Showing papers on "Vortex published in 1984"

The emergence of isolated coherent vortices in turbulent flow

Abstract: A study is made of some numerical calculations of two-dimensional and geostrophic turbulent flows. The primary result is that, under a broad range of circumstances, the flow structure has its vorticity concentrated in a small fraction of the spatial domain, and these concentrations typically have lifetimes long compared with the characteristic time for nonlinear interactions in turbulent flow (i.e. an eddy turnaround time). When such vorticity concentrations occur, they tend to assume an axisymmetric shape and persist under passive advection by the large-scale flow, except for relatively rare encounters with other centres of concentration. These structures can arise from random initial conditions without vorticity concentration, evolving in the midst of what has been traditionally characterized as the ‘cascade’ of isotropic, homogeneous, large-Reynolds-number turbulence: the systematic elongation of isolines of vorticity associated with the transfer of vorticity to smaller scales, eventually to dissipation scales, and the transfer of energy to larger scales. When the vorticity concentrations are a sufficiently dominant component of the total vorticity field, the cascade processes are suppressed. The demonstration of persistent vorticity concentrations on intermediate scales - smaller than the scale of the peak of the energy spectrum and larger than the dissipation scales - does not invalidate many of the traditional characterizations of two-dimensional and geostrophic turbulence, but I believe it shows them to be substantially incomplete with respect to a fundamental phenomenon in such flows.

The Aerodynamics of Hovering Insect Flight. IV. Aeorodynamic Mechanisms

Abstract: A full derivation is presented for the vortex theory of hovering flight outlined in preliminary reports. The theory relates the lift produced by flapping wings to the induced velocity and power of the wake. Suitable forms of the momentum theory are combined with the vortex approach to reduce the mathematical complexity as much as possible. Vorticity is continuously shed from the wings in sympathy with changes in wing circulation. The vortex sheet shed during a half-stroke convects downwards with the induced velocity field, and should be approximately planar at the end of a half-stroke. Vorticity within the sheet will roll up into complicated vortex rings, but the rate of this process is unknown. The exact state of the sheet is not crucial to the theory, however, since the impulse and energy of the vortex sheet do not change as it rolls up, and the theory is derived on the assumption that the extent of roll-up is negligible. The force impulse required to generate the sheet is derived from the vorticity of the sheet, and the mean wing lift is equal to that impulse divided by the period of generation. This method of calculating the mean lift is suitable for unsteady aerodynamic lift mechanisms as well as the quasi-steady mechanism. The relation between the mean lift and the impulse of the resulting vortex sheet is used to develop a conceptual artifice - a pulsed actuator disc - that approximates closely the net effect of the complicated lift forces produced in hovering. The disc periodically applies a pressure impulse over some defined area, and is a generalized form of the Froude actuator disc from propeller theory. The pulsed disc provides a convenient link between circulatory lift and the powerful momentum and vortex analyses of the wake. The induced velocity and power of the wake are derived in stages, starting with the simple Rankine-Froude theory for the wake produced by a Froude disc applying a uniform, continuous pressure to the air. The wake model is then improved by considering a `modified' Froude disc exerting a continuous, but non-uniform pressure. This step provides a spatial correction factor for the Rankine-Froude theory, by taking into account variations in pressure and circulation over the disc area. Finally, the wake produced by a pulsed Froude disc is analysed, and a temporal correction factor is derived for the periodic application of spatially uniform pressures. Both correction factors are generally small, and can be treated as independent perturbations of the Rankine-Froude model. Thus the corrections can be added linearly to obtain the total correction for the general case of a pulsed actuator disc with spatial and temporal pressure variations. The theory is compared with Rayner's vortex theory for hovering flight. Under identical test conditions, numerical results from the two theories agree to within 3%. Rayner presented approximations from his results to be used when applying his theory to hovering animals. These approximations are not consistent with my theory or with classical propeller theory, and reasons for the discrepancy are suggested.

