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NASA NTRS1987

The fully nonlinear development of Goertler vortices in growing boundary layers

The fully nonlinear development of small wavelength Goertler vortices in a growing boundary layer is investigated using a combination of asymptotic and numerical methods. The starting point for the analysis is the weakly nonlinear theory of Hall (1982b) who discussed the initial development of small amplitude vortices in a neighborhood of the location where they first become linearly unstable. That development is unusual in the context of nonlinear stability theory in that it is not described by the Stuart-Watson approach. In fact the development is governed by a pair of coupled nonlinear partial differential evolution equations for the vortex flow and the mean flow correction. Here the further development of this interaction is considered for vortices so large that the mean flow correction driven by them is as large as the basic state. Surprisingly it is found that such a nonlinear interaction can still be described by asymptotic means. It is shown that the vortices spread out across the boundary layer and effectively drive the boundary layer. In fact the system obtained by writing down the equations for the fundamental component of the vortex generate a differential equation for the basic state. Thus the mean flow adjusts so as to make these large amplitude vortices locally neutral. Moreover in the region where the vortices exist the mean flow has a square-root profile and the vortex velocity field can be written down in closed form. The upper and lower boundaries of the region of vortex activity are determined by a free-boundary problem involving the boundary layer equations. In general it is found that this region ultimately includes almost all of the original boundary layer and much of the free-stream. In this situation the mean flow has essentially no relationship to the flow which exists in the absence of the vortices.

Hall, Philip↗

NASA NTRS1994

Numerical simulation of baroclinic Jovian vortices

We examine the evolution of baroclinic vortices in a time-dependent, nonlinear numerical model of a Jovian atmosphere. The model uses a normal-mode expansion in the vertical, using the barotropic and first two baroclinic modes. Results for the stability of baroclinic vortices on an f plane in the absence of a mean zonal flow are similar to results of Earth vortex models, although the presence of a fluid interior on the Jovian planets shifts the stability boundaries to smaller length scales. The presence of a barotropic mean zonal flow in the interior stabilizes vortices against instability and significantly modifies the finite amplitude form of baroclinic instabilities. The effect of a zonal flow on a form of barotropic instability produces periodic oscillations in the latitude and longitude of the vortex as observed at the level of the cloud tops. This instability may explain some, but not all, observations of longitudinal oscillations of vortices on the outer planets. Oscillations in aspect ratio and orientation of stable vortices in a zonal shear flow are observed in this baroclinic model, as in simpler two-dimensional models. Such oscillations are also observed in the atmospheres of Jupiter and Neptune. The meridional propagation and decay of vortices on a beta plane is inhibited by the presence of a mean zonal flow. The direction of propagation of a vortex relative to the mean zonal flow depends upon the sign of the meridional potential vorticity gradient; combined with observations of vortex drift rates, this may provide a constraint on model assumption for the flow in the deep interior of the Jovian planets.

Achterberg, Richard K.↗

NASA NTRS1995

Gaseous Vortices in Barred Spiral Galaxies

During the course of examining many two-dimensional, as well as a smaller sample of three-dimensional, models of gas flows in barred spiral galaxies, we have been impressed by the ubiquitous presence fo vortex pairs, oriented roughly perpendicular to their bars, with one vortex on each side. The vortices are obvious only when viewed in the bar frame, and the centers of their velocity fields usually are near Lagrangian points L(sub 4,5). In all models that we have studied, the vortices form on essentially the same time scale as that for the development of gaseous spiral arms, typically two bar rotations. Usually the corotation radius, r(sub c), lies slightly beyond the end of the bar. Depending upon the mass distributions of the various components, gas spirals either into, or out of, the vortices: In the former case, the vortices become regions of high density, whereas the opposite is true if the gas spirals out of a vortex. The models described in this paper have low-density vortices, as do most of the models we have studied. Moreover, usually the vortex centers lie approximately within +/- 15 deg of L(sub 4,5). In the stellar dynamic limit, when pressure and viscous forces are absent, short-period orbits exist, centered on L(sub 4,5). These orbits need not cross and therefore their morphology is that of gas streamlines, that is, vortices. We believe that the gas vortices in our models are hydrodynamic analogues of closed, short-period, libration orbits centered on L(sub 4,5).

