Vortex Dissipation Research Articles

Filament surgery and temporal grid adaptivity extensions to a parallel tree code for simulation and diagnosis in 3D vortex dynamics

The vortex collapse-reconnection process presents behaviors commonly observed in turbulent flows: multiple spatial and temporal scales, rapid vorticity and strain-rate amplification and dissipation through generation of small scales. In this work we reduce the computational complexity of our problem by using hierarchical methods (tree codes), introducing a time extrapolation framework for each particle, and applying a filament algorithm, based on the energy density, as a regularization for vortex collapse. The high performance parallel implementation of Barnes-Hut algorithm permit us to increase by one order of magnitude the resolution of the vortex collapse simulations. The use of the time extrapolation for slow moving particles helps in concentrating the computational effort in the important dynamic domains. The vortex filament surgery regularizes effectively the growth of the number of particles in the collapse regions of the flow. The reduction in complexity achieved will contribute to optimize the use of the numerical simulations in the reduced model building process.

Measurements of the Tip Clearance Flow for a High-Reynolds-Number Axial-Flow Rotor

A high-Reynolds-number pump (HIREP) facility has been used to acquire flow measurements in the rotor blade tip clearance region, with blade chord Reynolds numbers of 3,900,000 and 5,500,000. The initial experiment involved rotor blades with varying tip clearances, while a second experiment involved a more detailed investigation of a rotor blade row with a single tip clearance. The flow visualization on the blade surface and within the flow field indicate the existence of a trailing-edge separation vortex, a vortex that migrates radially upward along the trailing edge and then turns in the circumferential direction near the casing, moving in the opposite direction of blade rotation. Flow visualization also helps in establishing the trajectory of the tip leakage vortex core and shows the unsteadiness of the vortex. Detailed measurements show the effects of tip clearance size and downstream distance on the structure of the rotor tip leakage vortex. The character of the velocity profile along the vortex core changes from a jetlike profile to a wakelike profile as the tip clearance becomes smaller. Also, for small clearances, the presence and proximity of the casing endwall affects the roll-up, shape, dissipation, and unsteadiness of the tip leakage vortex. Measurements also show how much circulation is retained by the blade tip and how much is shed into the vortex, a vortex associated with high losses.

Vorticity Dynamics and Zonally Averaged Ocean Circulation Models

Abstract Diagnostic equations relating the zonally averaged overturning circulation to north–south density variations are derived and used to determine a new closure scheme for use in zonally averaged ocean models. The presentation clarifies the dynamical link between vorticity dissipation in the western boundary layer and the meridional overturning circulation and provides insight into the relevance and limitations of zonally averaged models. The new closure scheme is substantially different from that introduced by Wright and Stocker. In particular, it includes nonlocal effects, which are potentially important. The model formulation results in a solution with three free parameters. A parameter representing the damping associated with meridional velocity gradients has very little effect on the solution and could be set to zero. The other two are used to tune the model to agree with results of a general circulation model. Good agreement is achieved for values consistent with expectations. The closure schem...

A numerical model for forestry aerial spraying

A numerical model for the aerial application of pesticides in forestry aerial spraying is described. The model predicts canopy and ground deposition and drift patterns for evaporating droplets released over a forest canopy by an aircraft flying at right angles to the wind direction. Droplet trajectories are initially calculated from aircraft wake velocities. Wake velocities are generated from a second-order closure model for the turbulent transport and dissipation of aircraft vortices. When the aircraft wake has decayed to background levels of turbulence, droplet trajectory calculations are continued with a Markov type of Lagrangian model for particle dispersion in a turbulent atmosphere. Modelled predictions for off-target drift, and foliage and ground deposit within a 400 m fetch are compared with field trial data for six different spray experiments each for insecticide application (foliage area index: 3.2 m 2 foliage per m 2 ground) and for herbicide application (foliage area index: 0.48 m 2 foliage per m 2 ground). Model predictions of the downwind location of peak canopy deposit are within 18% and 20% of the experimental values for the insecticide and herbicide cases, respectively, on average. Canopy deposit predictions are 10% higher and 26% lower on average than experimental values, for insecticide and herbicide tests, respectively. Ground deposit predictions for the herbicide tests are 12% higher than experimental values, on average, but for the insecticide tests, computed values were significantly higher than measured values partly because the measurements in that case are not accurate. Model predictions in general agree very well with experiments for a wide range of atmospheric stability values and it is concluded that the model is an ideal method of evaluating and optimizing aerial spray applications.

