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The vortex equation is often used to estimate the front velocity of debris flows using the lateral slope of the flow surface through a channel bend of a given radius. Here we report on laboratory experiments evaluating the application of the vortex equation to channelized debris flows. Systematic laboratory experiments were conducted in a 8 m long laboratory flume with a roughened bed, semi-circular cross section (top width 17 cm), and two different bend radii (1.0 and 1.5 m) with a common bend angle of 60°, and two channel inclinations (15° and 20°). Four sediment mixtures were used with systematic variations in the amount of fine sediment. In the experiments, 12 kg of water-saturated debris were released in a dam-break fashion, and multiple experiments were conducted to verify the repeatability for a given sediment mixture. Data are available for 69 experimental releases at a channel inclination of 20° and 16 releases at an inclination of 15°. Flow velocity was determined with high-speed video, and flow depth and the lateral inclination of the flow surface (superelevation) were measured using laser sensors. In general, the results from an individual sediment mixture are repeatable. We found that the channel slope as well as centerline radius have a significant influence on the correction factor k used in the vortex equation. Relatively coarse-grained sediment mixtures have larger superelevation angles than finer-grained mixtures. We found a statistically significant relation between the correction factor and Froude number. Correction factors of 1 < k Key words: debris flow, front velocity, superelevation, physical model, forced vortex equation. L'equation de vortex est souvent utilisee pour estimer la vitesse de front de coulees de debris a partir de l'inclinaison laterale de la surface d'ecoulement dans un canal au rayon de courbure determine. Nous decrivons ici les experiences de laboratoire qui ont permis d'evaluer l'application de l'equation de vortex aux coulees de debris canalisees. Des experiences ete realisees de maniere rigoureuse en laboratoire au moyen d'un canal experimental de 8 m de long a fond rugueux et a section transversale semi-circulaire (17 cm de largeur au sommet) formant deux courbes de rayons differents (1,0 et 1,5 m) et comportant une pente de 60° et deux inclinaisons differentes (de 15° et 20°). On a utilise quatre melanges sedimentaires en faisant varier regulierement la quantite de sediments fins. Les experiences realisees ont consiste a deverser d'un seul coup dans le canal 12 kg de debris satures en eau et ont ete repetes plusieurs fois afin de verifier repetitivite obtenue pour un melange sedimentaire donne. On dispose des donnees de 69 experiences de deversement realisees avec un degre d'inclinaison du canal du 20° et de 16 experiences effectuees avec un degre d'inclinaison de 15°. La vitesse d'ecoulement a ete determinee a l'aide d'une camera video a grande vitesse et la profondeur de l'ecoulement et l'inclinaison laterale de la surface d'ecoulement ont ete mesurees au moyen des capteurs laser. D'une maniere generale, les resultats obtenus pour un melange sedimentaire en particulier sont repetables. Nous avons constate que le degre d'inclinaison du canal et les rayons de courbure influaient beaucoup sur le facteur de correction k utilise dans l'equation de vortex. Par ailleurs, les angles d'inclinaison laterale sont plus eleves dans le cas des melanges sedimentaires a grains relativement gros que dans celui des melanges a grains plus petits. Nous avons en outre decouvert une correlation importante d'un point de vue statistique entre le facteur de correction et le nombre de Froude. Des valeurs du facteur de correction k superieures a 1 et inferieures a 5 ont egalement ete observees dans le cas d'ecoulements supercritiques. Cependant, dans ce dernier cas, le facteur de correction prend une valeur elevee, fonction du nombre de Froud, ce qui implique une adaptation de l'equation de vortex force qui tienne compte des pressions active et passive des terres. Enfin, en nous basant sur les resultats de nos experiences, nous presentons une equation de vortex force permettant de calculer la vitesse d'ecoulement de debris sans utiliser de facteur de correction. [Traduit par la Redaction] Mots-cles: coulee de debris, vitesse de front de coulee, inclinaison laterale, modele physique, equation de vortex force., Introduction Gravitational mass-movements like debris flows endanger human settlements all over the world, especially in densely-populated mountainous regions, where people are challenged to find a balance between spatial development and [...]

The physics of a parallel blade--vortex interaction is studied numerically and the predicted pressure and acoustic results are compared with experimental measurements. A high-resolution solution of the compressible Euler equations is performed on structured overset meshes. Initially, a two-dimensional airfoil--vortex interaction is studied for both a case where the vortex misses the blade and a case of direct impact. The vortex is initiated in the flow as a perturbation to the freestream conditions and is free to evolve, thus allowing for the deformation of the vortex as it interacts with the blade to be studied. The simulation is seen to accurately reproduce the experimental results and the emission of the acoustic waves from the airfoil surface is observed in detail. Acoustic energy generated by the interaction is seen to primarily radiate from the leading-edge section of the airfoil with a weaker contribution coming from the trailing edge. The simulations are then extended to three-dimensional moving overset meshes where the vortex generation and convection is also resolved. The numerical methodology is seen to accurately preserve the vortex strength and accurately reproduce the experimentally measured blade surface pressures and acoustics. The computations presented here face similar challenges to that encountered in the simulation of realistic helicopter blade--vortex interaction, but the computational costs are such that the solutions can be well resolved, and comprehensively validated using moderate resources. DOI: 10.2514/1.J050381

Recently, some riser vortex-induced vibrations (VIVs) experimental data have been made publicly available (oe.mit.edu/VIV/) including a 10 m riser VIV experiment performed by Marintek, Trondheim, Norway, and donated by ExxonMobil URC, Houston, TX, USA. This paper presents our numerical simulation results for this 10 m riser and the comparisons with the experimental results in uniform current. The riser was made of a 10 m brass pipe with an outer diameter of O.02 m (L/D = 482) and a mass ratio of 1.75. The riser was positioned vertically with top tension of 817 N and pinned at its two ends to the test rig. Rotating the rig in the wave tank would simulate the uniform current. In the present numerical simulation the riser's ends were pinned to the ground and a uniform far field incoming current was imposed. The riser and its surrounding fluid were discretized using 1.5 x [10.sup.6] elements. The flow field is solved using an unsteady Reynolds-averaged Navier-Stokes (RANS) numerical method in conjunction with a chimera domain decomposition approach with overset grids. The riser is also discretized into 250 segments. Its motion is predicted through a tensioned beam motion equation with external force obtained by integrating viscous and pressure loads on the riser surface. Then the critical parameters including riser VIV amplitude (a) to the riser outer diameter (D) ratio (a/D), vorticity contours, and motion trajectories were processed. The same parameters for the experimental data were also processed since these data sets are in 'raw time-histories' format. Finally, comparisons are made and conclusions are drawn. The present numerical method predicts similar dominant modes and amplitudes as the experiment. It is also shown that the cross flow VIV in the riser top section is not symmetric to that of the bottom section. One end has considerably higher cross flow vibrations than the other end, which is due to the nondominant modal vibrations in both in-line and cross flow directions. The computational fluid dynamics (CFD) simulation results also agree with the experimental results very well on the riser vibrating pattern and higher harmonics response. The higher harmonics were studied and it is found that they are related to the lift coefficients, hence the vortex shedding patterns. It is concluded that the present CFD approach is able to provide reasonable results and is suitable for 3D riser VIV analysis in deepwater and complex current conditions. [DOI: 10.1115/1.4000498]