Observations of the flow produced in a cylindrical container by a rotating endwall

Abstract: Observations made using the laser-induced fluorescence technique are presented of the steady swirling flow produced in a closed cylindrical container completely full of fluid (a glycerine/water mixture for the experiments reported here) by rotating one endwall. The flow behaviour is determined by two parameters: the height-to-radius ratioH/R and a rotation Reynolds number ΩR 2/ν. In an earlier study, Vogel (1968) defined the stability limit in the (H/R, Ω R2/ν) plane within which a vortex breakdown bubble occurred on the axis of symmetry. The results of Vogel's investigation are confirmed and extended by the present work. In particular, it is found that asH/R is increased two further stability limits can be determined within which two and ultimately three breakdown bubbles occur in succession. It is also found that there is a Reynolds number boundary above which the flow is oscillatory and at even higher Reynolds number the flow becomes turbulent. Until well into the unsteady-flow domain, the flow shows negligible departure from axisymmetry.

Structure of a Turbulent Separation Bubble

Abstract: Flow in the separation bubble formed along the sides of a blunt flat plate with right-angled corners has been studied in terms of extensive single- and two-point measurements of velocity and surface-pressure fluctuations. The cross-correlations between the surface-pressure and velocity fluctuations are found to be useful for the study of large-scale vortex structure in the bubble. Large-scale vortices are shed downstream from the separation bubble with a frequency of about 0.6U∞/xR, where U∞ is the approaching velocity and xR is the time-mean length of the bubble. On top of this regular vortex shedding, there exists a large-scale unsteadiness in the bubble. Vortices which are much larger than the regular vortices are shed with frequencies less than about 0.2U∞/xR. The large-scale unsteadiness is accompanied by enlargement and shrinkage of the bubble and also by a flapping motion of the shear layer near the separation line. The intermittent nature of the flow in the bubble is clarified in some detail. The distributions of the cross-correlations between the pressure and velocity fluctuations demonstrate the vortex structure in the reattaching zone. The longitudinal distance between the vortices is estimated to be (0.7–0.8) xR and their convection velocity is about 0.5U∞ near the reattachment line. The cross-correlations also suggest the existence of a longitudinal counter-rotating system in the bubble. The distance between the axes of the rotation is of the order of 0.6xR. Variations of timescales, lengthscales and phase velocities of the vortices are presented and discussed.

Streamwise Vorticity: The Origin of Updraft Rotation in Supercell Storms

Abstract: Linear (small amplitude) theory of shallow, inviscid, isentropic convection in a dry, unstably stratified, nonrotating atmosphere is used to investigate the rotational characteristics of an isolated, incipient convective storm in strong environmental shear. Environmental winds veering with height are associated with streamwise vorticity (i.e., a component of vorticity along the mean wind direction). We demonstrate that a roughly circular storm acquires net cyclonic (anticyclonic) rotation within its updraft (downdraft) when the storm-relative winds veer with height, or equivalently when the environmental flow possesses streamwise vorticity in a reference frame moving with the storm. A formula for the correlation coefficient between vertical velocity and vertical vorticity is obtained. The physical explanation for the correlation is as follows. Initially, the isentropic surfaces and vortex lines are horizontal. After the onset of convection, air parcels and vortex lines remain in their original is...

Vortex creep and the internal temperature of neutron stars. I - General theory

Abstract: The theory of a neutron star superfluid coupled to normal matter via thermal creep against pinning forces is developed in some detail. General equations of motion for a pinned rotating superfluid and their form for vortex creep are given. Steady state creep and the way in which the system approaches the steady state are discussed. The developed formalism is applied to the postglitch relaxation of a pulsar, and detailed models are developed which permit explicit calculation of the postglitch response. The energy dissipation associated with creep and glitches is considered.

Rapid postglitch spin-up of the superfluid core in pulsars

Abstract: Vortex lines in the superfluid cores of neutron stars carry flux due to the induced proton charge current which results from the Fermi liquid interaction between neutrons and protons. As a consequence the scatttering of charges off these magnetic vortex lines equilibrates the core superfluid to the plasma and the crust on time scales of order 1 second after a glitch. Thus, the core superfluid cannot be responsible for the observed time scales of the Vela and Crab pulsars. This result supports the theory of Alpar et al, in which both the glitch and the slow postglitch relaxation are determined by the interaction of vortices with nuclei in the crust.

