Evidence for Tilted Toroidal Circulations in Cumulus

Rick Damiani Department of Atmospheric Science, University of Wyoming, Laramie, Wyoming

Search for other papers by Rick Damiani in
Current site
Google Scholar
PubMed
Close
and
Gabor Vali Department of Atmospheric Science, University of Wyoming, Laramie, Wyoming

Search for other papers by Gabor Vali in
Current site
Google Scholar
PubMed
Close
Full access

Abstract

Intense vortical circulations, often organized in counterrotating vortex pairs, were detected in midcontinental cumulus congestus over southeast Wyoming in July 2003. The sampled clouds developed in dry environments and at cold temperatures, and were a few kilometers in depth and width. Observations were obtained with the Wyoming Cloud Radar from aboard the Wyoming King Air research aircraft. Dual-Doppler analyses of the data yielded high-resolution (30–45 m) depictions of the horizontal components of air motions across vigorously growing clouds. The vortices found in the horizontal cross sections are interpreted as components of the toroidal circulations in thermals when those are tilted because of the effect of ambient cross flow. This configuration also leads to a partial stabilization of the vertical trajectory of the updraft, by opposing the drag by the ambient wind. Additionally, dry air intrusions were seen to accompany these features when the vortices developed near the cloud outer boundaries; recirculation of hydrometeors occurred when the vortices were adjacent to in-cloud downdrafts. These features are also evident in the radar reflectivity patterns. In general, gradients of velocities and vorticity values in horizontal planes are comparable to those found in vertical planes.

Corresponding author address: Rick Damiani, University of Wyoming, 1000 E. University Ave., Laramie, WY 82071. Email: rdamiani@cppwind.com

Abstract

Intense vortical circulations, often organized in counterrotating vortex pairs, were detected in midcontinental cumulus congestus over southeast Wyoming in July 2003. The sampled clouds developed in dry environments and at cold temperatures, and were a few kilometers in depth and width. Observations were obtained with the Wyoming Cloud Radar from aboard the Wyoming King Air research aircraft. Dual-Doppler analyses of the data yielded high-resolution (30–45 m) depictions of the horizontal components of air motions across vigorously growing clouds. The vortices found in the horizontal cross sections are interpreted as components of the toroidal circulations in thermals when those are tilted because of the effect of ambient cross flow. This configuration also leads to a partial stabilization of the vertical trajectory of the updraft, by opposing the drag by the ambient wind. Additionally, dry air intrusions were seen to accompany these features when the vortices developed near the cloud outer boundaries; recirculation of hydrometeors occurred when the vortices were adjacent to in-cloud downdrafts. These features are also evident in the radar reflectivity patterns. In general, gradients of velocities and vorticity values in horizontal planes are comparable to those found in vertical planes.

Corresponding author address: Rick Damiani, University of Wyoming, 1000 E. University Ave., Laramie, WY 82071. Email: rdamiani@cppwind.com

1. Introduction

While there is broad agreement about the essential elements of cumulus formation and evolution, there is yet need for more detailed observations of cloud fluid dynamics and its effects on mixing and microphysics. Using information gained with the help of an airborne dual Doppler radar system, cumulus congestus are found by Damiani et al. (2006, hereafter DVH06) to contain successions of thermals exhibiting toroidal circulations. Conceptual models incorporating similar elements are suggested by Scorer and Ludlam (1953), Blyth et al. (1988), and Blyth (1993) among others, and receive support by recent numerical simulations (e.g., Carpenter et al. 1998; Zhao and Austin 2005). The two-dimensional (2D) velocity fields in vertical planes across the clouds, given in DVH06 at a resolution of a few tens of meters, are explicit depictions of these features. Accompanying the main vorticity structures, important entrainment events are seen to take place on the scale of a few hundred meters as intrusions toward the centers of the clouds, at the bases of the rising toroids, and as smaller swirls at the caps of the clouds. These observations pertain to cumulus congestus developing over the High Plains region of Wyoming, where the clouds grow in dry environments and develop precipitation via the ice process.