A hybrid vortex filament scheme with the capability of simulating bounded turbulent flows is described. Viscous generation of new vortex elements at solid surfaces is accomplished through the intermediary step of solving the viscous vorticity transport equation on a thin boundary mesh via a finite difference and finite volume method. The transitional and turbulent boundary-layer flow past a wide, finite thickness, flat plate with rounded edges is computed with a view toward validating the methodology and gaining new insight into the structural aspects of transition. The predicted mean velocity and related statistics are well matched to experimental and numerical data. The representation of the flow through vortex filaments reveals that a distinction needs to be made between vortical structures, on one hand, and the rotational motion that they produce in the flowfield, on the other hand. In particular, hairpin-shaped regions that are commonly found by vortex identification schemes are found to not be structures in their own right, but rather the rotational signature of raised furrows in the surface vortex sheet. The latter overlie low-speed streaks and evolve to include ejected mushroom-shaped structures as well as spanwise vortices associated with roll-up. DOI: 10.2514/1.J050224

This study develops a linear numerical model to address the source mechanism of the gravity waves generated within a vortex dipole simulated in a fully nonlinear nonhydrostatic mesoscale model. The background flow for this linear model is obtained from potential vorticity inversion constrained by the nonlinear balance equation. The forcing imposed in the linear model is derived from an imbalance in the large-scale flow--that is, the forcing or imbalance in the vorticity, divergence, and thermodynamic equations, respectively. The response from the sum of these imbalanced forcings obtained from the linear dynamics shows well-defined gravity wave signals, which compare reasonably well in terms of location, phase, and amplitude with the gravity waves simulated in a fully nonlinear nonhydrostatic mesoscale model. It is found that the vorticity forcing, largely due to the advection of balanced relative vorticity, is the leading contributor to the gravity waves in the exit region of the vortex-dipole jet. DOI: 10.1175/2010JAS3327.1

Atmospheric turbulence has significant influences on both the trajectories and strengths of wake vortices. In this paper, a quasi-wavelet method is used to generate a random atmospheric turbulence field based on the von Karman spectrum, in which atmospheric turbulence is represented by groups of random eddies. An inviscid wake vortex system, out-of-ground effect or in-ground effect, is immersed in the generated turbulence background to study the effects of random turbulence on wake vortices. The simulated wake trajectories are compared with literature data from several current prediction models as well as from field measurement. DOI: 10.2514/1.44288

The aim of this work is to provide a detailed two-dimensional numerical analysis of the physical phenomena occurring during dynamic stall of a Darrieus wind turbine. The flow is particularly complex because as the turbine rotates, the incidence angle and the blade Reynolds number vary, causing unsteady effects in the flow field. At low tip speed ratio, a deep dynamic stall occurs on blades, leading to large hysteresis lift and drag loops (primary effects). On the other hand, high tip speed ratio corresponds to attached boundary layers on blades (secondary effects). The optimal efficiency occurs in the middle range of the tip speed ratio where primary and secondary effects cohabit. To prove the capacity of the modeling to handle the physics in the whole range of operating condition, it is chosen to consider two tip speed ratios ([lambda] = 2 and [lambda] = 7), the first in the primary effect region and the second in the secondary effect region. The numerical analysis is performed with an explicit, compressible RANS [kappa]-[omega] code TURBFLOW, in a multiblock structured mesh configuration. The time step and grid refinement sensitivities are examined. Results are compared qualitatively with the visualization of the vortex shedding of Brochier (1986, 'Water channel experiments of dynamic stall on Darrieus wind turbine blades,' J. Propul. Power, 2(5), pp. 445-449). Hysteresis lift and drag curves are compared with the data of Laneville and Vitecoq (1986, 'Dynamic stall: the case of the vertical axis wind turbine,' Prog. Aerosp. Sci., 32, pp. 523-573). [DOI: 10.1115/1.4000258] Keywords: VAWT, RANS modeling, dynamic stall, hysteresis

A nonlinear, two-layer, vortex-tracking semispectral model (i.e., Fourier transformed in azimuth only) is used to study the evolution of dry, but otherwise hurricane-like, initially tilted vortices in quiescent surroundings on f and [beta] planes. The tilt projects onto vorticity asymmetries that are dynamically vortex Rossby waves. Since the swirling wind in the principal mean vortex used here decays exponentially outside the eyewall, it has an initial potential vorticity (PV) minimum. The resulting reversal of PV gradient meets the necessary condition for inflectional (i.e., barotropic or baroclinic) instability. Thus, the vortex may be inflectionally stable or unstable. On an f plane, the tilt precesses relatively slowly because the critical radius, where the phase speeds of the waves match the mean swirling flow, is far from the center. An alternative Gaussian-like PV monopole that has a monotonic outward decrease of PV is stable to inflectional instability. It has a smaller critical radius and rapid tilt precession. Generally, vortices with fast tilt precession are more stable, as are stronger vortices in higher latitudes. On a [beta] plane, the interaction between the symmetric vortex and the planetary PV gradient induces [beta] gyres that push the vortex poleward and westward. The interaction between the [beta] gyres and the planetary PV gradient may either create a PV minimum or intensify a minimum inherited from the initial condition. Thus, the nonlinear [beta] effect reduces the ability of the vortex to recover from initial tilt, relative to the same vortex on an f plane. This result contrasts with previous studies of barotropic vortices on f planes, where the linear and nonlinear solutions were nearly identical.