Stationary and Moving Convective Bands in Hurricanes

Abstract: Aircraft observations in hurricanes indicate that the hurricane vortex may be subdivided into an inner gyre where the air trajectories form closed paths and an outer envelope where they do not. In the closed gyre, a core of air moves with the vortex; in the envelope, environmental air passes through the vortex and around the core. A system of spiral bands, termed the stationary band complex (SBC), forms near the boundary between the core and the envelope where the Rossby number is of order unity. The SBC differs dynamically both from convective rings because it is asymmetric and from propagating gravity-wave bands because its Doppler-shifted frequency is below the local inertia frequency. In more intense systems with stronger convective instability, the SBC may evolve into a convective ring and move into the vortex core. Outward propagating gravity-wave bands have also been observed. Such bands are often associated with track oscillations as the storm makes landfall or recurves. Spiral-shaped ent...

Structure and mixing of a transverse jet in incompressible flow

Abstract: The flow field induced by a jet in incompressible cross-flow is analysed and the results compared with those obtained in a reacting water-jet experiment. It is argued that the axial vortex pair in the flow arises from the jet momentum normal to the free stream, the momentum flux being equivalent to a normal force, i.e. to a lift.

The structure of the vorticity field in turbulent channel flow. Part 1: Analysis of instantaneous fields and statistical correlations

Abstract: An investigation into the existence of hairpin vortices in turbulent channel flow is conducted using a database generated by the large eddy simulation technique. It is shown that away from the wall the distribution of the inclination angle of vorticity vector attains its maximum at about 45 deg to the wall. Two point correlations of velocity and vorticity fluctuations strongly support a flow model consisting of vortical structures inclined at 45 deg to the wall. The instantaneous vorticity vectors plotted in planes inclined at 45 deg show that the flow contains an appreciable number of hairpins. Vortex lines are used to display the three dimensional structure of hairpins, which are shown to be generated from deformation of transverse vortex filaments.

The aerodynamics of hovering insect flight. v. a vortex theory

Abstract: A full derivation is presented for the vortex theory of hovering flight outlined in preliminary reports. The theory relates the lift produced by flapping wings to the induced velocity and power of the wake. Suitable forms of the momentum theory are combined with the vortex approach to reduce the mathematical complexity as much as possible. Vorticity is continuously shed from the wings in sympathy with changes in wing circulation. The vortex sheet shed during a half-stroke convects downwards with the induced velocity field, and should be approximately planar at the end of a half-stroke. Vorticity within the sheet will roll up into complicated vortex rings, but the rate of this process is unknown. The exact state of the sheet is not crucial to the theory, however, since the impulse and energy of the vortex sheet do not change as it rolls up, and the theory is derived on the assumption that the extent of roll-up is negligible. The force impulse required to generate the sheet is derived from the vorticity of the sheet, and the mean wing lift is equal to that impulse divided by the period of generation. This method of calculating the mean lift is suitable for unsteady aerodynamic lift mechanisms as well as the quasi-steady mechanism. The relation between the mean lift and the impulse of the resulting vortex sheet is used to develop a conceptual artifice - a pulsed actuator disc - that approximates closely the net effect of the complicated lift forces produced in hovering. T he disc periodically applies a pressure impulse over some defined area, and is a generalized form of the Froude actuator disc from propeller theory. The pulsed disc provides a convenient link between circulatory lift and the powerful momentum and vortex analyses of the wake. The induced velocity and power of the wake are derived in stages, starting with the simple Rankine-Froude theory for the wake produced by a Froude disc applying a uniform, continuous pressure to the air. The wake model is then improved by considering a ‘modified’ Froude disc exerting a continuous, but non-uniform pressure. This step provides a spatial correction factor for the Rankine-Froude theory, by taking into account variations in pressure and circulation over the disc area. Finally, the wake produced by a pulsed Froude disc is analysed, and a temporal correction factor is derived for the periodic application of spatially uniform pressures. Both correction factors are generally small, and can be treated as independent perturbations of the Rankine-Froude model. Thus the corrections can be added linearly to obtain the total correction for the general case of a pulsed actuator disc with spatial and temporal pressure variations. The theory is compared with Rayner’s vortex theory for hovering flight. Under identical test conditions, numerical results from the two theories agree to within 3%. Rayner presented approximations from his results to be used when applying his theory to hovering animals. These approximations are not consistent with my theory or with classical propeller theory, and reasons for the discrepancy are suggested.

