Significant Vorticity Research Articles

Cold pools in shear

AbstractGravity currents exist in many forms and develop within many types of flow. The dynamics of long‐lived cumulonimbus are thought to be strongly influenced by the interaction of a spreading pool of cold, low‐level air, which may act as a gravity current, and the ambient sheared flow in the boundary layer. In interpreting two‐ and three‐dimensional numerical models of such phenomena, the behaviour of the vorticity dynamics in the ambient flow and the spreading cold air is commonly discussed. In order to investigate these vorticity ideas from a gravitycurrent perspective, three‐dimensional numerical simulations have been performed in which a cold pool spreads from an isolated source in the presence of a horizontal flow that is sheared with height. It has been found that the shear of the incoming ambient flow does not qualitatively alter the horizontal spread of the cold pool, and that the location of the region of maximum horizontal convergence remains on the along‐wind axis: the actual strength of the ambient wind, which is shown analytically to be measured by the wind strength at the head height, has a greater bearing on the cold‐pool shape than the shear. Consequently, it must be the details of the moist convection which play a crucial role in determining the cold pool's development in sheared flows. As such, this model is a general indication of the robustness of gravity‐current theory, even in the presence of mean shear. The vortex structure on the flanks of the spreading cold air is found to be significantly modified, with a reversal in the dominant sign of vorticity and an increase in its intensity, when such mean shear exists.

On the nature of vortex interactions and models in unforced nearly-inviscid two-dimensional turbulence

A powerful feature-tracking tool is applied to several high-resolution, very long-duration, regularized contour dynamics (contour surgery) simulations of unforced nearly-inviscid two-dimensional turbulence (2DT) on the surface of a sphere. Particularly low density gases of vortices (i.e. on average, very widely separated vortices) are examined to ascertain the nature of their interactions. The simplest (minimal) model system is studied, namely a set of vortex patches of just two vorticity values, ±ω0, whose total circulation is zero. The areas of the patches are selected initially from a pre-assigned, stable (nearly time invariant) power-law distribution. When the vorticity occupation fraction f≳0.01, often more than three vortices are found relatively close together at the onset of a strong interaction. But, when f≲0.01, all such interactions involve only three nearby vortex patches, not all having the same sign of vorticity. This is related to the well-known collapse of three singular (point) vortices. Thus, under these conditions, isolated two-vortex interactions, which have figured in recent ad hoc theories and models for decaying 2DT, cannot occur. Taking into account these results, we propose an asymptotically-motivated and computationally-efficient ‘‘reduced’’ model.

Vorticity Concentration at the Edge of the Inboard Vortex Sheet

Flow visualization and velocity measurements are used to show that the outer edge of the trailing vortex sheet from an untwisted rotor blade rolls up into a discrete vortical structure which is opposite in sense and comparable in strength to the tip vortex. This occurs both in hover and forward flight, and at both upstream and downstream edges of the wake in forward flight. The roll-up process and the trajectories of the tip vortex and the counterrotating vortex are examined using digitized laser sheet video images. Azimuth-resolved velocity data, obtained under an isolated, two-bladed teetering rotor in a wind tunnel at low advance ratio, are used to quantify vortex strengths. INTRODUCTION Figure 1 shows the classical model of the rotor wake in hover, developed from the early experimental work of Gray1 and Landgrebe2. The wake is dominated by the tip vortices, which concentrate vorticity in small core regions, and carry a large amount of kinetic energy with them. Early attempts to model the behavior of the rotor wake used simple models of the velocity field induced by these vortices. To get better accuracy in modeling the wake and the loads on the rotor blades, it was found necessary to include the vorticity trailed 1: Graduate Research Assistant. Member, AHS 2: Associate Professor. Member, AHS 3: Post-Doctoral Fellow. member, AHS behind the blade in a thin shear layer, which can be modeled as an vortex There is also some rollup of vorticity at the hub into a root vortex; however, this contains relatively little kinetic energy. Examination of Figure 1(a) shows that the outer edge of the vortex sheet moves down faster than the corresponding tip vortex. This can be seen by considering the signs of vorticity of the tip vortex and the vortex sheet, as shown in Figure 1(b). Unlike the circulation distribution of a fixed wing, the bound circulation of the rotating blade generally peaks well inboard of the tip, so that the sign of DΓ/Dr changes. Thus, the tip vortex leaves the blade with a sense of rotation opposite to that of the inboard vortex sheet. Mutual induction between the tip vortex and the vortex sheet must thus inhibit the downward motion of the tip vortex, and accelerate that of the edge of the sheet. Figure 1 was developed by detailed observation of patterns formed by clouds of microscopic particles, illuminated by strobed lights or continuous lights. The patterns were captured using cameras with short shutter exposure times. The figure leaves unspecified the continuity between the tip vortex and the vortex sheet. This aspect of the rotor wake is the subject of this paper. Early experimental investigations of the rotor wake were motivated by pursuit of precise rotor performance prediction. Gray1 modeled the rotor wake by a tip vortex filament and an inboard vortex sheet composed of several vortex filaments based on the visualization of a single-bladed rotor in hover. In his experiments, the visible portions of the inboard vortex sheet and the tip vortex were not close enough to permit observation of the phenomena at the junction. Distortion of the inboard vortex sheet was not observed in the visualization. Landgrebe et al.2 extended such models to multi-bladed rotors. The interaction between the vortex sheet and the tip vortex was neglected and consequently the inboard vortex sheet was prescribed as a rigid sheet of distributed vorticity fixed to the spatial locations of blade passage. Later vortex modeling of prescribed wake analysis for the rotor wake in hover3 or in forward flight4 also treated the inboard vortex sheet as an undistorted sheet of vortex filaments. These models contributed to a very large