England, Martin N.↗

NASA NTRS1996

Spanwise Spacing Effects on the Initial Structure and Decay of Axial Vortices

The initial structure and axial decay of an array of streamwise vortices embedded in a turbulent pipe boundary layer is experimentally investigated. The vortices are shed in counter-rotating fashion from an array of equally-spaced symmetric airfoil vortex generators. Vortex structure is quantified in terms of crossplane circulation and peak streamwise vorticity. Flow conditions are subsonic and incompressible. The focus of this study is on the effect of the initial spacing between the parent vortex generators. Arrays with vortex generators spaced at 15 and 30 degrees apart are considered. When the spacing between vortex generators is decreased the circulation and peak vorticity of the shed vortices increases. Analysis indicates this strengthening results from regions of fluid acceleration in the vicinity of the vortex generator array. Decreased spacing between the constituent vortices also produces increased rates of circulation and peak vorticity decay.

Wendt, B. J.↗

NASA NTRS2006

MHD Flow Visualization of Magnetopause and Polar Cusps Vortices

Detailed analysis of Wind, Geotail, and Cluster data shows how magnetopause boundary and polar cusps vortices associated with high speed streams can be a carrier of energy flux to the Earth s magnetosphere. For our analysis time interval, March 29 . - April 5 2002, the Interplanetary Magnetic Field (IMF) is primarily northward and MHD simulations of vortices along the flanks within nine hours of the time interval suggest that a Kelvin Helmholtz (KH) instability is likely present. Vortices were classified by solar wind input provided by the Wind satellite located 70-80 RE upstream from Earth. We present statistics for a total of 304 vortices found near the ecliptic plane on the magnetopause flanks, 273 with northward IMF and 31 with southward IMF. The vortices generated under northward IMF were more driven into the dawnside than into the duskside, being substantially more ordered on the duskside. Most of the vortices were large in scale, up to 10 RE, and with a rotation axis closely aligned with the ZGSE direction. They rotated preferentially clockwise on the dawnside, and. counter-clockwise on the duskside. Those generated under southward IMF were less ordered, fewer in number, and also smaller in diameter. Significant vortex activity occurred on the nightside region of the magnetosphere for these southward cases in contrast to the northward IMF cases on which most of the activity was driven onto the magnetopause flanks. Magnetopause crossings seen by the Geotail spacecraft for the time interval were analyzed and compared with the MHD simulation to validate our results. Vortices over the polar cusps are also being analyzed and the simulation results will be compared to the multi-point measurements of the four Cluster satellites.

Collado-Vega, Y. M.↗

NASA NTRS2007

MHD Flow Visualization of Magnetopause and Polar Cusps Vortices

Detailed analysis of Wind, Geotail, and Cluster data shows how magnetopause boundary and polar cusps vortices associated with high speed streams can be a carrier of energy flux to the Earth's magnetosphere. For our analysis time interval, March 29 . - April 5 2002, the Interplanetary Magnetic Field (IMF) is primarily northward and MHD simulations of vortices along the flanks within nine hours of the time interval suggest that a Kelvin Helmholtz (KH) instability is likely present. Vortices were classified by solar wind input provided by the Wind satellite located 70-80 RE upstream from Earth. We present statistics for a total of 304 vortices found near the ecliptic plane on the magnetopause flanks, 273 with northward IMF and 31 with southward IMF. The vortices generated under northward IMF were more driven into the dawnside than into the duskside, being substantially more ordered on the duskside. Most of the vortices were large in scale, up to 10 RE, and with a rotation axis closely aligned with the Z(sub GSE) direction. They rotated preferentially clockwise on the dawnside, and. counter-clockwise on the duskside. Those generated under southward IMF were less ordered, fewer in number, and also smaller in diameter. Significant vortex activity occurred on the nightside region of the magnetosphere for these southward cases in contrast to the northward IMF cases on which most of the activity was driven onto the magnetopause flanks. Magnetopause crossings seen by the Geotail spacecraft for the time interval were analyzed and compared with the MHD simulation to validate our results. Vortices over the polar cusps are also being analyzed and the simulation results will be compared to the multi-point measurements of the four Cluster satellites.

Collado-Vega, Y. M.↗

NASA NTRS1986

Numerical studies of the margin of vortices with decaying cores

The merging of vortices to a single one is a canonical incompressible viscous flow problem. The merging process begins when the core sizes or the vortices are comparable to their distances and ends when the contour lines of constant vorticity lines are circularized around one center. Approximate solutions to this problem are constructed by adapting the asymptotic solutions for distinct vortices. For the early stage of merging, the next-order terms in the asymptotic solutions are added to the leading term. For the later stage of merging, the vorticity distribution is reinitialized by vortices with overlapping core structures guided by the 'rule of merging' and the velocity of the 'vortex centers' are then defined by a minimum principle. To show the accuracy of the approximate solution, it is compared with the finite-difference solution.