An inviscid tornadolike vortex is analytically modeled using a free narrow jet solution combined with a modified Rankine vortex. An empirical and simplified solution to existing models is defined for flows similar to the ones simulated in Ward-type vortex chambers. Velocity profiles are calculated for a particular swirl ratio [S.sub.r] = 0.28. The model shows reasonable agreement with existing experimental measurements by Baker (1981, ' Boundary Layers in Laminar Vortex Flows,' Ph.D. thesis, Purdue University, West Lafayette, IN) and the numerical simulation by Wilson and Rotunno (1986, 'Numerical Simulation of a Laminar End-Wall Vortex and Boundary Layer,' Phys. Fluids, 29(12), pp. 3993-4005). [DOI: 10.1115/1.3063632] Keywords: tornadolike vortex, analytical model

The behavior of a vortex flow through a Laval nozzle was studied in connection with the purification of natural gas. By creating a vortex and passing it through a Laval nozzle, the gas will be cooled, and water droplets will form and will be centrifuged out of the gas. This system is named the Condi-Cyclone. An analytical theory is developed to reveal the most important phenomena of the flow, to first order accuracy. Experiments have been performed with a prototype of the Condi-Cyclone. A Euler numerical simulation was performed, using the geometry of the test channel. This paper presents an analytical theory for a vortex flow through a Laval nozzle. It will demonstrate that when a vortex is present the total velocity reaches sonic conditions upstream of the nozzle throat, that the axial component of the velocity in the nozzle throat is equal to the local speed of sound and that the mass flow through the Laval nozzle decreases with increasing vortex strength. The predictions of the analytical theory have been compared with the results of the experiments and the Euler numerical simulation, and it can be concluded that the analytical theory describes the main characteristics of the flow very well. [DOI: 10.1115/1.3089532] Keywords: Laval nozzle, vortex flow, natural gas, Condi-Cyclone

Simulations of two cases of developing mesoscale convective vortices (MCVs) are examined to determine the dynamics governing the origin and vertical structure of these features. Although one case evolves in strong vertical wind shear and the other evolves in modest shear, the evolutions are remarkably similar. In addition to the well-known mesoscale convergence that spins up vorticity in the midtroposphere, the generation of vorticity in the lower troposphere occurs along the convergent outflow boundary of the parent mesoscale convective system (MCS). Lateral transport of this vorticity from the convective region back beneath the midtropospheric vorticity center is important for obtaining a deep column of cyclonic vorticity. However, this behavior would be only transient without a secondary phase of vorticity growth in the lower troposphere that results from a radical change in the divergence profile favoring lower-tropospheric convergence. Following the decay of the nocturnal MCS. subsequent convection occurs in a condition of greater relative humidity through the lower troposphere and small conditional instability. Vorticity anal potential vorticity are efficiently produced near the top of the boundary layer anda cyclonic circulation appears at the surface.

The flow inside a vortex trapping cavity is simulated by a suite of models: point vortex, Prandtl--Batchelor flow, and Reynolds-averaged Navier--Stokes equations. The scope is to ascertain to what extent an inviscid model can be used to design vortex cells. It turns out that the Prandtl--Batchelor flow, with an appropriate jump in the Bernoulli constant across the dividing streamline, gives an acceptable representation of the solution found by the Reynolds- averaged Navier--Stokes equations, which in turn compares well with experimental results when an appropriate turbulence model is selected.

An optical vortex is a screw dislocation in a light field that carries quantized orbital angular momentum and, due to cancellations of the twisting along the propagation axis, experiences zero intensity at its center. When viewed in a perpendicular plane along the propagation axis, the vortex appears as a dark region in the center surrounded by a bright concentric ring of light. We give detailed instructions for generating optical vortices and optical vortex structures by computer-generated holograms and describe various methods for manipulating the resulting structures. [DOI: 10.1119/1.2955792]

A new aerodynamic wake model has been developed for horizontal axis wind turbines. The aim is to develop an engineering tool for investigation and design of furling turbines. The prescribed vortex wake code HAWTDAWG, developed at the University of Glasgow, has been extended for dynamic flow conditions. This dynamic prescribed wake model is built into the aerodynamic code AERODYN and linked to the structural dynamics code FAST. The new model has been compared to unsteady aerodynamic experiment Phase VI wind tunnel data. Comparisons are also made to blade element momentum and generalized dynamic wake models built into AERODYN. Results are encouraging and justify further investigation. [DOI: 10.1115/1.2931503]

To reduce the level of uncertainty associated with current rotor aerodynamics codes, improved understanding of rotor aerodynamics is required. Wind tunnel measurements on model rotors contribute to advancing our knowledge on rotor aerodynamics. The combined recording of blade loads and rotor wake is desired, because of the coupled blade and wake aerodynamics. In general, however, the small size of model rotors prohibits detailed blade load measurements; only the rotor wake is recorded. To estimate the experimental blade flow conditions, a measurement analysis tool is developed: the inverse vortex wake model. The rotor wake is approximated by a lifting line model, using rotor wake measurements to reconstruct the vortex wake. Conservation of circulation, combined with the Biot-Savart law, allows the induced velocity to be expressed in terms of the bound circulation. The unknown bound circulation can be solved for, since the velocity is known from rotor wake measurements. The inverse vortex wake model is subsequently applied to measurements on the near wake of a model rotor subject to both axial and yawed flow conditions, performed at a TUDelft open jet wind tunnel. The inverse vortex wake model estimates the unsteady experimental blade flow conditions and loads that otherwise would have remained obscured. [DOI: 10.1115/1.2931508]

The structure and formation of an annular hurricane simulated in a fully compressible, nonhydrostatic tropical cyclone model--TCM4--are analyzed. The model is initialized with an axisymmetric vortex on an f plane in a quiescent environment, and thus the transition from the nonannular hurricane to the annular hurricane is attributed to the internal dynamics. The simulated annular hurricane has all characteristics of those recently documented by Knaff et al. from satellite observations: quasi-axisymmetric structure, large eye and wide eyewall, high intensity, and suppressed major spiral rainbands. A striking feature of the simulated annular hurricane is its large outward tilt of the wide eyewall, which is critical to the quasi-steady high intensity and is responsible for the maintenance of the large size of the eye and eyewall of the storm. Although the annular hurricane has a quasi-axisymmetric structure, marked low-wavenumber asymmetries exist in the eyewall region. The formation of the simulated annular hurricane is found to be closely related to the interaction between the inner spiral rainbands and the eyewall convection. As the inner rainbands spiral cyclonically inward, they experience axisymmetrization due to strong shear deformation and filamentation outside the eyewall and evolve into a quasi-symmetric convective ring, which intensifies as it contracts while the eyewall breaks down and weakens. Eventually, the convective ring replaces the original eyewall. The new eyewall formed in such a way is wider and tilts more outward with height than the original eyewall. Several such eyewall cycles in our simulation produce an annular hurricane with large eyewall slope, large eye, and wide eyewall. The response of low-level winds to the tilted convective heating in the eyewall is an increase outside and a decrease inside the radius of maximum wind, prohibiting further contraction of the new eyewall. Strong convective mass flux in the eyewall updraft corresponds to strong convective overturning subsidence outside the eyewall, greatly suppressing the development of any major rainbands outside the eyewall. Although the eyewall cycle documented in this study contributes to the formation of annular hurricanes, it could be a general process causing the increase in eye size of real tropical cyclones as well.