It is clear that thermals frequently take asymmetric forms in the presence of background flow. This is evident in several of the cases described in DVH06, in the models referenced above, and in the analyses of Morton (1997a, b). It follows that the horizontal components of motion need to be taken into account and, to the extent possible, three-dimensional (3D) descriptions need to be constructed. Indications of significant horizontal gradients in the velocity fields of small cumuli can be found as early as in the works of Woodward (1959), Emmitt (1978), and Kitchen and Caughey (1981). Tank experiments (Morton 1997b; Fric and Roshko 1994; Kelso et al. 1996) show how convective entities such as plumes in cross flows can develop complex 3D vortical structures. Furthermore, as emphasized by Morton (1997b), vorticity in both the horizontal and in the vertical plays a key role in the dynamics of convective systems and in entrainment.

While horizontal vorticity associated with buoyant fluid volumes can be explained by horizontal buoyancy gradients across their boundaries, the generation of vertical vorticity in small-scale systems is not readily unraveled. Investigators have focused on the mechanics of vertically oriented vortices such as dust devils, for they represent a tangible class of phenomena involving the generation of vertical vorticity, and for their similarities to tornadoes (e.g., Maxworthy 1973; Kanak et al. 2000; Bluestein and Weiss 2004). Following Maxworthy (1973), vertical vorticity in these systems arises from a tilt of the ambient horizontal vorticity as buoyant air rises. The source of horizontal vorticity lies in the ambient vertical shear near the ground. More recently, this mechanism has been expanded to explain the development of supercell thunderstorms, where other elements, namely vorticity-generating dynamics due to gust fronts, and evaporative cooling effects, play important roles in augmenting horizontal, and ultimately vertical, vorticity (e.g., Rotunno 1981; Davies-Jones 1984; Klemp 1987).

Hauf (1985) reports evidence of vertical axis rotation in clouds within cloud streets as a consequence of enhancement of ambient vorticity near the surface by the convective-roll circulation. Preexisting weak vertical or horizontal shear (hence vorticity) near the surface, produced by interaction between boundary layer flow and topography (Carroll and Ryan 1970), can also be found at the intersections of convective cells present in typical boundary layers in Rayleigh–Bénard regime (Cortese and Balachandar 1993; Kanak et al. 2000). From a fundamental dynamics point of view, externally forced helical flows, such as those just mentioned, may be more stable than nonhelical ones due to the suppression of nonlinear interactions between turbulent scales (Etling 1985; Lilly 1986; Fernando and Smith 2001). Rotating vertical columns and counterrotating vortex pairs (CVPs) have been observed along the flanks and downstream of buoyant plumes and nonbuoyant jets (e.g., Church et al. 1980; Kelso et al. 1996; Lim et al. 2001; Cunningham et al. 2005). The generation of columnar dust-devil-type vortices in the wakes of plumes is yet to be fully understood, but an interaction of ambient vorticity (associated with wind vertical shear) and plume baroclinically generated vorticity is considered to be key to their existence (Morton 1997b; Cunningham et al. 2005). These vortices have been observed to shed in an oscillatory fashion from the main updraft volumes and advect downstream with the cross flow, resembling the classic vortex shedding behind bluff bodies. Organized vertical vorticity in CVPs is also found within rising plume (or jet) volumes, and can lead to a bifurcation of the plumes. This vorticity eventually gets tilted in the streamwise direction, forming horizontally aligned CVPs.

When no external forcing (ambient wind or shear) is present, Shapiro and Kanak (2002) argue that vertical vorticity can still arise when asymmetry within a thermal leads to tilting of the baroclinically generated horizontal vorticity. The result is a clover-leaf pattern of alternate sign vertical vorticity within the bubble. Although all these findings point to the importance of the evolution in three dimensions of the vortical structures within thermals and cumulus, no comprehensive descriptions have yet emerged.