Evidence for two vortex phase transitions in Tl2Ba2CaCu2O8 thin films.

Consistent with various models of quasi-two-dimensional behavior in strongly anisotropic superconductors, evidence for two separate vortex phase transitions is observed for an epitaxial thin film of the high-temperature superconductor ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$. Based on electric field as a function of current density E(J) behavior, the temperature dependencies of the resistivity \ensuremath{\rho}(T) and dc magnetization M(T), as well as the frequency dependence of the ac susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{ac}}$(f), there is strong evidence for a lower-temperature vortex-solid (glass) phase transition to a true superconducting state that is characterized by a loss of linear resistivity. In addition, \ensuremath{\rho}(T) and M(T) results provide evidence for a higher-temperature transition, or crossover, at which the vortex dissipation processes undergo distinctive changes. This transition or crossover may be associated with the coupling of unbound two-dimensional vortices (pancake-vortex liquid) into a liquid of vortex lines as temperature decreases.

Vorticity Dissipation by Western Boundary Currents in the Presence of Outcropping Layers

Abstract In an exploration of the dynamics of current separation and vorticity dissipation in a two-layer model, the following is found. 1) Results obtained in a barotropic context remain valid; namely, two major dissipation regimes can be found: either a “loop current” or a recirculating gyre. 2) A transition from one regime to the other can be achieved if one increases the strength of the front associated with the outcrop, regardless of the specified boundary conditions. 3) Separation will depend upon the choice of lateral boundary conditions if the upper-layer flow is not highly inertial.

Scale Effects in Cross Flow Fans. Effects of Fan Dimensions on Flow Details and the Universal Representation of Performances.

Laser doppler velocimeter (LDV) measurements of velocity fields and the determination of static pressure distributions in the rotors of cross flow fans with good geometrical similarity but different dimensions have been performed, and the peculiar scale effects appearing in the flow details have been shown. The internal flow fields tend to be more active with increasing rotor size, and normalized velocity, vorticity, velocity fluctuations and pressure drops in the eccentric vortex increase as the fan dimensions increase. The mechanisms of generation and dissipation of vorticity in the eccentric vortex in rotor have been discussed, and it is suggested that the scale effects may be attributed to differences in the rate of diffusion of the circulation vortices in the recirculatory region. By analyzing the influences of Reynolds number and fan dimensions on performance curves, a new procedure for representing the performance of cross flow fans in a universal form has been proposed.

Magnetic and transport studies of Bi2223/Ag tapes

The technological importance of the Bi2223/Ag tapes has been widely recognised and yet their electrical transport properties, particularly in an applied magnetic field, remain inconclusively. We present analysis of magnetisation loops and transport current-voltage characteristics taken on the same sample. Using the dynamic relaxation technique and the transport data we can extend our E- J curves over 5 orders of magnitude in electric field. The resultant E- J characteristics reveal clues as to the current limitation between the grains and the vortex dissipation within the grains. In an applied magnetic field J c behaves hysteretically giving further insight as to the granularity of these samples. We offer a comparative study of tapes with differing values of J c.