We have developed a numerical simulation scheme combining a vortex method and a particle trajectory tracking method, which is applicable to internal unsteady two-phase flows. It is a completely grid-free Lagrangian-Lagrangian simulation, which is able to simulate the primary, effect of vortical flow on the unsteady particle motion and dispersion. It can handle unsteady high Reynolds number flows. So far, no one has applied this kind of method internal multiphase flows, though many industrial multiphase flows are internal. In this study, internal liquid-solid two-phase flows in a vertical channel and a mixing tee have been calculated by the new method, in which use of the vortex introduction model enables the simulation of the dynamic behavior of separation or reattachment. In the mixing tee, solid particle phenomena such as depositions or particle-wall collisions have been simulated and measured. Numerical results based on simple two-dimensional flow and one-way model show good agreement with the experimental data. The results show that turbulent vortices dominate particle motion. It has been shown that the present method can be useful in the design of industrial multiphase flows with particle mixing, dispersion, deposition, and particle-wall collision because it is possible to simulate the effect of turbulent vortices on the particle motion. [DOI: 10.1115/1.2813139] Keywords: vortex method, particle trajectory tracking method, fluid-solid two-phase flow, internal unsteady flow, grid-free simulation, lagrangian-lagrangian simulation,

The presence of streamwise vorticity in the vicinity of the wing tip contributes to lift in thin flat plate zero pitch angle flapping wings in quiescent air. In creating flapping wing micro air vehicles it is desirable to maintain only the mechanical and kinematic complexity absolutely necessary to artificially duplicate flapping wing flight. This study quantifies the lift generated from a flapping motion of absolute minimum complexity thought to be capable of generating lift. Using a flapping wing micro air vehicle with wings fabricated in-house, streamwise vortices were identified along the span of wings of various aspect ratios and at numerous different points throughout the flapping cycle under a variety of operating conditions. The lift generated by the flapping mechanism was quantified experimentally using a force transducer and a high speed camera. Digital particle image velocimetry was used to determine the contributions of streamwise vorticity to the total measured lift. Further evidence was found of the importance of the relationship between wing span and flapping frequency in the nature of the formation and shedding of vortices. DOI: 10.2514/1.27824

A numerical method based on the vortex methodology is presented for unsteady solution of the aerodynamics coefficients of a thin profile in subsonic and supersonic compressible flows. The numerical model is made through the airfoil discretization in uniform segments, and the singularity used is a vortex in compressible flow. Results for the proposed model are presented as the lift and pressure coefficients along the profile chord for some instants of time. The indicial response (unit step function) of the profile is obtained numerically. The method is also compared with solutions available in the literature. DOI: 10.2514/1.27441

A new analytical solution for self-similar compressible vortices is derived in this paper. Based on the previous incompressible formulation of intense vortices, we derived a theoretical model that includes density and temperature variations. The governing equations are simplified assuming strong vortex conditions. Part of the hydrodynamic problem (mass and momentum) is shown to be analogous to the incompressible kind and as such the velocity is obtained through a straightforward variable transformation. Since all the velocity components are bounded in the radial direction, the density and pressure are then determined by standard numerical integration without the usual stringent simplification for the radial velocity. While compressibility is shown not to affect the tangential velocity, it influences only the meridional flow (radial and axial velocities). The temperature, pressure, and density are found to decrease along the converging flow direction. The traditional homentropic flow hypothesis, often employed in vortex stability and optical studies, is shown to undervalue the density and greatly overestimate the temperature. Comparable to vorticity diffusion balance for the incompressible case, the incoming flow carries the required energy to offset the contributions of conduction, viscous dissipation, and material expansion, thus keeping the temperature steady. This model is general and can be used to obtain a compressible version for all classical previous incompressible analysis from the literature such as Rankine, Burgers, Taylor, and Sullivan vortices. [DOI: 10.1115/1.2746897]

A possible sound emission mechanism of aircraft wake vortices has been identified by using both measurement data and theoretical results. This mechanism relates consistently to a dominant frequency of sound pressure matching the rotation frequency of a Kirchhoff vortex. The rotation of the Kirchhoff vortex is due to the self- induction inside the vortex core. Numerical simulations are necessary for a more realistic wake consisting of a counterrotating vortex pair with inviscid ground effects and shear flow. The simulations are carried out using a vortex particle method. A far-field vortex sound formulation, based on asymptotic expansions, is developed to calculate acoustic pressure from the wake vortices. The simulation results confirm that the frequency of the wake sound emission is essentially the same as the classical Kirchhoff vortex, even under the influences of an inviscid ground effect or a weak-shear cross wind. The aforementioned results suggest that the identified mechanism should be fairly robust, which demonstrates its persistency under several different environmental conditions.

The article studies a model of the vortex paths of the high temperature superconductors (HTS) for measuring the densities of the defects in the substances. The analysis reveals that the fields parallel to the plane of the pinning defects exhibit greater noise in the critical currents.

A simplified inflow model called the 'ring vortex model' is developed for a rotor in descent condition. The ring vortex model accounts for the flow interaction between rotor wake and surrounding airflow in descent flight by using a series of vortex rings along the rotor wake. Important features of the ring vortex model are illustrated in detail, including the convection speed, the vortex strength, and the number of vortex rings. An augmentation to total mass flow parameter in the existing inflow equation is proposed to create a steady-state transition between the helicopter and the windmill branches. With the ring vortex model, it is feasible to predict rotor inflow over a wide range of descent conditions. Numerical results show good correlation with experimental data for both axial and inclined descent. In addition, the ring vortex model is used to explain the influence of model parameters (such as blade twist and blade taper) on rotor-induced velocity during descent flight.