A numerical-experimental study of confined flow around rectangular cylinders

Abstract: A previous numerical study by Davis and Moore of vortex shedding from rectangles in infinite domains is extended to include the effects of confining walls. The major changes to the numerical modeling are the addition of a direct solver for the pressure equation and the use of an infinite‐to‐finite mapping downstream of the rectangle. The parameters in the problem are now Reynolds number, rectangle aspect ratio, blockage ratio, and upstream velocity profile. As each of these is varied, the effects upon the forces acting on the rectangle and the structure of the wake are discussed. Streakline plots composed of multishaped passive marker particles provide a clear visualization of the vortices. These plots are compared with smoke‐wire photographs taken from a wind tunnel test. Strouhal numbers obtained both computationally and experimentally are compared for two values of the blockage ratio. Moving recirculation zones which appear between the wake and the walls are discussed.

The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices

Abstract: … in hydrodynamic turbulence … the fate of vortices extending in the direction of motion is of great importance (J. M. Burgers 1948).We examine an elementary model of the dynamics of streamwise vorticity in a plane mixing layer. We assume that the vorticity is unidirectional and subjected to a two-dimensional spatially uniform strain, positive along the direction of vorticity. The equations of motion are solved numerically with initial conditions corresponding to a strain-viscous-diffusion balance for a layer with a sinusoidal variation of vorticity. The numerical results are interpreted physically and compared to those of an asymptotic analysis of the same problem by Neu. It is found that strained vortex sheets are fundamentally unstable unless their local strength nowhere exceeds a constant (somewhat larger than 2) times the square root of the product of strain and viscosity. The instability manifests itself by the spanwise redistribution of the vorticity towards the regions of maximum strength. This is accompanied by the local rotation of the layer and the intensification of the vorticity. The end result of this evolution is a set of discrete round vortices whose structure is well approximated by that of axially symmetric vortices in an axially symmetric strain. The phenomenon can proceed (possibly simultaneously) on two separate lengthscales and with two correspondingly different timescales. The first lengthscale is the initial spanwise extent of vorticity of a given sign. The second, relevant to initially thin and spanwise slowly varying vortex layers, is proportional to the layer thickness. The two types of vorticity focusing or collapse are studied separately. The effect of the first on the diffusion rate of a scalar across the layer is calculated. The second is examined in detail for a spanwise-uniform layer: First we solve the eigenvalue problem for infinitesimal perturbations and then use the eigenfunctions as initial conditions for a numerical finite-differences solution. We find that the initial instability is similar to that of unstrained layers, in that roll-up and pairings also follow. However, at each stage a strain-diffusion balance eventually imposes the same cross-sectional lengthscale and each of these events leads to an intensification of the local value of the vorticity.The parameters upon which collapse and its timescale depend are related to those which are known to govern a mixing layer. The results suggest that the conditions for collapse of strained vortex sheets into concentrated round vortices are easily met in a mixing layer, even at low Reynolds numbers, so that these structures whose size is the Taylor microscale are far more plausibly typical than are vortex sheets on that scale. We found that they raise significantly the diffusion rate of scalar attributes by enhancing the rate of growth of material surfaces across which diffusion takes place. Finally, experimental methods that rely on the visualization of the gradient of scalar concentration are shown to be unable to reveal the presence of streamwise vorticity unless that vorticity has already gathered into concentrated vortex tubes.

Flow around a Finite Circular Cylinder on a Flat Plate : Cylinder height greater than turbulent boundary layer thickness

Abstract: Some flow visualization experiments and measurements of surface pressure, Strouhal number, etc. around a finite circular cylinder on a flat plate have been performed in order to study the effect of a three-dimensional flow. The slenderness parameter of the cylinder is in a range of l/d=1∼8, where the slenderness parameter influences remarkably the flow behavior. From an analysis of mean and periodical motion in the near-wake flow, the following results are obtained. (1) The separation velocity at the side wall is lower than that of a two-dimensional cylinder, and this decreases the drag coefficients. (2) A pair of trailing vortices exist right below the free-end. (3) Down-wash flow and the trailing vortex near the free-end dominate the behavior of Karman vortex shedding. Finally, based on these results, the flow models around the finite height cylinder are presented.