The asymptotic study of dissipation and breakdown of a wing-tip vortex

The steady axisymmetrical wing-tip vortex is studied in this paper by means of asymptotic methods within the limit of high Reynolds numbers. The smooth regrouping of the vortex under the action of viscous forces is described by a quasicylindrical approximation. The solutions of the quasi-cylindrical approximation are thoroughly analysed numerically and it is shown that a saddle-point bifurcation appears at certain critical values of circulation. At these values the solution may be continued in two ways: as a supercritical branch which approaches the Batchelor limit far downstream; and a subcritical one, which passes the second, nodal-point bifurcation. The parabolic quasi-cylindrical equations past this point allow the downstream disturbances to propagate upstream, like for example, boundary-layer equations in the regime of strong hypersonic interaction. The flow past the second bifurcation point was studied numerically and it was shown that solutions of the quasicylindrical approximation with large reversed-flow regions exist. An asymptotic expansion of such solutions far downstream was constructed, and it turned out that the reversed-flow region expands exponentially. This process is halted by elliptical effects in the external flow. An asymptotic theory of large reversed-flow regions is suggested including viscosity and elliptical effects. Numerical solutions for unbounded vortex breakdown parabolically expanding far downstream are presented. Then the general asymptotic problem statement which describes the flow near the bifurcation points is used to study the asymptotic solutions near the first bifurcation point. The problem is investigated numerically and two kinds of solution, which may be treated as transcritical jumps and marginal vortex breakdown, are found and discussed.

Flux noise and vortex dissipation for two-dimensional superconductors.

A relation is presented which relates the flux noise spectrum and vortex dissipation for two-dimensional superconductors. The explicit forms of the noise spectrum and vortex dissipation are obtained from simulations of a two-dimensional [ital XY]-type model with time-dependent Ginzburg-Landau dynamics. The results are discussed in terms of a phenomenological description and good agreement is found. Consequences for, and comparisons with, experimental data are discussed.

Heat‐transfer characteristics in viscous gas‐liquid and gas‐liquid‐solid systems

AbstractLocal heat‐transfer measurements are performed using a special heat‐transfer probe in gas‐liquid and gas‐liquid‐solid systems with viscous Newtonian liquids as the continuous phase. Effects of viscosity on bubble‐liquid and bubble‐liquid‐solid interactions affecting local heat transfer are studied through heat‐transfer experiments with simultaneous flow visualization in a simplified system involving single bubbles or a chain of gas bubbles moving in viscous liquids and liquid‐solid systems. Effects of viscosity on bubble wake and local heat transfer are examined with reference to heat transfer in freely‐bubbling beds (bubble columns and three‐phase fluidized beds). The kinematic viscosity of the fluid greatly influences the nature of flow in the wake which affects local heat transfer in the bed. The local heat transfer decreases with the viscosity due to the rapid decay in the circulation strength of the bubble wake caused by increased viscous dissipation of vorticity. Local heat transfer due to cyclic/periodic injection of bubbles is significantly enhanced due to increased bubble‐wake interactions which rapidly accelerate bubbles and increase average bubble rise velocity. Heat transfer in simplified liquid and liquid‐solid systems with single‐ and chain‐bubble injections characterizes the local heat‐transfer performance of freely‐bubbling beds (bubble columns and three‐phase fluidized beds). A mechanistic model developed accounts for the heat‐transfer behavior in bubble columns and three‐phase fluidized beds with viscous liquids.

Vorticity and viscous dissipation in an incompressible flow

The relation between the vorticity and viscous dissipation in an incompressible flow has been investigated. It is shown that the square of relative vorticity with respect to the coordinate system fixed to the container or to the flow at infinity gives the global rate of viscous dissipation, that is, the viscous dissipation is proportional to the volume integral of the square of relative vorticity. Thus, the total rate of viscous dissipation in the flow produced by the motion of a rigid body is proportional to the integral of the square of vorticity taken over the whole space including the region occupied by the volume of the rigid body in which the vorticity is assumed to be the twice of the angular velocity of the body.

The effects of anisotropy on the vortex dynamics and transport dissipation in Bi-Sr-Ca-Cu-0 compounds

Abstract The effects of the high anisotropy of Bi2Sr2CaCu2O8 on vortex dynamics and dissipation is reviewed. This high anisotropy results from the very weak coupling of conduction-electron states across the double Bi-O layers separating the conducting Cu-O bilayers. A model, based on Josephson coupling between the Cu-O bilayers, is shown to be consistent with the irreversibility behavior and the c-axis resistivity. The implications for conductor applications are described.