Trailing vortices from a NACA0015 (AR = 5) wing were formed with spanwise tip jets to allow the study of vortex core distortions on the development of vortex size and speed. The wing-tip jets were formed from small holes arranged along the periphery of the wing cross section. Experiments covered a wide range of tip jet blowing rates for a fixed-wing incidence of 5 deg and chord Reynolds number of [10.sup.5]. Measurements of mean velocity, mean vorticity, and turbulence kinetic energy in the wake were made up to 32 chords downwind using hot-wire anemometry. The tip vortex was observed to envelop the jet and subsequently grow in diameter at a substantially higher rate than the vortex formed without tip jets. The circumferential speed of the vortex formed with tip jets was higher in the near field, but declined sharply with downstream distance. At 32 chords downwind, the vortex formed with tip jets evolved into an axisymmetric form similar to a natural vortex, but with a diameter up to three times larger and a peak circumferential velocity three times less. The turbulence intensity measured on the vortex core was 30% in the near wake and 10% at 32 chords downwind.

This paper derives a system of equations that approximately govern small-amplitude perturbations in a nonprecipitating cloudy vortex. The cloud coverage can be partial or complete. The model is used to examine moist vortex Rossby wave dynamics analytically and computationally. One example shows that clouds can slow the growth of phase-locked counter-propagating vortex Rossby waves in the eyewall of a hurricane-like vortex. Another example shows that clouds can (indirectly) damp discrete vortex Rossby waves that would otherwise grow and excite spiral inertia gravity wave radiation from a monotonic cyclone at high Rossby number.

The interactions of pairs of corotating vortex filaments have been investigated experimentally in a water tunnel. The time history of the motion of each filament has been recorded at several downstream locations to analyze its spatial and temporal behavior. Two sets of data are presented in which the vortices have been excited over a range of frequencies using a shaker. The excitation frequency and its multiples have been shown to be present in the downstream flow. At each downstream position, the filaments have been shown to move along preferred directions, suggesting their tendency to form planar waves, inclined relative to the line connecting them. The amplitudes of these waves have been shown to grow, implying unstable interaction between the vortices. The angles of the planes containing the motion have been presented and compared with the predictions of two analytical models. The scatter in the data prevented quantitative comparison with the analytical predictions. However, the flow is shown to contain all of the essential features predicted by two analytical models.

Wind tunnel measurements were done to investigate the effect of leading-edge flaps on the rolling moment characteristics of the cranked arrow wing for the supersonic transport. Static rolling moment measurements, flow visualization studies, and crossflow velocity measurements by a particle image velocimetry were made at Re = 6.2 x [10.sup.4]. Static rolling moment measurements confirmed linear restoring moment at [alpha] < 16deg for the models both with and without flap deflection. When the outboard leading-edge flap is deflected 12 deg, rolling moment hysteresis is observed at the roll angle of [phi] [approximately equal to] 20 deg and [alpha] [approximately equal to] 20 deg. The experimental results indicate that the hysteresis is caused by different vortex breakdown behaviors on the inboard wing when the wing is rotated in the clockwise and counterclockwise directions. DOI: 10.2514/1.21470

This article summarizes the results of an optimization study of a microvortex generator flow control in an inlet. Five parameters optimization was carried out using the classical design of experiment method. Two main objectives were in focus: first, to develop the methodology and skills necessary to conduct a design of experiment optimization study in area of the flow control; and second, to develop the procedures which would be used during design of vortex generator flow control in inlets. New information about the dependency of the vortex generator flow control in inlet on its geometrical parameters were obtained. Several interesting configurations were located. The parameters of optimal settings were then used to set up the vortex generator installation in a generic inlet. DOI: 10.2514/1.21364

The interactions between two corotating vortex filaments of equal strength are investigated analytically. The Biot-Savart law is used to develop the equations of motion of the filaments, consistent with Crow's formulation. Consistent with previous work, two modes of motion are defined and analyzed for stability. It is demonstrated that the mutual induction between the vortices leads to unstable motion of the filaments in the antisymmetric mode over a significant range of frequencies. Furthermore, the oscillatory motion of the filaments is proven to have a preferred direction.

The formation and near-field development of a wing-tip vortex under the influence of freestream turbulence were examined using flow visualization and hot-wire anemometry. A low turbulence freestream as well as two eases of grid turbulence with different intensities and length scales were considered. In all cases, the tip vortex was found to form from three smaller vortices, but the turbulence in its core was found to intensify with increasing freestream turbulence. The vortex trajectory was found to be unaffected by freestream turbulence, but the wing wake that was rolling up around the vortex was observed to have a curvature that decreased as freestream turbulence increased. The mean axial velocity distribution in the low-turbulence case was neither jetlike nor wakelike but had an annular shape. Time-averaged velocity profiles measured in the turbulent freestream cases were wakelike, and it was inferred that the instantaneous profiles would be significantly affected by vortex meandering. Mean circumferential velocity distributions in the vortex core displayed self-similar developments in all eases examined. Finally, it was found that the apparent diffusion in the shear layer shed from the wing increased with increasing freestream turbulence.

The origin of the exact, closed-form, self-similar exponential solution for the laminar decay of an isolated two-dimensional vortex in a viscous incompressible fluid is studied to find a proper name for the function. Two major contributions to the solution are the similarity parameter derived by Boltzmann and the derivation of the form of the solution by Carslaw for the diffusion of heat from a line source, that is, a spark or lightning stroke. Lamb adapted the heat transfer solution derived by Carslaw to the time-dependent diffusion of vorticity from a potential line vortex, and, after publication of his book, has provided a short, complete, and readily available derivation. Oseen's derivation followed about four years later and is not as complete. Various titles for the solution are believed to be appropriate, including a generic name such as exponential vortex solution, or the name of Lamb. The name of Lamb is probably the most appropriate because he was the first in existing literature to put the entire derivation together and because the presentation is compact, complete, and readily available.