Wake-induced galloping of two interfering circular cylinders

Abstract: Measurements are presented of fluid-dynamic instability of a smooth circular cylinder, free to oscillate laterally against linear springs in the wake from an identical stationary neighbouring body. The observations also encompassed determination of static forces on the downstream cylinder as functions of relative position of the cylinder pair. Most of the experiments were performed under two conditions of free-stream turbulence. Static tests indicated that both the drag coefficient and the Strouhal number of the downstream body are continuous functions of its relative position. The drag forces were found to be negative at small gaps. It was observed that the transverse extent of the force field increases with increasing streamwise gap.In the dynamic experiments, depending on the cylinders’ separation and structural damping, the cylinder exhibited a vortex-resonance, or a galloping, or a combined vortex-resonance and galloping, or a separated vortex-resonance and galloping. Whilst the characteristics of wake-excited motion were found to be essentially unaffected by a limited change in free-stream turbulence intensity, the galloping amplitudes were observed to be sensitive to the cylinders’ aspect ratio. An increase in the stability parameter caused significant effects on the cylinder response in amplitude domain. Wake observations behind the oscillating body indicated that in vortex lock-in the frequency of vortex-shedding locked to vibration frequency, but during small-amplitude galloping motion the shedding frequency behaved as if the cylinder was stationary.

Visualization Studies of a Shear Driven Three-Dimensional Recirculating Flow

Abstract: A facility has been constructed to study shear-driven, recirculating flows. In this particular study, the circulation cell structure in the lid-driven cavity was studied as a function of the speed of the lid which provides the shearing force to a constant and uniform density fluid. The flow is three-dimensional and exhibits regions where Taylor-type instabilities and Taylor Goertler-like vortices are present. One main circulation cell and three secondary cells are present for the Reynolds number (based on cavity width and lid speed) range considered, viz., 1000-10000. The flows becomes turbulent at Reynolds numbers between 6000 to 8000. The transverse fluid motions (in the direction perpendicular to the lid motion) are significant. In spite of this, some key results from two-dimensional numerical simulations agree well with the results of the present cavity experiments.

Momentum and energy in the wake of a pigeon (Columba livia) in slow flight

Abstract: A technique is described whereby the vortex wake of birds in slow forward flight may be investigated with a view towards testing some of the assumptions and predictions of existing theoretical models of bird flight. Multiflash stereophotogrammetry was used to analyse the wake as a pigeon passed through a cloud of neutrally-buoyant helium bubbles. All photographs obtained support the hypothesis that the wake is composed of a chain of discrete, small-cored vortex rings. This being the case, velocity profiles taken from sections through the wake allow us to estimate the momentum in the wake as represented by vortex rings. The momentum in the wake appears to be approximately half that required for weight support in unaccelerated, level flight. The possible causes and consequences of this paradoxical result are discussed.

The structure of the vorticity field in turbulent channel flow. Part 2: Study of ensemble-averaged fields

Abstract: Several conditional sampling techniques are applied to a data base generated by large-eddy simulation of turbulent channel flow. It is shown that the bursting process is associated with well-organized horseshoe vortices inclined at about 45 deg. to the wall. These vortical structures are identified by examining the vortex lines of three-dimensional, ensemble averaged vorticity fields. Two distinct horseshoe-shaped vortices corresponding to the sweep and ejection events are detected. These vortices are associated with high Reynolds shear stress and hence make a significant contribution to turbulent energy production. The dependency of the ensemble averaged vortical structures on the detection criteria, and the question of whether this ensemble-averaged structure is an artifact of the ensemble averaging process are examined. The ensemble-averaged pattern of these vortical structures that emerge from the analysis could provide the basis for a hypothetical model of the organized structures of wall-bounded shear flows.

Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave

Abstract: We use a numerical method that was described in Part 1 (Marcus 1984 a ) to solve the time-dependent Navier-Stokes equation and boundary conditions that govern Taylor-Couette flow. We compute several stable axisymmetric Taylor-vortex equilibria and several stable non-axisymmetric wavy-vortex flows that correspond to one travelling wave. For each flow we compute the energy, angular momentum, torque, wave speed, energy dissipation rate, enstrophy, and energy and enstrophy spectra. We also plot several 2-dimensional projections of the velocity field. Using the results of the numerical calculations, we conjecture that the travelling waves are a secondary instability caused by the strong radial motion in the outflow boundaries of the Taylor vortices and are not shear instabilities associated with inflection points of the azimuthal flow. We demonstrate numerically that, at the critical Reynolds number where Taylor-vortex flow becomes unstable to wavy-vortex flow, the speed of the travelling wave is equal to the azimuthal angular velocity of the fluid at the centre of the Taylor vortices. For Reynolds numbers larger than the critical value, the travelling waves have their maximum amplitude at the comoving surface, where the comoving surface is defined to be the surface of fluid that has the same azimuthal velocity as the velocity of the travelling wave. We propose a model that explains the numerically discovered fact that both Taylor-vortex flow and the one-travelling-wave flow have exponential energy spectra such that In [E(k)] ∝ k 1 , where k is the Fourier harmonic number in the axial direction.