鉛直シアーを持った基本流における、熱帯加熱によって励起される外部モードとその伝播

The generation of the external-mode ("barotropic" mode) motions from the internal-mode ("baroclinic„ mode) motions which are directly forced by stationary tropical heating is investigated with a two-level global model. The equations are linearized with respect to a solid-body rotation basic flow with vertical shear. We examine in detail the effect of this vertical shear which permits the coupling of the external mode with the internal mode. First, we determine the internal-mode motions forced by internal heating; second, from the vertical shear of the basic flow and the internal-mode motions, we determine the external-mode motions. In this treatment the equations governing internal and external modes can be reduced to the shallow water equations with different values of equivalent depth.The results show that the amplitude of the external mode induced in this way is smaller than that of the internal mode in the tropics, but becomes predominant in the extra-tropics. The external-mode wavetrains emanating northeastward and southeastward from the localized heating region are formed. These wavetrains extend to the antipodes of the emanating region. We examine respective effects of the several terms which express the excitation of the external mode from the coupling between the internal mode and the vertical shear of the basic flow. It is found that the term which expresses an advection of internal-mode vorticity by the basic flow with vertical shear is the most important. By a speculation concerning this forcing term and an inspection of the result of the numerical calculation, we examine in detail the sign of vorticity of the external-mode motions in the region where the internal mode has a large amplitude.Further, we examine the effects of the differential damping and the Ekman pumping on the excitation of the external mode.The external-mode wavetrains are formed by these effects also. The sign of the vorticity of the external-mode motions in the heating region is discussed.

Flame Generation of Vorticity: Vortex Dipoles from Monopoles

Abstract Numerical simulation of premixed flame propagation through a two-dimensional vorticity distribution exhibits the coupling between combustion heat release and fluid dynamics. Effects of both thermal expansion and vorticity generation via baroclinic torques are considered. The rotational part of the velocity field is described by discrete vorticity. The irrotational velocity. given by a velocity potential. is determined by a Poisson equation where the chemical reaction determines the spatial distribution of volume expansion. The transport of a single reacting scalar is computed on an Eulerian mesh with a small-Mach-number flow assumption so that the density gradient is nonzero only within the reaction zone. The vector cross product of density gradient and pressure gradient defines the baroclinic generation of vorticity. With a single initial vortical region-the monopole interacting with a premixed flame-the baroclinic effect produces opposite circulation, and thus. creates a dipole configuration. We use the dipole description in a loose sense. because in some solutions the two signs of vorticity are spatially intermingled. However. in comparison to the monopole. the "dipole" solution has stronger local velocity fluctuations but weaker long-range velocities. Thus, the turbulence in the burnt gas is more intense with smaller length scales than the configuration before the flame-vortex interaction.

Three-dimensional shear layers via vortex dynamics

The evolution of the two- and three-dimensional structures in a temporally growing plane shear layer is numerically simulated with the discrete vortex dynamics method. We include two signs of vorticity and thus account for the effect of the weaker boundary layer leaving the splitter plate which is used to create a spatially developing mixing layer. The interaction between the two layers changes the symmetry properties seen in a single vorticity-layer calculation and results in closer agreement with experimental observations of the interface between the two streams. Our calculations show the formation of concentrated streamwise vortices in the braid region between the spanwise rollers, whereas the spanwise core instability is observed to grow only initially. Comparison with flow visualization experiments is given, and we find that the processes dominating the early stages of the mixing-layer development can be understood in terms of essentially inviscid vortex dynamics.

中規模渦の数値実験と木星南熱帯撹乱

Numerical experiments are carried out by using the Yamagata-Flierl equation for eddies of a scale intermediate between the Rossby deformation radius and the beta-scale. These experiments are performed for two types of zonal flows, one has a linear shear and the other is sinusoidal velocity profile along meridian. Through these experiments, we tried to investigate the motion and the life time of the intermediate scale eddies in the cases of linear shear zonal flow, and attempted to compare the results with the development of the South Tropical Disturbance (STrD) observed in 1979-81 on Jupiter for the cases of sinusoidal velocity profile.From the experiments for the case of linear shear flow, we found the following facts.(1) If the eddy and zonal flow have the same sign of vorticity, the eddy can survive stably. If the eddy and zonal flow have the opposite sign of vorticity, the eddy disappears or is deformed remarkably. (2) In the case of uniform zonal flow, a cyclonic eddy can survive stably in a high speed westward flow, whereas an anticyclonic eddy can survive in a low speed westward flow. When the westward zonal flow has the non-dispersive wave velocity, both cyclonic and anticyclonic eddies can survive stably. (3) In a low speed westward flow, a cyclonic eddy shifts poleward and an anticyclonic one equatorward. In a high speed westward flow, a cyclonic eddy shifts equatorward and an anticyclonic one poleward. (4) Anticyclonic eddies move westward with higher speed than that of non-dispersive wave. On the other hand, many of cyclonic eddies move westward with lower speed. In one of our experiments for the sinusoidal velocity profile, a cyclonic eddy, whose radius is comparable to the latitudinal width of the westward jet, can go poleward through this jet, and is elongated in northeast and southwest direction in the northern hemisphere before it disappears. The STrD seems to be this kind of cyclonic eddy, because the STrD also had cyclonic vorticity and developed poleward, and because the STrD also was elongated in the same direction as our results. The life time and longitudinal motion of this eddy is not consistent with those of the STrD, but through collisions with small vortices the STrD may get a long life time.