Showing papers on "Vortex published in 1979"

Dayside merging and cusp geometry

Abstract: Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 deg provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle.

Resistive transition in superconducting films

Abstract: The consequences of a vortex unbinding picture of two-dimensional superconductivity are worked out. Although there is no true finite-temperature phase transition, dirty superconducting films should display anomalous behavior below the BCS transition temperature and above an effective Kosterlitz-Thouless vortex unbinding temperature. In particular, both the conductivity and fluctuation diamagnetism behave like ξ + 2 in this regime, where ξ+ is the correlation length calculated by Kosterlitz, ξ+-ξ c exp (B/T − T c)1/2. We estimate ξc, B, and the vortex unbinding temperature, and determine the nonlinear resistivity below T c. A recent theory of vortex dynamics, together with a time-dependent Ginzburg-Landau theory, lead to a determination of the frequency-dependent conductivity.

The laminar horseshoe vortex

Abstract: The horseshoe vortex formed around the base of a cylinder by a separating laminar boundary layer has been investigated experimentally. Smoke flow visualization shows that both steady and unsteady vortex systems exist. Pressure distributions beneath both types of vortex system have been measured and the variation of the horseshoe vortex position on the plane of symmetry upstream of the cylinder has been determined. Unsteady horseshoe vortex systems are shown to have a complex oscillatory behaviour and the nature of this oscillatory behaviour is described. Using smoke flow visualization techniques some measurements have been made of the velocity distributions within horseshoe vortex systems.

The Spontaneous Appearance of a Singularity in the Shape of an Evolving Vortex Sheet

Abstract: The evolution of a small amplitude initial disturbance to a straight uniform vortex sheet is described by the Fourier coefficients of the disturbance. An approximation to the exact evolution equation for these coefficients is proposed and it is shown, by an asymptotic analysis valid at large times, that the solution of the approximate equations develops a singularity at a critical time. The critical time is proportional to ln $(\epsilon ^{-1})$, where $\epsilon $ is the initial amplitude of the disturbance and the singularity itself is such that the nth Fourier coefficient decays like $n^{-2.5}$ instead of exponentially. Evidence-not conclusive, however-is present to show that the approximation used is adequate. It is concluded that the class of vortex layer motions correctly modelled by replacing the vortex layer by a vortex sheet is very restricted; the vortex sheet is an inadequate approximation unless it is everywhere undergoing rapid stretching.

Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight. Part 1. Dynamics of the ‘fling’

Abstract: From a series of experiments using simplified mechanical models we suggest certain minor modifications to the Weis-Fogh (1973)–Lighthill (1973) explanation of the so-called ‘clap and fling’ mechanism for the generation of large lift coefficients by insects in hovering flight. Of particular importance is the production and motion of a leading edge, separation vortex that accounts for virtually all of the circulation generated during the initial phase of the ‘fling’ process. The magnitude of this circulation is substantially larger than that calculated using inviscid theory. During the motion that subsequently separates the wings, the vorticity over each of them is convected and combined to become a tip vortex of uniform circulation spanning the space between them. This combined vortex moves downwards as a part of a ring, of large impulse, that is then continuously fed from quasi-steady separation bubbles that move with the wings as they continue to open at a large angle of attack. Such effects are able to account for the large lift forces generated by the insect.

On the formation of vortex rings: Rolling-up and production of circulation

Abstract: The temporal development of the rolling-up process of vortex rings produced in water at a circular nozzle is investigated by flow visualization. The results are compared with similarity laws for the rolling-up of vortex sheets in plane flow. The unsteady flow field in the nozzle-exit plane is measured by laser anemometry. The vorticity distribution in the boundary layers at the inner and outer nozzle wall and the vorticity flux through the exit plane are derived from the measurements. The flow conditions measured at the nozzle are used to explain the production of the ring-vortex circulation (measured three nozzle-diameters downstream) in relation to the generation conditions.

On the evolution of isolated, nonlinear vortices

Abstract: The evolution of an isolated, axially symmetric vortex is calculated with a quasi-geostrophic, adiabatic, hydrostatic. β-plane, two vertical mode model. The circumstances of greatest interest are those of weak friction and large vortex amplitude (strong nonlinearity). Systematic studies are made of the consequences of varying the frictional coefficient, the vortex amplitude, the vortex radius (relative to the deformation radius), the degree of nonlinear coupling between the two vertical modes and the initial vertical structure of the vortex. Results of note include the following. Within the approximation of a single vertical mode model (i.e., in the absence of modal coupling), a baroclinic vortex has an increased westward and a finite meridional propagation speed when its amplitude is greater than infinitesimal. Both of these speeds, however, are limited by the wave speeds (as determined from infinitesimal amplitude theory) of the weak dispersion field outside the vortex. The vortex amplitude dec...