A comparison of vaporization models in spray calculations

Abstract: : The effects of different gas- and liquid-phase models on the vaporization behavior of a single-component isolated droplet are studied for both stagnant and convection situations in a high-temperature gas environment. In conjunction with four different liquid-phase models, namely, d2 law, infinite conductivity, diffusion limit, and internal vortex circulation, the different gas-phase models include a spherically symmetric model in the stagnant case and Ranz-Marshall correlation plus two other axisymmetric models in the convective case. A critical comparison of all these models is made. The use of these models in a spray situation is examined. A transient one-dimensional flow of an air- fuel droplet mixture is considered. It is shown that the fuel vapor mass fraction can be very sensitive to the particular liquid- and gas-phase models. The spherically symmetric conduction or diffusion limit model is recommended when the droplet Reynolds number is negligible compared to unity, while the simplified vortex model accounting for internal circulation is suggested when the droplet Reynolds number is large compared to unity. Keywords include: Spray; Droplet; Evaporation; Combustion; Modeling.

Minimum enstrophy vortices

Abstract: Two kinds of minimum enstrophy vortices in two‐dimensional flows are found by variational analysis. Each represents the ideal limit of a selective decay of enstrophy with energy and angular momentum or circulation, respectively, remaining fixed. For each, the vorticity is confined to a disk whose radius is determined by the fixed integrals. The definition of the vortices assures a large degree of stability, but many questions about their formation and destruction have not yet been answered.

Small-scale structure of the Taylor-Green vortex

Abstract: The dynamics of both the inviscid and viscous Taylor-Green (TG) three-dimensional vortex flows are investigated. This flow is perhaps the simplest system in which one can study the generation of small scales by three-dimensional vortex stretching and the resulting turbulence. The problem is studied by both direct spectral numerical solution of the Navier-Stokes equations (with up to 2563 modes) and by power-series analysis in time. The inviscid dynamics are strongly influenced by symmetries which confine the flow to an impermeable box with stress-free boundaries. There is an early stage during which the flow is strongly anisotropic with well-organized (laminar) small-scale excitation in the form of vortex sheets located near the walls of this box. The flow is smooth but has complex-space singularities within a distance cf(ct) of real (physical) space which give rise to an exponential tail in the energy spectrum. It is found that b(t) decreases exponentially in time to the limit of our resolution. Indirect evidence is presented that more violent vortex stretching takes place at later times, possibly leading to a real singularity (6 = 0) at a finite time. These direct integration results are consistent with new temporal power-series results that extend the Morf, Orszag Rr. Frisch (1980) analysis from order t4* to order Po. Still, convincing evidence for or against the existence of a real singularity will require even more sophisticated analysis. The viscous dynamics (decay) have been studied for Reynolds numbers R (based on an integral scale) up to 3000 and beyond the time t,,, at which the maximum energy dissipation is achieved. Early-time, high-R dynamics are essentially inviscid and laminar. The inviscidly formed vortex sheets are observed to roll up and are then subject to instabilities accompanied by reconnection processes which make the flow increasingly chaotic (turbulent) with extended high-vorticity patches appearing away from the impermeable walls. Near t,,, the small scales of the flow are nearly isotropic provided that R 1000. Various features characteristic of fully developed turbulence are observed near t,,, when R = 3000 and R, = 110: (i) a k-n inertial range in the energy spectrum is obtained with n z 1.G2.2 (in contrast with a much steeper spectrum at earlier times) ;