A Study On Pool Flame Structure Using Thermography

Pool flames of heptane, kerosene, and crude oil in a 2.7m square tank were measured by thermography, storing thermal images as TV color images with 25,600 data points every 0.1 second. These apparent temperature images can be converted to irradiance by simple approximations. A series of data recorded continuously at 0.1 second intervals (70 images for one fuel) were analyzed statistically to obtain the distribution of mean radiance, standard deviation and coefficient of variation in the thermography image. The contours of mean radiance, standard deviation and coefficient of variation related to radiance were made, and the flame structure of pool flames are considered from a radiation point of view. The height of maximum radiance from the tank top are obtained from the contours of the mean radiance. Mean paths of formation, growth, and dissipation of vortices are obtained by the contours of the standard deviation on radiance. The stable flame regions and the lower part of plume regions are also obtained by using the contours of the coefficient of variation based on radiance. Flame structures obtained by processing thermographic data are also compared with previous work by McCaffrey who defined flame, intermittent, and plume regions by the temperature and velocity distribution along the center line of flames. By this comparison, statistical analysis using thermographic data is also useful to assess the flame structure of large pool fire flames. Finally, the radiative characteristics of the continuous flame, intermittent, and plume regions, are established.

NUMERICAL STUDY ON CUT-AND-CONNECT OF TWO VORTEX RINGS ALONG PARALLEL AXES

SUMMARY A numerical study has been conducted to investigate the interaction of two viscous vortex rings along parallel axes. The generation of two vortex rings created by the ejection of a fluid through orifices and their cut-and-connect process were numerically simulated by solving the three-dimensional and time-dependent Navier-Stokes equations. Based on the quantitative velocity and pressure data obtained from the Navier-Stokes simulation, the distribution and the evolution of the vorticity, helicity density and energy dissipation function were analyzed. The helicity density and its relation with the energy dissipation function in three-dimensional flow fields were also examined. It was found that the energy dissipation plays an important role in the cancellation of the vortex circulation during the vortex tubes cutting. This energy dissipation process may be used to explain the cut-and-connect of vortex tubes in the high Reynolds number turbulent flow. The numerical solutions were compared with the experimental observations and measurements under the similar condition. The correspondence between the numerical simulation and the experimental measurement was satisfactory.

Nonlinear Resonance and Instability of Planetary Waves and Low-Frequency Variability in the Atmosphere

It is demonstrated in this work that linearly unstable planetary waves can be resonantly excited to finite amplitude in a nonlinear barotropic atmosphere with vorticity forcing and dissipation. In a weakly forced/dissipated atmosphere, it is shown that barotropic instability may provide a dynamic mechanism of transition between different “flow regimes.” It is suggested that nonlinear resonance and instability of planetary waves, which seen to be common with finite amplitude steady free solutions, may play a role in producing low- frequency variability observed in the real atmosphere. A type of nonlinear free solution with realistically sheared zonal flow is described in spherical geometry, and normal-mode instability analysis is performed to examine its stability. A time-dependent spectral model is employed to demonstrate the resonant excitation and breakdown of unstable planetary waves that results in low-frequency variability. The steady free solution is barotropically unstable to large-scale, low-frequency perturbations. Even though unstable, it can be resonantly excited from many initial conditions by a stationary vorticity forcing that projects onto it. The leading low-frequency oscillation has a period of about 20 days and the model flow hemispherically alternates between an almost zonal flow and a blocking regime, reminiscent of the multiple equilibria found by Charney and DeVore.

Microwave vortex dissipation of superconducting Nd-Ce-Cu-O epitaxial films in high magnetic fields.