Dynamical instabilities and the transition to chaotic Taylor vortex flow

Abstract: We have used the technique of laser-Doppler velocimetry to study the transition to turbulence in a fluid contained between concentric cylinders with the inner cylinder rotating The experiment was designed to test recent proposals for the number and types of dynamical regimes exhibited by a flow before it becomes turbulent For different Reynolds numbers the radial component of the local velocity was recorded as a function of time in a computer, and the records were then Fourier-transformed to obtain velocity power spectra The first two instabilities in the flow, to time-independent Taylor vortex flow and then to time-dependent wavy vortex flow, are well known, but the present experiment provides the first quantitative information on the subsequent regimes that precede turbulent flow Beyond the onset of wavy vortex flow the velocity spectra contain a single sharp frequency component and its harmonics; the flow is strictly periodic As the Reynolds number is increased, a previously unobserved second sharp frequency component appears at R/Rc = 10·1, where Rc is the critical Reynolds number for the Taylor instability The two frequencies appear to be irrationally related; hence this is a quasi-periodic flow A chaotic element appears in the flow at R/Rc ≃ 12, where a weak broadband component is observed in addition to the sharp components; this flow can be described as weakly turbulent As R is increased further, the component that appeared at R/Rc= 10·1 disappears at R/Rc = 19·3, and the remaining sharp component disappears at R/Rc = 21·9, leaving a spectrum with only the broad component and a background continuum The observance of only two discrete frequencies and then chaotic flow is contrary to Landau's picture of an infinite sequence of instabilities, each adding a new frequency to the motion However, recent studies of nonlinear models with a few degrees of freedom show a behaviour similar in most respects to that observed

Observation of Stationary Vortex Arrays in Rotating Superfluid Helium

Abstract: The positions of quantized vortex lines in rotating superfluid helium have been recorded using a photographic technique. The photographs show stationary arrays of vortices. The observed patterns are in good agreement with theoretical predictions.

A Vortex Model of the Darrieus Turbine: An Analytical and Experimental Study

Abstract: A preliminary aerodynamic performance prediction model has been constructed for the Darrieus turbine using a vortex lattice method of analysis. A series of experiments were conducted for the express purpose of validating the analytical model. These experiments were conducted on a series of two dimensional rotor configurations which were towed in a large tank of water. The use of water as a working fluid was intended to facilitate both flow visualization and the ability to measure aerodynamic blade forces while allowing operation at sufficiently high Reynolds numbers. The primary purpose of this research was to allow reasonable predictions of aerodynamic blade forces and moments to be made.

Streamwise vortices associated with the bursting phenomenon

Abstract: The streamwise and spanwise velocity components and the gradients of these components normal to the wall were examined by using hot-film sensors and flush-mounted wall elements to study the vortex structures associated with the bursting phenomenon. Quadrant probability analysis and conditional sampling techniques indicated that pairs of counter-rotating streamwise vortices occur frequently in the wall region of a bounded turbulent shear flow. A streamwise momentum defect occurred between the vortices as low-speed fluid was ‘pumped’ away from the wall by the vortex pair. The defect region was long and narrow and possibly forms the low-speed streak as observed in visualization studies. The velocity defect was terminated by a strong acceleration followed by a high speed region.

Motion of three vortices

Abstract: A qualitative analysis of the motion of three point vortices with arbitrary strengths is given. This simplifies and extends recent work by Novikov on the motion of three identical vortices. Using a phase diagram technique, the possible regimes of motion are classified according to the signs of the arithmetic, geometric, and harmonic means of the three vortex strengths. For the special case where the vortex strengths (κ1,κ2,κ3) take the values (+κ,+κ,−κ), the diagram has an interpretation in terms of the scattering of a neutral pair by a single vortex. Quantitative details are presented for this case. If the harmonic mean of the three vortex strengths is zero, the triangle of vortices can collapse to a point in a finite time for certain initial conditions.