Further developments, applications, and assessments of the probabilistic two-phase aircraft wake-vortex model P2P are described. The wake-vortex model is applied to data of two field measurement campaigns accomplished at Tarbes airport, France. Measurements corroborate unambiguously the two-phase circulation decay anticipated by theory and parameterized by P2P Vortex age and descent speed are adjusted to match effects of axial wind and glide-slope angle. Envelopes of vortex trajectories are expanded to consider tilting, stalling, and rebounding wake vortices caused by axial- and crosswind shear. For probabilistic model output a choice between arbitrary degrees of probability is established, and a stochastic prediction mode is introduced. In a deterministic scoring procedure, model perfomance is compared to the skill of another model. Probabilistic model performance is evaluated by the compilation of probability density distributions that relate wake vortex measurement data to the predicted envelopes.

Radar echo images demonstrate that mature tropical cyclones frequently have a concentric eyewall structure, which consists of the inner eyewall, echo-free moat, and outer eyewall regions. Near the inner and outer eyewalls, well-defined wind maxima are generally observed. This indicates that two large vertical vorticity regions exist just inside radii of the two wind maxima near the inner and outer eyewalls. Therefore, the concentric eyewall structure can be considered to be a double vortex composed of the inner vortex and the outer vortex ring. In this study, the contour dynamics model is used on the f plane to analyze the characteristics of flows with either a symmetric double vortex or an asymmetric one, and examined the relationship between the movement of the inner vortex in an asymmetric double vortex and a trochoidal motion of a tropical cyclone with an asymmetric concentric eyewall structure. Results show that, depending on the degree of an interaction of a double vortex, the evolution of the inner vortex is classified into three patterns: the first is that the center of the inner vortex is stationary, which is seen only for the symmetric double vortex; the second is that the track of the center of the inner vortex draws a circle; and the third is that it draws a spiral. A numerical experiment based on an observed flow around Typhoon Herb was also performed. The time evolution of the double vortex is very similar to that of radar echo intensity of Typhoon Herb. Also the rotation period and amplitude of the inner vortex in the numerical experiment were comparable with those of the trochoidal motion in the observation. These suggest that, in tropical cyclones with the concentric eyewall structure, the interaction of an asymmetric double vortex can become a cause of trochoidal motion.

The integral of the vector vorticity equation for the vorticity of a moving parcel in 3D baroclinic flow with friction is cast in a new form. This integral of the vorticity equation applies to synoptic-scale or mesoscale flows and to deep compressible or shallow Boussinesq motions of perfectly clear or universally saturated air. The present integral is equivalent to that of Epifanio and Durran in the Boussinesq limit, but its simpler form reduces easily to Dutton's integral when the flow is assumed to be isentropic and frictionless. The integral for vorticity has the following physical interpretation. The vorticity of a parcel is composed of barotropic vorticity; baroclinic vorticity, which originates from solenoidal generation; and vorticity stemming from frictional generation. Its barotropic vorticity is the result of freezing into the fluid the w field (specific volume times vorticity) that is present at the initial time. Its baroclinic vorticity is the vector sum of contributions from small subintervals of time that partition the interval between initial and current times. In each subinterval, the baroclinic torque generates a small vector element of vorticity and hence w. The contribution to the current baroclinic vorticity is the result of freezing this element of w into the fluid immediately after its formation. The physical interpretation of vorticity owing to frictional generation is identical except the torque is frictional rather than solenoidal. The baroclinic vorticity is decomposed into a part that would occur if the current entropy of the flow were conserved materially backward in time to the initial time and an adjustment term that accounts for production of entropy gradients in material coordinates during this interval. A method for computing all the vorticity parts in an Eulerian framework within a 3D numerical model is outlined. The usefulness of the 3D vorticity integral is demonstrated further by deriving Eckart's, Bjerknes's, and Kelvin's circulation theorems from it in relatively few steps, and by showing that the associated expression for potental vorticity is an integral of the potential vorticity equation and implies conservation of potential vorticity for isentropic frictionless motion of clear air (Ertel's theorem). Last, a formula for the helicity density of a parcel is obtained from the vorticity integral and an expression for the parcel's velocity, and is verified by proving that it is an integral of the equation for helicity density.

In Part I, a general integral of the 2D vorticity equation was obtained. This is a formal solution for the vorticity of a moving tube of air in a 2D unsteady stratified shear flow with friction. This formula is specialized here to various types of 2D flow. For steady inviscid flow, the integral reduces to an integral found by Moncrieff and Green if the flow is Boussinesq and to one obtained by Lilly if the flow is isentropic. For steady isentropic frictionless motion of clear air, several quantities that are invariant along streamlines are found. These invariants provide another way to obtain Lilly's integral from ] the general integral.

A new vortex-generator model is introduced, the jBAY model, which provides an efficient method flit computational-fluid-dynamics (CFD) simulation of flow systems with vortex-generator arrays. The jBAY model is based on the lifting force theory of Bender, Anderson, and Yagle (Bender, E. E., Anderson, B. H., and Yagle, P. J., 'Vortex Generator Modelling for Navier-Stokes Codes,' American Society of Mechanical Engineers, FEDSM 99-6919, New York, July 1999) but uses a novel technique for defining the model control points. This greatly simplifies usage of the model as well as improving its performance and accuracy. The jBAY model is described in the context of its implementation in the CFD code Edge, an unstructured Reynolds-averaged Navier-Stokes solver. Results are presented for a single vortex generator on a flat plate and two flow control eases: an S-duct air intake and a high-lift wing configuration. The model is shown to give good agreement with both experimental results and with CFD computations where the vortex generator is fully gridded. It is demonstrated that the jBAY model is simple to apply and efficiently captures the effect of vortex generator arrays for both internal and external flows.

The relative importance of interactions between deformation and potential vorticity (PV) as a blockonset mechanism is examined in 30 cases of atmospheric blocking over the Southern Hemisphere (SH). The blocking cases are diagnosed with a quasigeostrophic model for the u component of the geostrophic wind tendency. In this model, two mechanisms, the advection of the meridional gradient of PV and interactions between deformation and PV, can force the weakening of westerly flow or increasing easterly flow associated with blocking. The first forcing mechanism, which does not directly include deformation, indicates that the advection of equatorward increasing cyclonic PV (or equatorward decreasing anticyclonic PV) could force a local weakening of geostrophic westerlies or increasing easterlies. The second forcing mechanism, which represents the net effect of interactions between deformation and PV, indicates that eastward increasing PV embedded in a cyclonically sheared flow or equatorward increasing PV coincident with a stretching (diffluent) flow could each force a weakening in the westerlies. While deformation is a distinct signature of blocking, it may not always actively participate in the formation of blocking. Advection and interaction contributions generally opposed each other in both the diagnosed blocking and nonblocking cases. Weakening westerlies associated with block onset would occur when one effect (usually the advection effect) contributes more negatively to the wind tendency than the opposing, positive contribution from the other effect. When deformation is actively involved in the formation of blocking, self-interactions between synoptic-scale PV and deformation and self-interactions between planetary-scale PV and deformation contribute more importantly than synoptic-to-planetary-scale interactions between PV and deformation fields to the weakening of westerlies associated with block onsets.

