braking probability. In the case of v_max=1,E_d is proportional to the mean density of “go and stop” car per time step ρ_gs, which is equal to n₀(1−n₀) where n₀ is the fraction of stopped car. Theoretical analyses give an excellent agreement with numerical results.     

On the damping of unsteady flow by compliant boundaries

This paper concerns unsteady motion of an incompressible inviscid fluid near a flexible surface which, in responding to the surface pressure field, absorbs energy. The modification of the flow consequent on energy removal at the boundaries is examined. Energy absorption always occurs when the mechanical surface properties include an element of dissipation. But surface dissipation is not essential; surface waves have a similar property. Unsteady fluid induced forces excite surface waves which carry with them energy that must have originated in the flow. The question of how flow characteristics change as energy is gradually given up to the boundary is examined through a particular model problem from which it becomes evident that surface motion draws vorticity towards the surface. The model chosen is that of a rectilinear vortex adjacent to a weakly responding boundary. Surface motion induces a velocity perturbation which is shown to move the vortex towards the surface whenever the fluid gives energy to that surface.     

Experimental study on the local similarity scaling of the turbulence spectrum in the turbulent boundary layer

The streamwise fluctuating velocity in the turbulent boundary layer is measured under approximately medium Reynolds Number by hot wire in order to investigate the scaling properties of the overlapped turbulent spectrum among energy-containing area, inertial subrange and dissipation range based on FFT analysis. The experiment indicates that the high Reynolds flow reported before is not indispensable to produce −1 scaling. So far as the measured position is provided with much higher spatial resolution and enough closing to the wall, −1 scaling is determinate to exist when approaching medium Reynolds. The scaling ranges are supposed to begin at inner scale and end in outer scale, which reveals the local similarity of the energy spectrum over the energy-containing eddies near the wall. In the logarithmic area (y ⁺ > 130), −5/3 scaling occurs in the energy spectrum, while moving away from the wall with Reynolds numbers increasing, the inertial subrange extends to the lower wavenumbers. On the condition k ₁ η ≫ 0.1, the curves of the turbulence spectrum in the logarithmic layer are superposed, which expresses the similarity of turbulence energy distributed in Komogorov scaling area and exhibits local isotropy characteristics by virtue of the viscous dissipation. Supported by the National Natural Science Foundation of China (Grant Nos. 10832001 and 10872145), the Program for New Century Excellent Talents in Universities of Education Ministry of China, and the Plan of Tianjin Science and Technology Development (Grant No. 06TXTJJC13800)     

Application of nano-scale Josephson junction as phase sensitive detector for analysis of vortex states in mesoscopic superconductors

We study phase shifts in a Josephson junction induced by vortices in superconducting mesoscopic electrodes. The position of the vortices are controlled by suitable geometry of a nano-scale Nb–Pt_1−xNi_x–Nb junction of the overlap type made by Focused Ion Beam (FIB) sculpturing. The vortex is kept outside the junction, parallel to the junction plane. From the measured Fraunhofer characteristics the entrance and exit of vortices are detected. By changing the bias current through the junction at constant magnetic field the vortices can be manipulated and the system can be switched between two consecutive vortex states which are characterized by different critical currents of the junction. A mesoscopic superconductor thus acts as a non-volatile memory cell in which the junction is used both for reading and writing information (vortex). Furthermore, we observe that the critical current density of Nb–Pt_1−xNi_x–Nb junctions decreases non-monotonously with increasing Ni concentration. It exhibits a minimum at ∼40 at.% Ni, which is an indication of switching into the π state.     

Intermittency in the atmospheric surface layer: Unresolved or slowly varying?

We present streamwise velocity structure functions 〈δv_L(τ)〉=〈|v(t+τ)−v(t)|^p〉 (with p=1:5) obtained in the near neutral atmospheric surface layer at the Utah SLTEST site at the highest terrestrial Reynolds number Re_τ=O(10⁶). We show that the occurrence of very large scale coherent oscillations in the streamwise velocity throughout the wall region, interpreted as genuine structural features of the canonical turbulent boundary layer, affects the scaling exponents of the p>3 order structure functions. This results in a slight alteration of the intermittent behavior of the velocity field. It was found that for positive (fast) large scale oscillation of the low-pass filtered velocity signal, deviations from the Kolmogorov K41 prediction (absence of multiscaling) are more marked, as compared to negative (slow) excursion. The results are discussed in terms of convergence of statistics from atmospheric boundary layer measurements.     

Vortex structure of Gross-Pitaevskii model

The vortex line of the Gross-Pitaevskii model is studied. The kinetic helicity of the vortex is discussed, and vortex structure is classified by the Hopf index, linking number in geometry. A mechanism of generation and annihilation of vortex lines is given by the method of phase singularity theory. The dynamic behavior of the vortex at the critical points is discussed in detail, and three kinds of length approximation relations at the neighborhood of a critical point are given: l ∝ (t − t^∗)^1/2, l ∝ t − t^∗, l = const.     