Characteristics of Tornado-Like Vortices as a Function of Swirl Ratio: A Laboratory Investigation

Abstract: The investigation of tornado vortex dynamics by means of a laboratory simulation is described. Based on observations from nature and an examination of the Navier-Stokes equations, a laboratory simulator of the Ward type has been constructed. This simulator generates various vortex configurations as a function of swirl ratio, radial Reynolds number and aspect ratio. Configurations which are described are 1) a single laminar vortex; 2) a single vortex with breakdown bubble separating the upper turbulent region from the lower laminar region; 3) a fully developed turbulent core, where the breakdown bubble penetrates to the bottom of the experimental chamber; 4) vortex transition to two intertwined helical vortices; and 5) examples of higher order multiple-vortex configurations that form in the core region. Hot-film anemometry measurements of the magnitude of the velocity vector and inflow (swirl) angle have been obtained in a sequence of flows characterized by progressively increasing values of swirl...

A vortex theory of animal flight. Part 1. The vortex wake of a hovering animal

Abstract: The distribution of vorticity in the wake of a hovering bird or insect is considered. The wake is modelled by a chain of coaxial small-cored circular vortex rings stacked one upon another; each member of the chain is generated by a single wing-stroke. Circulation is determined by the animal's weight and the time for which a single ring must provide lift; ring size is calculated from the circulation distribution on the animal's wing. The theory is equally applicable to birds and insects, although the mechanism of ring formation differs. This approach avoids the use of lift and drag coefficients and is not bound by the constraints of steady-state aerodynamics; it gives a wake configuration in agreement with experimental observations. The classical momentum jet approach has steady momentum flux in the wake, and is difficult to relate to the wing motions of a hovering bird or insect; the vortex wake can be related to the momentum jet, but adjacent vortex elements are disjoint and momentum flux is periodic.The evolution of the wake starting from rest is considered by releasing vortex rings at appropriate time intervals and allowing them to interact in their own velocity fields. The resulting configuration depends on the feathering parameter f (which depends on the animal's morphology); f increases with body size. At the lower end of the wake rings coalesce to form a single large vortex, which breaks away from the rest of the wake at intervals. Wake contraction depends on f; the minimum areal contraction of one-half (as in momentum-jet theory) occurs only in the limit f → 0, but values calculated for smaller insects of just over one-half suggest that the momentum jet may be a good approximation to the wake when f is small.Induced power in hovering is calculated as the limit of the mean rate of increase of wake kinetic energy as time progresses. It can be related to the classical momentum-jet induced power by a simple conversion factor. For an insect or hummingbird the usual momentum-jet estimate may be between 10 and 15% too low, but for a bird it may be as much as 50% too low. This suggests that few, if any, birds are able to sustain aerobic hovering, and that as small a value of f as possible would be necessary if the bird were to hover.Tip losses (energy cost of the vortex-ring wake compared with the equivalent momentum jet) are negligible for insects, but can be in the range 15–20% for birds.

A vortex theory of animal flight. Part 2. The forward flight of birds

Abstract: The vortex wake of a bird in steady forward flight is modelled by a chain of elliptical vortex rings, each generated by a single downstroke. The shape and inclination of each ring are determined by the downstroke geometry, and the size of each ring by the wing circulation; the momentum of the ring must overcome parasitic and profile drags and the bird's weight for the duration of a stroke period. From the equation of motion it is possible to determine exactly the kinematics of the wing-stroke for any flight velocity. This approach agrees more readily with the nature of the wing-stroke than the classical actuator disk and momentum-jet theory; it also dispenses with lift and induced drag coefficients and is not bound by the constraints of steady-state aerodynamics. The induced power is calculated as the mean rate of increase of wake kinetic energy. The remaining components of the flight power (parasite and profile) are calculated by traditional methods; there is some consideration of different representations of body parasite drag. The lift coefficient required for flight is also calculated; for virtually all birds the lift coefficient in slow flight and hovering is too large to be consistent with steady-state aerodynamics. A bird is concerned largely to reduce its power consumption on all but the shortest flights. The model suggests that there are a number of ways in which power reduction can be achieved. These various strategies are in good agreement with observation.

Theory of Electron Holes

Abstract: We present analytical solutions for the electron holes discovered recently and for the `Gould-Trivelpiece-Soliton'. Based on appropriate electron distribution functions, stationary solutions of the Vlasov-Poisson-system adopted to finite geometry are constructed. It is shown that the electron hole found experimentally and by numerical simulations is well described by this solution. It represents a nonlinear version of the slow-electron acoustic mode and exists due to a distortion of the electron distribution in the resonant region, forming a hollow vortex in phase space. Its importance for studying nonlinear diffusion processes in phase space is emphasized.