In this paper, we focus on features of the air motion in horizontal planes across cumulus. We extend the generally employed strategy of radar observations in vertical planes by applying the same radar system as in DVH06, but with horizontally pointing antennas. The most interesting feature that emerged from these observations is the presence of persistent vorticity organized in CVPs. Similarly to the role played by vortices seen in the vertical, this dynamics plays an important role in the thermodynamic and microphysical development of the clouds. Vertically oriented vortices are believed to be generated by the tilting of the main azimuthal vorticity of the rising toroidal thermals due to the cross-flow action. In general, gradients and length scales of the horizontal motion fields are comparable to those found in the vertical, underlining the importance that this perspective should be given in the analysis of cloud development.

The text is organized as follows. In section 2, the dual-Doppler radar system (Wyoming Cloud Radar; WCR) on the Wyoming King Air (UWKA) is briefly presented together with a summary of the technique to retrieve two-dimensional kinematic fields. The environment and basic properties of the investigated clouds are described in section 3. Observations of the main features of the internal velocity fields and associated radar reflectivities are given in section 4. Sections 5 and 6 discuss aspects of both horizontal and vertical dynamics of cumulus growth, identify the mechanism for the generation of vertical vorticity, and elaborate on the consequences of the tilting of toroidal thermals. Section 7 reports a summary of the results.

2. The Wyoming Cloud Radar dual-Doppler setup

Data reported in this paper were collected by means of the Wyoming King Air (more information at http://flights.uwyo.edu/) and the onboard Wyoming Cloud Radar (more information at http://www-das.uwyo.edu/wcr). The WCR is a 95-GHz Doppler radar with four fixed antennas. The antennas form two pairs: beams from one pair scan a horizontal plane to the right side of the aircraft (Fig. 1); the other two beams scan a vertical plane below the aircraft. Each pair has one beam at 90° to the aircraft longitudinal axis, the other at about 55°; these pairs are used for the horizontal beam dual-Doppler (HBDD) and the vertical plane dual-Doppler (VPDD) modes. In addition, use was made of the profiling (up–down) mode, in which an upward- and a downward-pointing antenna are used simultaneously.

The closest usable radar range gates were at ∼100 m from the aircraft. Measured reflectivity has an estimated absolute accuracy of ±2.5 dB, and a precision, for the full dynamic range of the receivers, better than 1 dB. Reflectivity data were accepted for signals exceeding the mean noise-level by 2.5–3 standard deviations. The sensitivity of the slanted-pointing antennas is the limiting factor for the dual-Doppler retrieval; the minimum detectable signal at 1 km for such analyses was ∼−25 dBZ for the VPDD mode and ∼−23 dBZ for the HBDD mode (data based on 250-ns pulse width). No correction for attenuation was applied to the reflectivity due to the unknown and highly nonhomogeneous distribution of liquid water in the clouds. The terminal velocity of the scatterers was not removed; the effect of particle fall speed on the deduced motion fields is discussed in detail in DVH06. Attenuation and limited sensitivity are responsible for some loss of data in areas of the clouds with low reflectivity. The accuracy of calculated velocities is estimated as ±1–2 m s−1.

The plots shown in the following sections present velocity vector fields overlaid on reflectivity fields (filled contours of reflectivity factors, in dBZ). Selected streamlines from integration of the 2D fields are plotted with solid lines. Mean horizontal ambient winds, due to the absence of accurate soundings in the area of study, were derived from flight level measurements in the proximity of the clouds investigated over time scales of 5–10 min. These wind velocities were subtracted from the data. The adopted reference frame is therefore an approximation to some more ideal one, namely one translating horizontally with the updraft center or the cloud as a whole. Incomplete radar coverage, or Doppler uncertainties in cloud regions with low reflectivity, in fact, did not allow for better estimates of the ideal advecting velocities. Dual-Doppler retrieved velocities averaged over the observed cross sections, however, differed by only about 10% from the adopted ambient winds, thus indicating that the choice of the advection velocity is not critical. We also take that difference as a measure of the relative airspeed for the cloud volumes investigated in this study.