The boundary layer induced by a convected two-dimensional vortex

Abstract: The response of a wall boundary layer to the motion of a convected vortex is investigated. The principal cases considered are for a rectilinear filament of strength –κ located a distance a above a plane wall and convected to the right in a uniform flow of speed U∞*. The inviscid solution predicts that such a vortex will remain at constant height a above the wall and be convected with constant speed αU∞*. Here α is termed the fractional convection rate of the vortex, and cases in the parameter range 0 [les ] α < 1 are considered. The motion is initiated at time t* = 0 and numerical calculations of the developing boundary-layer flow are carried out for α = 0, 0.2, 0.4, 0.55, 0.7, 0.75 and 0.8. For α < 0.75, a rapid lift-up of the boundary-layer streamlines and strong boundary-layer growth occurs in the region behind the vortex; in addition an unusual separation phenomenon is observed for α [les ] 0.55. For α [ges ] 0.75, the boundary-layer development is more gradual, but ultimately substantial localized boundary-layer growth also occurs. In all cases, it is argued that a strong inviscid–viscous interaction will take place in the form of an eruption of the boundary-layer flow. The generalization of these results to two-dimensional vortices with cores of finite dimension is discussed.

Hurricane structure and evolution as simulated by an axisymmetric, nonhydrostatic numerical model

Abstract: This paper reports numerical simulations of the hurricane vortex by an axisymmetric, nonhydrostatic numerical model with 2 km maximum horizontal resolution. Moist convection is modeled explicitly using two different microphysical parameterizations. The first simulates liquid water processes only, whereas the second includes ice processes as well. Although concentric rings of convection associated with local maxima of the tangential wind form in both versions of the model, they are much more common when ice processes are included. As they contract about the vortex center, the outer ones supplant the inner. Their contraction follows the mechanism suggested by balanced-vortex models. Some of the rings appear to form through symmetric instability of the vortex, and others—particularly when ice processes are included—through interactions between precipitation-induced downdrafts and the boundary layer. Both the rings’ evolution and the detailed structure of the vortex core are similar to recent aircraf...

Vortex creep and the internal temperature of neutron stars. II - Vela pulsar

Abstract: The observed complex postglitch behavior of the Vela pulsar is explained as resulting from coupling of the crust to crustal neutron superfluid, specifically that part of the superfluid in which vortex lines are pinned to crustal nuclei. It is shown how the general theory of vortex creep provides an excellent fit to the timing observations of Downs which span the decade 1969-1979 and include four giant glitches. Relaxation times, inertial moments, and limits on superfluid pinning parameters are extracted for three distinct regions of vortex pinning in the star, with results which are consistent with microscopic theories of its internal structure. Relaxation times due to vortex creep are directly proportional to the internal temperature of the star, so that the limits obtained for pinning parameters translate to bounds on this temperature. It is concluded that the internal temperature of the Vela pulsar is about 10-million K and discuss the extent to which improved calculations of vortex pinning as well as soft X-ray observations of other stars will make possible an improved determination of the pulsar temperature.

Geostrophic Regimes, Intermediate Solitary Vortices and Jovian Eddies

Abstract: We examine the relevance to Jupiter's atmosphere of the solitary vortices favored at scales intermediate to those of the quasi-geostrophic (QG) and planetary-geostrophic motions. Horizontal divergence plays a crucial role in the intermediate-geostrophic (IG) dynamics and leads to asymmetries in vortex behavior; in partcular, anticyclonic vortices are generally more stable than cyclonic vortices when the mean flow is weak or westerly. The IG vortices always propagate westward at close to the planetary long-wave speed, regardless of the mean zonal flow. Meridional shear influences only secondary aspects of vortex behavior. Although governed by a form of the Korteweg-deVries (KdV) equation, vortex encounters produce coalescence not soliton behavior. Jupiter's Great Red Spot and Large Ovals appear to be in, or close to, an IG balance while the Small Ovals lie in a QG balance. The stability of anticyclonic IG vortices may explain why most of Jupiter's super-eddies prefer anticyclonic spin. Solutions t...

Study on boundary layer transition of a rotating disk

Abstract: Behaviour of spiral vortices being generated in transition regime of a disk rotating in otherwise undisturbed fluid is experimentally studied in detail. Through visualizations of the transition regime by using close-up camera, new striped flow patterns originating along the axis of spital vortices are found to be ring-like vortices which occur on the surfaces of each spiral vortices. Mechanism of the spiral vortex is clarified by cutting the vortices by strobo slit light. It is also found out experimentally that the phase velocity of the vortices is zero.

Hyperbolicity and change of type in the flow of viscoelastic fluids. Technical summary report

Abstract: The equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators. Propagation of singularities is discussed and conditions for a change of type are investigated. The vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied. This leads to a partitioning of the field of flow into subcritical and supercritical regions, as in the problem of transonic flow.