Spectral characteristics of vortex breakdown flowfields

Abstract: Laser‐Doppler anemometer measurements upstream and in the wakes of vortex breakdowns of bubble and spiral types are described. Spectral analysis of the data indicates prominent oscillations in the wakes at less than 10 Hz. These oscillations correspond closely to theoretical predictions of the linearly most unstable normal modes of the time‐averaged mean flow profiles. The oscillations are more energetic, and vortex core expansions are greater for flows with a bubble form of vortex breakdown, which is therefore regarded as the stronger form of breakdown.

Applications of a stretch model to mixing, diffusion, and reaction in laminar and turbulent flows

Abstract: In a Lagrangian frame of reference based on lamina (fluid filament) thickness and in a warped time scale based on a single, flow dependent quantity, mixing, diffusion, and reaction can be described in a relatively simple way. Applications are presented for stretch and fold in taffy pull, egg beater and static mixer, shear stretch, stretch of laminae in a vortex, mixing with diffusion, reaction rate controlled by diffusion of reactant through a product layer, and very fast reactions in a turbulent flow.

The Dilemma of Defining a Vortex

Abstract: The problem of defining a vortex in a real fluid is discussed. The definition and identification of a vortex in unsteady motions is difficult since streamlines and pathlines are not invariant with respect to Galilean and rotational transformations. Recirculatory streamline patterns at a certain instant in time do not necessarily represent vortex motions in which fluid particles are moving around a common axis. Thus, instantaneous streamline patterns do not provide enough information to be used for the definition of a vortex. Extremal properties of the vorticity field are not helpful either, since a local extremum in the vorticity is not necessary for the existence of a vortex. A proposal for a definition based on pathlines is presented.

Vortex patterns and energies in a rotating superfluid

Abstract: The two-dimensional vortex patterns that occur in a rotating cylinder of superfluid $^{4}\mathrm{He}$ are systematically ordered for numbers of vortices $N=1,2,\dots{},30,37,50$ using a prescription for their free energy that is independent of angular velocity and is based upon the justified omission of images. Barrier energies between patterns of the same $N$ and of neighboring $N$ are discussed. A new derivation of the vortex free energy for perfect square and triangular lattices gives the result in terms of $\ensuremath{\Gamma}(x)$. Patterns that are expected to display high triangular symmetry are studied up to $N=217$, but circular distortion strongly reduces the region of triangular symmetry even in an unbounded fluid, as shown by the scattering structure factor. According to calculations on arrays containing over one million vortices, the destabilizing velocity at the vortex position $R$ in a finite circular region of a perfect triangular lattice is proportional to ${(\frac{R}{{R}_{0}})}^{5}$ where ${R}_{0}$ is the radius of the circular region.

Attenuation of Sound in a Low Mach Number Nozzle Flow

Abstract: This paper examines the energy conversion mechanisms which govern the emission of low frequency sound from an axisymmetric jet pipe of arbitrary nozzle contraction ratio in the case of low Mach number nozzle flow. The incident acoustic energy which escapes from the nozzle is partitioned between two distinct disturbances in the exterior fluid. The first of these is the free-space radiation, whose directivity is equivalent to that produced by monopole and dipole sources. Second, essentially incompressible vortex waves are excited by the shedding of vorticity from the nozzle lip, and may be associated with the large-scale instabilities of the jet. Two linearized theoretical models are discussed. One of these is an exact linear theory in which the boundary of the jet is treated as an unstable vortex sheet. The second assumes that the finite width of the mean shear layer of the real jet cannot be neglected. The analytical results are shown to compare favourably with recent attenuation measurements.

Forced secondary circulations in hurricanes

Abstract: In this study, application of Eliassen's (1951) forced secondary circulation model to the hurricane vortex is reexamined. It is shown by scale analysis that the symmetric tangential flow is in hydrostatic and gradient balance if the asymmetric part of the tangential flow and the radial and vertical symmetric motions are appreciably smaller than the symmetric tangential flow. When surface friction and cumulus transports of heat and momentum are included, the forced symmetric radial and vertical motions may be diagnosed. The approximations on which this system of balanced equations is based are valid everywhere in the hurricane vortex except in the upper tropospheric outflow layer. In the absence of Fickian diffusion of momentum and heat, both deep inflow in the outer vortex and subsidence within the eye are forced by radial gradients of convective heating. If corresponding gradients of cooling arise in the upper troposphere by mechanisms such as detrainment from overshooting cumuli, descent may be induced in the lower stratosphere above and around the eye. Convective momentum transports act to weaken the thermally induced secondary flow somewhat. If the vertical resolution of the finite difference mesh is too coarse to resolve the detrainment layer properly, the model may diagnose an unrealistic secondary flow with ascent throughout the eye. In the absence of all cumulus processes, the frictionally converged air no longer rises to the tropopause but rather flows outward in a shallow layer in the lower troposphere.