Liu, G. C.↗

NASA NTRS1986

Quasi-instantaneous transverse vorticity measurements in an excited, two-dimensional, single stream mixing layer

Quasi-instantaneous transverse vorticity time series were obtained with a four-wire array at each of the 414 points in the measurement grid. These vorticity measurements indicate absolute values of peak vorticity which are an order of magnitude greater than those indicated by phase averaged transverse vorticity measurements. These large quasi-instantaneous transverse vorticity fluctuations indicate strong mixing throughout the core and periphery of the newly formed and saturated vortical structures. Although the magnitude is approximately the same throughout these structures, the frequency of occurrence of these large fluctuations appears to be less on the low speed side of the newly formed vortex.

Disimile, P. J.↗

NASA NTRS1986

Interaction of decaying trailing vortices in ground shear

The drift of trailing vortices in a cross wind near to the ground is modeled by an unsteady, two-dimensional, rotational flowfield with a concentration of large vorticity in spots having finite total strength. The problem is analyzed by a combination of the method of matched asymptotic analyses for the decay of the vortical spots and the Euler solution for the unsteady rotational flow. A primary feature of the numerical scheme is that the grid size and time step depend only the length and velocity scales of the background flow and is independent of the effective core size of a vortical spot which can be much smaller than the grid size. Numerical results are presented to demonstrated the strong interaction between the trajectjories of the vortical spots and the redistribution of vorticity in the background flowfield.

Liu, C. H.↗

NASA NTRS1987

Three-dimensional vortical structures of transition in plane channel flow

Three-dimensional visualization of flwo field structures in transitional plane channel flow obtained from a numerical simulation are presented at two Reynolds numbers. It is revealed that at the one-spike stage, independent of Reynolds number, the flow is characterized by a multi-layer vortex system. In the upper layer, total vorticity vector plots indicate a high-shear layer dominated by spanwise vorticity, whereas the middle layer (corresponding approximately to the critical layer) forms a vortex loop (alpha-vortex) consisting of strong streamwise and spanwise vorticity components. At the three-spike stage, the breakdown of the vortical structure proceeds in a manner similar to frontal relaminarization of turbulent spots. This process is accompanied by intense vortex lift-up activity near the wall which seems to originate at the legs of the vortex loop trailing the high-shear layer. Finally, at the five-spike stage, it is shown that high-vorticity regions (vortical structures) develop into horseshow eddies in planes inclined to the main flow direction.

Biringen, S.↗

NASA NTRS1988

Graphical representation of three-dimensional vortical flows by means of helicity density and normalized helicity

The helicity density and normalized helicity are introduced as important tools for the graphical representation of three-dimensional flowfields that contain concentrated vortices. The use of these two quantities filters out the graphical representation of the flowfield regions of low vorticity, as well as regions of high vorticity but low speed where the angle between the velocity and vorticity vectors is large (such as in the boundary layer). Their use permits the researcher to identify and accentuate the concentrated vortices, differentiate between primary and secondary vortices and mark their separation and reattachment lines. The method allows locating the singular points in type I primary separations and tracing the vortex-core streamlines that emanate from them. It also allows locating the vortex-core axes in flows of other types.

Seginer, Arnan↗

NASA NTRS1988

Analysis of LIMS data by potential vorticity inversion

This paper analyzes LIMS data for a minor warming of January 1979 by potential vorticity inversion, to investigate how flows in the middle atmosphere were determined. The inversion problem of calculating the flow from the potential vorticity is solved repeatedly, including and excluding different portions of the potential vorticity, thus revealing which bits of potential vorticity were important in determining the flow at a time and location of interest. The results of the analysis of LIMS data indicate that the middle stratospheric flow is dominated by potential vorticity that is local in height and in latitude, while planetary-scale mesospheric flows are primarily induced by potential vorticity in the stratosphere. A possible explanation for this difference is proposed.

Robinson, Walter A.↗

NASA NTRS1988

Observations of ionospheric convection vortices - Signatures of momentum transfer

Several classes of traveling vortices in the dayside ionospheric flow have been detected and tracked using the Greenland magnetometer chain. One class observed during quiet times consists of a continuous series of vortices moving generally antisunward for several hours at a time. Assuming each vortex to be the convection pattern produced by a small field aligned current moving across the ionosphere, the amount of field aligned current was found by fitting a modeled ground magnetic signature to measurements from the chain of magnetometers. The calculated field aligned current is seen to be steady for each vortex and neighboring vortices have currents of opposite sign. Low altitude DMSP observations indicate the vortices are on field lines which map to the inner edge of the low latitude boundary layer. Because the vortices are conjugate to the boundary layer, repeat in a regular fashion and travel antisunward, it is argued that this class of vortices is caused by surface waves at the magnetopause. No strong correlations between field aligned current strength and solar wind density, velocity, or Bz is found.