The microwave vortex dissipation of superconducting ${\mathrm{Nd}}_{1.85}$${\mathrm{Ce}}_{0.15}$${\mathrm{CuO}}_{\mathit{x}}$ epitaxial films is investigated by use of a sapphire dielectric-ring resonator in the whispering gallery modes, and in dc magnetic fields ranging from 0 to 25 kG. By extending the Coffey-Clem model to the thin-film and finite-grain-size limit, we infer important material parameters, including the irreversibility line, vortex pinning potential, pinning force constant and viscosity, through a direct least-squares fit to the microwave-absorption data.

Rectification of the wind-driven ocean circulation on the beta plane

Abstract A nonlinear Stommel model of the ocean circulation on the beta plane, driven by a time periodic wind stress, is investigated in order to study symmetry properties of the observed time-mean ocean gyres. Due to the presence of vorticity advection terms the model will have a steady or rectified response to fluctuating wind fields. In this paper a small inverse Ekman number, “the small beta regime”, is considered. It is demonstrated that for this case all qualitative features of the residual circulation, obtained numerically by Veronis (1970). are reproduced in an analytical way. They include the dipole character of the gyre, its maximum symmetry breaking around the north-south axis for intermediate Reynolds numbers, measuring the ratio of vorticity forcing and dissipation, and the maximum residual response for intermediate forcing frequencies.

Nonlinear and dissipative dynamics in the connection region between western boundary currents and equatorial currents

The roles of nonlinearity and dissipation in connecting a western boundary current to an equatorial current are explored with a 1½ ‐layer numerical model. A permanent western boundary current ‐ equatorial current system is maintained between a mass source located near the western boundary several deformation radii from the equator and a sponge layer located along the eastern boundary. When a no‐slip boundary condition is used, the western boundary current separates within two deformation radii after crossing the equator to feed the eastward equatorial current. Because of equatorial scalings, flow within the connection region between these two currents is nearly nondivergent, and similarities with barotropic models of western boundary current extensions are emphasized by potential vorticity analysis. A series of experiments explores the relative importance of inertia to dissipation, measured by the Reynolds number, by varying the forcing strength. For small Reynolds numbers advection of relative vorticity out of the western boundary layer eastward results in a meandering equatorial current, which is interpreted as a damped, stationary Rossby wave. At higher Reynolds numbers, the boundary current is susceptible to horizontal shear instability, resulting in eddies which translate along the western boundary. At yet higher Reynolds numbers, eddy variability is not confined to the western boundary. Disturbances are advected out of the boundary layer, producing large (300 km diameter) eddies in the connection region. Variability also radiates eastward along the equator as free Yanai wave packets with periods between 30 and 70 days. Even in the presence of energetic eddies, net flow across the equator is due mostly to vorticity dissipation in the western boundary current. The effect of different boundary conditions is also examined. When a free‐slip rather than no‐slip boundary condition is used, the boundary current overshoots well outside the equatorial waveguide, but all flow returns to the equatorial region in an offshore countercurrent, and the solution is otherwise similar to solutions with a no‐slip boundary condition.

Anomaly in magnetic field dependence of microwave absorption at vortex pinning to depinning transition in Bi 2− xPb xSr 2Ca 2Cu 3O 10 superconductor

Previous measurements have shown that the pinning to depinning transition of vortices in the copper oxide superconductors can be observed at constant temperature by a change in the slope of the linear dependence of the microwave absorption on B at a field B ′. In this work measurements of the magnetic field dependence of the microwve absorption in N=3B-Pb-Sr-Ca-Cu-O at 9.2 GHz at constant temperature at small magnetic field intervals in the transition region reveal a marked from the B dependence. On the other hand measurements of the temperature dependence of the microwave absorption due to vortex dissipation at constant magnetic field at one degree temperature intervals show an abrupt transition inconsistent with a second order character required for a transition from a vortex glass to a fluid. The anomaly in the magnetic field dependence of the absorption at the depenning to spinning transition is shown to be consistent with field dependent of the barriers in the flux solid leading to an intermediate phase consisting of a mixture of vortex fluid and solid.