This is the first in a three-part series of papers that present the first applications of principal component analysis (PCA) to Doppler radar data. Although this novel approach has potential applications to many types of atmospheric phenomena, the specific goal of this series is to describe and verify a methodology that establishes the position and radial extent of the core region of atmospheric vortices. The underlying assumption in the current application is that the streamlines of the nondivergent component of the horizontal wind are predominantly circular, which is a characteristic often observed in intense vortices such as tropical cyclones. The method employs an [S.sup.2]-mode PCA on the Doppler velocity data taken from a single surveillance scan and arranged sequentially in a matrix according to the range and azimuth coordinates. Part I begins the series by examining the eigenvectors obtained from such a PCA applied to a Doppler velocity model for a modified, Rankine-combined vortex, where the ratio of the radius of maximum wind to the range from the radar to the circulation center is varied over a wide range of values typically encountered in the field. Results show that the first two eigenvectors within the eigenspace of range coordinates represent over 99% of the total variance in the data. It is also demonstrated that the coordinates of particular cusps in the curves of the eigenvector coefficients plotted against their indices are geometrically related to both the position of circulation center and the radius of maximum wind.

A series of numerical simulations of dry, axisymmetric hurricane-like vortices is performed to examine the growth of barotropic and baroclinie eddies and their potential impacts on hurricane core structure and intensity. The numerical experiments are performed using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research (PSU-NCAR) Mesoscale Model (MM5) with a 6-km horizontal grid. To examine internal effects on the stability of vortices, all external forcings are eliminated. Axisymmetric vortices that resemble observed hurricane structures are constructed on an f plane, and the experiments are performed without moist and boundary layer processes. Three vortices are designed for this study. A balanced control vortex is built based on the results of a full-physics simulation of Hurricane Floyd (1999). Then, two other axisymmetric vortices, EXP-1 and EXP-2, are constructed by modifying the wind and mass fields of the control vortex. The EXP-I vortex is designed to satisfy the necessary condition of baroclinic instability, while the EXP-2 vortex satisfies the necessary condition of barotropic instability. These modified vortices are thought to lie within the natural range of structural variability of hurricanes. The EXP-1 and EXP-2 vortices are found to be unstable with respect to small imposed perturbations, while the control vortex is stable. Small perturbations added to the EXP-1 and EXP-2 vortices grow exponentially at the expense of available potential energy and kinetic energy of the primary vortex, respectively. The most unstable normal modes of both vortices are obtained via a numerical method. The most unstable mode of the EXP-1 (baroclinically unstable) vortex vertically tilts against shear, and the maximum growth occurs near a height of 14 km and a radius of 20 km. On the other hand, the most unstable normal mode of the EXP-2 (barotropically unstable) vortex has horizontal tilting against the mean angular velocity shear, and the maximum perturbations are located at a lower altitude (around 4 km) and at larger radius (around 100 km). Despite these differences, the normal modes of both vortices have a wavenumber-1 structure. The energy budget analysis shows that the growing baroclinic and barotropic perturbations have opposite effects on the vortex intensity in terms of kinetic energy. Baroclinic eddies strengthen, whereas barotropic eddies weaken, the primary vortex. It is hypothesized that fluctuations in hurricane core structure and intensity can occur due to eddy processes triggered by alternating periods of barotropic and baroclinic eddy growth in the core. Once formed, these eddies may interact with the intense diabatic energy sources in real hurricanes. A similar study of eddy behaviors in a more realistic hurricane, which includes moist and boundary layer processes and uses a finer grid mesh, will be the topic of Part II.

This study provides a preliminary, but concrete, assessment of the potential benefits of causing the breakup of airplane trailing vortices via large-scale instability, resulting in vortex rings. The 737-300 flight simulator is used to model the autopiloted response of an airplane encountering the vortices at different stages in the breakup process. A series of encounters with straight vortices is used to establish a baseline response. For the early stages of the vortex breakup, the vortices are modeled as wavy vortex filaments. For the late stages of the vortex breakup, the vortices are modeled as vortex rings, whose shape is based on experimental observation. The primary results of the study are presented in a collection of contour plots for the maximum bank angle that occurs during an encounter. The bank angles are given as a function of the horizontal and vertical vortex-intercept angles. The results show a significant reduction in the maximum bank angle, experienced by the encountering airplane, as a result of the vortex breakup. The simulations show a continuous reduction in the level of upset as the vortices become increasingly wavy and ultimately break up into rings. The most significant reductions (both in terms of the magnitudes of the upset and the likelihood of their occurrence) result from the formation of vortex rings. The results suggest that the controlled breakup of the vortices could be exploited to enable reduced airplane separations, based on a vortex-destruction concept in addition to vortex avoidance.

Shear layers shed by aircraft wings roll up into vortices. A similar, though far less common, phenomenon can occur in the wake of a turbomachine blade. This paper presents experimental data from a new single-stage turbine that has been commissioned at the Whittle Laboratory. Two low-aspect ratio stators have been tested with the same rotor row. Surface flow visualization illustrates the extremely strong secondary flows present in both NGV designs. These secondary flows lead to conventional passage vortices, but also to an intense vortex sheet which is shed from the trailing edge of the blades. Pneumatic probe traverses show how this sheet rolls up into a concentrated vortex in the second stator design, but not in the first. A simple numerical experiment is used to model the shear layer instability and the effects of trailing edge shape and exit yaw angle distribution are investigated. It is found that the latter has a strong influence on shear layer rollup: inhibiting the formation of a vortex downstream of NGV 1 but encouraging it behind NGV 2. [DOI: 10.1115/1.1545766]