Mchenry, M. A.↗

NASA NTRS1989

A study of the temporal stability of multiple cell vortices

The effect of initial mean velocity field on the stability characteristics of longitudinal vortices is documented in detail. The temporal stability of isolated multiple cell vortices is considered. The types of vortices studied include single cell as well as two and three cell vortices. It is shown that cell multiplicity in the vortex core has drastic effects on the stability characteristics. On the basis of numerical calculations, it is concluded that the growth rates of instabilities in multiple cell vortices are substantially larger (two to threefold increases are observed) than those of a single cell vortex. It is also determined that there is a substantial increase in the effective range of axial and azimuthal wavenumbers where instabilities are present. But most importantly, there is the appearance of a variety of viscous modes of instability. In the case of vortices, these latter instabilities which highlight the importance of viscous forces have never been reported before. These effects are discussed in detail for the case of a two cell vortex.

Khorrami, Mehdi R.↗

NASA NTRS1989

Goertler vortices in growing boundary layers: The leading edge receptivity problem, linear growth and the nonlinear breakdown stage

Goertler vortices are thought to be the cause of transition in many fluid flows of practical importance. A review of the different stages of vortex growth is given. In the linear regime, nonparallel effects completely govern this growth, and parallel flow theories do not capture the essential features of the development of the vortices. A detailed comparison between the parallel and nonparallel theories is given and it is shown that at small vortex wavelengths, the parallel flow theories have some validity; otherwise nonparallel effects are dominant. New results for the receptivity problem for Goertler vortices are given; in particular vortices induced by free stream perturbations impinging on the leading edge of the walls are considered. It is found that the most dangerous mode of this type can be isolated and it's neutral curve is determined. This curve agrees very closely with the available experimental data. A discussion of the different regimes of growth of nonlinear vortices is also given. Again it is shown that, unless the vortex wavelength is small, nonparallel effects are dominant. Some new results for nonlinear vortices of 0(1) wavelengths are given and compared to experimental observations.

Hall, Philip↗

NASA NTRS1989

Vortical sources of aerodynamic force and moment

It is shown that the aerodynamic force and moment can be expressed in terms of vorticity distribution (and entropy variation for compressible flow) on near wake plane, or in terms of boundary vorticity flux on the body surface. Thus the vortical sources of lift and drag are clearly identified, which is the real physical basis of optimal aerodynamic design. Moreover, these sources are highly compact, hence allowing one to concentrate on key local regions of the configuration, which have dominating effect to the lift and drag. A detail knowledge of the vortical low requires measuring or calculating the vorticity and dilatation field, which is however still a challenging task. Nevertheless, this type of formulation has some unique advantages; and how to set up a well-posed problem, in particular how to establish vorticity-dilatation boundary conditions, is addressed.

Wu, J. Z.↗

NASA NTRS1990

Stellar and Jovian vortices

The characteristics of 'Jovian' vortices (the large vortices observed in the atmospheres of Jupiter, Saturn, Neptune) are summarized, and the existence of similar structures in the atmospheres of stars is considered theoretically. The problem of vortex maintenance is addressed, including potential vorticity, numerical simulations of Jovian vortices, and cyclones and anticyclones; the Great Red Spot of Jupiter is described on the basis of Voyager data; the evidence for convective generation of vertical vorticity in the sun is examined; the possibly vortical nature of the large spots of RS CVn stars is discussed; and models of spots on rapidly rotating hot stars are surveyed.

Dowling, T. E.↗

NASA NTRS1991

Evolution of streamwise vortices and generation of small-scale motion in a plane mixing layer

The present study investigates the evolution of streamwise vortices in a plane mixing layer and their role in the generation of small-scale 3D motion in a closed-return water facility. Spanwise-periodic streamwise vortices are excited by a time-harmonic wavetrain with spanwise-periodic amplitude variations synthesized by a mosaic of 32 surface film heaters flush-mounted on the low partition. The onset of streamwise vortices is accompanied by significant distortion in the transverse distribution of the streamwise velocity component. The presence of inflexion points, absent in corresponding velocity distributions of the unforced flow, suggests the formation of locally unstable regions of large shear in which broadband perturbations already present in the base flow undergo rapid amplification, followed by breakdown to small-scale motion. The cores of the primary vortices are significantly altered as a result of spanwise nonuniform excitation. The 3D features of the streamwise vortices and their interaction with the base flow are inferred from surfaces or rms velocity fluctuations and an approximation to cross-stream vorticity using 3D single component velocity data.

Nygaard, K. J.↗