Sustained turbulence in the three-dimensional Gross-Pitaevskii model

We study the three-dimensional forced-dissipated Gross-Pitaevskii equation. We force at relatively low wave numbers, expecting to observe a direct energy cascade and a consequent power-law spectrum of the form k^−α. Our numerical results show that the exponent α strongly depends on how the inverse particle cascade is attenuated at ks lower than the forcing wave-number. If the inverse cascade is arrested by a friction at low ks, we observe an exponent which is in good agreement with the weak wave turbulence prediction k⁻¹. For a hypo-viscosity, a k⁻² spectrum is observed which we explain using a critical balance argument. In simulations without any low k dissipation, a condensate at k=0 is growing and the system goes through a strongly turbulent transition from a 4-wave to a 3-wave weak turbulence acoustic regime with evidence of k^−3/2 Zakharov-Sagdeev spectrum. In this regime, we also observe a spectrum for the incompressible kinetic energy which formally resembles the Kolmogorov k^−5/3, but whose correct explanation should be in terms of the Kelvin wave turbulence. The probability density functions for the velocities and the densities are also discussed.     

The effective activation energy Ueff(T,B,J) in Hg-1223 single phase superconductors

We review the methods of calculating the effective activation energy U_eff(T,B,J) for both transport measurements and magnetic decay, together with some theoretical models. Then, we apply these methods to our Hg-1223 single-phase superconductor to obtain the activation energy. Transport results give that the magnetic field and temperature dependence of the U_eff can be well described as U₀B^−α(1−T/T_c)^m. Magnetic relaxation shows that the current density dependence of U(J) can be scaled onto a single curve, which can be considered as the activation energy at some temperature T₀. The pinning mechanism in the measured temperature range does not change, and the activation energy depends separately on the three variables: T, B, and J, are responsible for the magnetic decay data scaling onto a single curve at various temperatures. As temperatures close to zero and near T_c, thermally assisted flux motion model is no longer valid since other processes dominate.     

Scaling laws of design parameters for plasma wakefield accelerators

Simple scaling laws for the design parameters of plasma wakefield accelerators were obtained using a theoretical model, which were confirmed via particle simulation studies. It was found that the acceleration length was given by Δx=0.804λp/(1−βg), where λp is the plasma wavelength and βgc the propagation velocity of the ion cavity. The acceleration energy can also be given by ΔE=(γm−1)mc²=2.645mc²/(1−βg), where m is the electron rest mass. As expected, the acceleration length and energy increase drastically as βg approached unity. These simple scaling laws can be very instrumental in the design of better-performing plasma wakefield accelerators.     

Hole transport in solid xenon

The hole mobility μ_η in solid Xe has been investigated by drift mobility techniques in the temperature range from 110K to 160K. μ_η = 1.8 × 10⁻²cm²Sec⁻¹V⁻¹ at 160K and has a temperature dependence of the form μ_η ∞ T^−1.6. It is concluded that a non-adiabatic hopping transport with a small polaron binding energy and small intermolecular overlap is the most likely transport mechanism.     

Effective activation energy U(J,H) in epitaxial YBa2Cu3O7−δ thin films

We have measured the resistivity of epitaxial YBa₂Cu₃O_7?δ thin film as a function of temperature, current density and the magnetic field up to 8 T. The current density dependence of the effective activation energy exhibits a slight increase in the low current density range below 10³ A/cm² and a logarithmic decline in higher current density with increasing current density. The magnetic field dependence of the effective activation energy showed a crossover of vortex state from a quasi-2D for H//ab-plane to a 3D line liquid state for H//c-axis. The possible dissipation mechanisms responsible for the ln H dependence of the effective activation energy were discussed.     

Broadening, shifting, and line mixing in the 030 ← 010 parallel Q branch of N2O

The 03¹0 ← 01¹0 parallel Q branch of N₂O has been studied at 297 K and over the pressure range 1-130 torr. Absorption spectra were recorded using a high resolution (1.5 MHz or 5 × 10⁻⁵ cm⁻¹) and high signal-to-noise (>3500:1) mid-infrared spectrometer based on difference-frequency infrared generation in AgGaS₂. In the low-pressure range (1-11 torr) we obtained accurate values for the line strengths, the broadening coefficients, the weak mixing coefficients, and the overall shifting of the branch. The medium pressure results, ranging from 23 to 130 torr, were analyzed by treating the band as a whole, using a relaxation matrix formalism, based on an energy gap scaling law. We find, effectively, that only 36% of the rotationally inelastic collisions are associated with Q branch mixing, the rest presumably being associated with Q-P and Q-R mixing in the same vibrational band. The pressure shifting coefficient of the 03¹0 ← 01¹0 Q branch as a whole was also determined and found to be 5.8 × 10⁻³ cm⁻¹/atm towards lower frequencies.     

Dynamics of vortices in type-II superconductors with periodic square columnar pins

The dynamics of a two-dimensional vortex system with strong periodic square columnar pins is investigated. For the case vortex number matching pinning number, we find that the vortex liquid is frozen into square lattice via a continuous transition, and the freezing (melting) temperature T_m is the same as the thermal depinning temperature of vortices, which are different from the first-order phase transition at weak pinning. The zero-temperature critical depinning force F_c0 is exactly the same as the maximum pinning force, and the depinning property at T = 0 can be expressed by scaling v ～ (F ? F_c0)^β with the exponent β close to 0.5. The v–F curves at temperatures below T_m show that vortices are pinned at small driving force.