Vortex ring formation at tube and orifice openings

Abstract: The formation, at tube and orifice openings, of vortex rings generated by a piston moving with velocity proportional to time to some power m, is considered. The expansion of the axisymmetric generating flow about the circular forming edge is used in conjunction with the similarity theory of edge vortex growth to model the ring formation process. For large Reynolds numbers the ring diameter and circulation are not strongly dependent on the piston velocity profile. However, the ring viscous subcore shows peaks in the tangential velocity profile only if m < (π–θ)/(2π–θ), where θ is the edge forming angle.

Axial flow in trailing line vortices

Abstract: Axial flow in the core of a laminar steady trailing vortex from the tip of a semi‐infinite wing is analyzed assuming small departure of the axial velocity from the free‐stream velocity. It is further assumed that the axial pressure gradient is determined by the swirl velocities of an ideal infinite line vortex in which the radial and the associated axial velocity variations are neglected in the equation for the angular momentum. The axial and lateral variations of the axial velocity depend on the strength of the vortex and initial axial velocity distribution which must be specified at some station behind the wing except at the virtual origin of the vortex where a nonintegrable singularity exists. Numerical solutions for the axial velocity are obtained using the axial pressure gradient given by the line vortex and analytical solutions are obtained using an equivalent axial pressure gradient with good agreement between the two sets of axial velocity distributions. Resolution of the previous uncertainties in this field is given which were due to the unrecognized singularity at the virtual origin of the vortex. Using the calculated axial velocity the neglected radial and the associated axial fluxes of angular momentum are determined and the limits of validity of the theory presented here in terms of a suitably defined vortex Reynolds number and a nondimensional distance measured from the virtual origin of the vortex are given.

On the perseverance of a quasi-two-dimensional eddy-structure in a turbulent mixing layer

Abstract: Strong external disturbances were introduced into a mixing layer in order to test the formation of the quasi two-dimensional coherent eddies and their survival under less than ideal conditions. Velocity and temperature correlation measurements, flow visualization, and the simultaneous use of a large number of sensors suggest that these eddies are very stable in the range of Reynolds numbers considered and they persevere in spite of the external buffeting imposed. Some measurements were carried out in a mixing layer between two parallel streams and some in a mixing layer entraining quiescent surrounding fluid. In both cases the large eddies could be described. as vortex rolls spanning the test section; these rolls may be contorted and sometimes skewed, but they are basically two-dimensional.

Inviscid Model of Two-Dimensional Vortex Shedding by a Circular Cylinder

Abstract: A discrete vortex model based on potential flow and boundary-layer interaction, rediscretization of shear layers, and circulation dissipation is developed to determine the characteristics of an impulsively started flow about a circular cylinder. The evolution of the flow from the start to very large times, lift and drag forces, Strouhal number, oscillations of the separation and stagnation points, and the vortex-street characteristics are calculated and compared with experiments. b CD CL Cpb c D fv h / j m N n q Re St s ds t At U u v w z F 7 6 X v p Nomenclature = longitudinal spacing of vortices = drag coefficient = lift coefficient = base pressure coefficient = radius of the cylinder - diameter of the cylinder ,D = 2c = vortex shedding frequency = transverse spacing of vortices = an index = distance to nascent vortex from cylinder = number of vortices on a sheet = an index = total velocity at a point = Reynolds number, UD/v = Strouhal number, fvD/ U = distance along a sheet = point vortex spacing = time or Ut/c for U= 1 and c = 1 - numerical step size = velocity of the ambient flow = x component of velocity -y component of velocity = complex velocity potential = complex variable = circulation = circulation per unit length = angle measured from ( - c,0) = dissipation parameter = kinematic viscosity of fluid = density of fluid = vorticity

A Study in Tornado-Like Vortex Dynamics

Abstract: Fine-resolution calculations using an axisymmetric numerical model of the flow within a Ward-type vortex chamber are discussed. Particular attention is paid to the vortex-ground interaction. Variations in the swirl ratio S from zero to unity lead to radically different vortex structure in the “corner” region (i.e., near r = z = 0). For S Lt; 1, a concentrated vortex forms in the upper chamber but not in the corner. At moderate S, we observe vortex breakdown, large-amplitude inertial waves, and very intense swirling motion in the corner. When S = 1, the central downdraft penetrates to the lower surface and the vortex breakdown occurs within the boundary layer. These results are consistent with experimental observations and suggest the explanation of a number of observed facets of tornadoes.