Keywords: Inertial instability; eccentrically cyclogeostrophic current; natural coordinates; parcel method; virtual deflection; instability frequency; ring; subsolid rotation; supersolid rotation; zero potential vorticity Abstract: Using natural coordinates, we have derived a criterion for the inertial instability of arbitrarily meandering currents. Such currents, governed by the eccentrically cyclogeostrophic equation, are adopted as the basic current field for the parcel method. We assume that any virtual displacement which is given to a water parcel moving in the basic field has no influence on this field. From the conservation of mechanical energy for a virtual displacement we derive an inertial instability frequency [omega].sub.m = [(f + 2u/r)Z].sup.0.5 for the eccentrically cyclogeostrophic current, where f is the Coriolis parameter, u the velocity (always positive), r the radius of curvature of a streamline (negative for an anticyclonic meander), and Z the vertical component of absolute vorticity. If [omega].sub.m .sup.2 is negative, the eccentrically cyclogeostrophic current becomes unstable. Although the conventional, centrifugal instability criterion, derived from the conservation of angular momentum in a circularly symmetric current field, has a certain meaning for a monopolar vortex, it contains a radial shear vorticity that is difficult to use in arbitrarily meandering currents. The new criterion [omega].sub.m .sup.2 contains a lateral shear vorticity that is applicable to arbitrarily meandering currents. Examining instabilities of concentric rings with radii of 50--100 km, we consider reasons why the anticyclonic supersolid rotation has been very much less frequently observed than the cyclonic supersolid rotation, despite a prediction of some common stability and a rapid change in radial velocity gradient for the former. Classifying eccentric streamlines into the large and small curvature-gradient types, we point out that the large-gradient curvature in anticyclonic rings is apt to be unstable. Article History: Registration Date: 06/10/2004

A Wells turbine for wave power conversion has hysteretic characteristics in a reciprocating flow. The counterclockwise hysteretic loop of the Wells turbine is opposite to the clockwise one of the well-known dynamic stall of an airfoil. In this paper, the mechanism of the hysteretic behavior was elucidated by an unsteady three-dimensional Navier-Stokes numerical simulation. It was found that the hysteretic behavior was associated with a streamwise vortical flow appearing near the blade suction surface. In the accelerating process of axial flow velocity, the vortex is intensified to enlarge the flow separation area on the blade suction surface. In the decelerating flow process, the flow separation area is reduced because of the weakened vortex. Therefore, the aerodynamic performance in the accelerating flow process is lower than in the decelerating flow process, unlike the dynamic stall. Based on the vortex theorem, the mechanism to vary the intensity of the vortex can be explained by the trailing vortices associated with the change in the blade circulation.

This paper presents a study of the three-dimensional flow field within the blade rows of a high-pressure axial flow steam turbine stage. Compound lean angles have been employed to achieve relatively low blade loading for hub and tip sections and so reduce the secondary losses. The flow field is investigated in a low-speed research turbine using pneumatic and hot-wire probes downstream of the blade row. Steady and unsteady numerical simulations were performed using structured 3-D Navier-Stokes solver to further understand the flow field. Agreement between the simulations and the measurements has been found. The unsteady measurements indicate that there is a significant effect of the stator flow interaction in the downstream rotor blade. The transport of the stator viscous flow through the rotor blade row is described. Unsteady numerical simulations were found to be successful in predicting accurately the flow near the secondary flow interaction regions compared to steady simulations. A method to calculate the unsteady loss generated inside the blade row was developed from the unsteady numerical simulations. The contribution of various regions in the blade to the unsteady loss generation was evaluated. This method can assist the designer in identifying and optimizing the features of the flow that are responsible for the majority of the unsteady loss production. An analytical model was developed to quantify this effect for the vortex transport inside the downstream blade.

If a cyclonic vortex is bounded by a zero isotach surrounding its center at some radius, it is inevitably accompanied by negative vorticity regions somewhere within it. Since the radial gradient of vorticity changes its sign at the negative vorticity regions, it is thought to cause instability of the vortex and the resultant secondary circulation. It is attempted to attribute the origin of the oscillatory motion and/or the multiple structure observed in natural vortices to this instability. For this purpose, a simple axisymmetric vortex having a negative vorticity region between the solidly rotating core and a potentially rotating outer part is assumed, and its linear stability to asymmetric disturbances is examined with a quasigeostrophic model. The results indicate that the disturbances with azimuthal wavenumber m [greater than or equal to] 1 are destabilized under certain conditions. The most unstable mode changes from an internal disturbance for m = 1 to an internal or an external disturbance for m [greater than or equal to] 2 dependent on the magnitude and width of the negative vorticity region. Such effects of the negative vorticity may be relevant to the formation of the oscillatory motion and the multiple structures of natural vortices.

A wake-dominated unsteady flow of Mach number 0.2 past a cone of vertex angle 60 deg is calculated numerically using high-order finite difference schemes on structured grids. The three-dimensional compressible Euler equations are solved to simulate an inviscid flow that exhibits large fluctuations of pressure and velocity as a result of the shedding of vortices behind the cone. An axisymmetric structured grid system is used. It is generated by rotating a two-dimensional grid plane around a centerline. The grid singularity at the centerline, where the Jacobian and some grid metrics approach infinity, is avoided by changing the form of the flux vectors in the Euler equations without any asymptotic assumption or simplification. Fourth- and sixth-order finite difference schemes are used for the evaluation of spatial derivatives, and a fourth-order Runge-Kutta scheme is used for marching the solution in time. The complex wake structures and motions behind the cone are investigated by visualizing the vorticity field. The mean flow pattern and periodic phenomena are analyzed and compared with experimental data. This demonstrates the accuracy of the present approach to further analyses of wake-dominated flows past axisymmetric blunt-based bodies.

A two-dimensional Euler flow solver has been developed for the simulation of unsteady, blade--vortex interaction problems on unstructured meshes. The Euler solver is based on a second-order-accurate implicit time integration using a point Gauss--Seidel relaxation scheme and a dual time-step subiteration. A vertex-centered, finite volume discretization is used in conjunction with the Roe's flux-difference splitting. An Unsteady solution-adaptive dynamic mesh scheme is used by adding and deleting mesh points at every adaptation step to take account of not only spatial but also of temporal variations of the flowfield. Unsteady flow around a harmonically oscillating airfoil and traveling vortex in a freestream were simulated to validate the accuracy of the dynamic mesh adaptation procedure. Three blade--vortex interaction problems, two at transonic freestream speeds and one with vortex--airfoil collision, were investigated. Computed results show good agreements with existing experimental and computational results within the accuracy of the present inviscid solver. It is found that the evolution of vorticies and propagation of acoustic waves can be accurately simulated using the present unstructured dynamic mesh adaptation procedure.