Further details about the radar installation, the available scanning modes, calibration, dual-Doppler retrieval procedure, and data uncertainty analysis are given in Damiani et al. (2005) and Damiani and Haimov (2006).

3. Characteristics of cloud and environment during the HiCuO3 experiment

This study focused on moderately deep continental cumulus over the southeastern part of the state of Wyoming in July–August 2003. Clouds had high bases, near 5 km MSL and at 0° to −5°C, and grew in a dry environment. Figure 2 shows a typical sounding from aircraft data near the observed clouds. Cloud depths were not constrained by significant inversions, whereas cloud bases coincided with a wind shift zone at the top of a relatively dry layer. The lapse rate was approximately dry adiabatic below 600 hPa, and close to moist adiabatic above 500 hPa. Cloud-base altitudes and atmospheric stability parameters could not be computed precisely from available data. Cloud-base altitude was estimated visually as well as from equating observed peak LWC values with adiabatic values. When sampling was done within few hundred meters of the flight altitude, cloud base from WCR data matched visual observations; from larger distances, however, newly formed cloud could not be detected. Our observations concentrated on isolated cumuli, turrets, and intense towers emerging from larger clusters. Cloud depths extended up to 3 km and maximum cloud diameters were ∼3.5 km; that is, the clouds had aspect ratios near unity. Droplet concentrations were of the continental type with correspondingly small droplet sizes. Low temperatures at cloud tops led to relatively rapid glaciation, accompanied by visually softer cloud boundaries than during the initial rise of turrets. More details on the physical properties of the clouds studied are given in DVH06.

Figure 3 illustrates many common features of the observed clouds with data assembled from two consecutive cloud penetrations. The first of these passes yielded the up–down vertical section and in situ data shown in Figs. 3a–d; the subsequent pass led to the dual-Doppler analysis shown in Fig. 3e. The location of the first pass, in cloud-relative terms, is shown by the thick horizontal line near the lower part of the image in the bottom panel. Flight level was about 7900 m MSL for both passes. Inferred cloud base altitude was near 5900 m MSL (not detected by the radar). The time lapse between the two scans was 3.5 min.

Cloud top altitude at the time of sampling was visually estimated near 8400 m MSL and at a temperature of −21°C. Echo top, and the band of high reflectivity below, rose at an approximate rate of 2.5 m s−1 during this period. That value is about half the maximum vertical speed within the updraft core. As seen in Fig. 3b, the updraft extends to the top of the cloud, and there is clear horizontal divergence at flight level. Preceding the penetrations here described, cloud top was observed to subside and exhibited lower reflectivity. The vertical section thus portrays the rise of a new thermal into an already mature congestus. The lower portion of the updraft is not detected by the radar, hence the dome-like appearance of the echo. The relatively large reflectivities at the top of the updraft are due to ice crystals. Particle images recorded along the flight path, in the upper portion of the thermal, indicated aggregates or graupel up to 1 mm in diameter. The large patch of high reflectivity on the right-hand side in Fig. 3 coincides with the downdrafts measured in situ (Fig. 3b) and seen in the Doppler velocities exceeding expected fall speeds (Fig. 3c).

The updraft is seen in the horizontal radar section (Fig. 3e) as the region with reflectivities in the range of −25 to −10 dBZ, roughly centered on the white marker in the image, and with diverging flow vectors surrounding it. Maximum horizontal divergence on a 100-m scale is 0.04 s−1. Downdrafts are characterized by larger reflectivities (∼5 dBZ) and chaotic flow mainly on the northeastern side of the image. Ambient wind vertical shear within the cloud layer was ∼0.006 s−1 and directed northeast; the line connecting the regions of low and high reflectivity is roughly aligned in the same direction.

The highly inhomogeneous distribution of the reflectivity, and thus of hydrometeors, is attributable to the multithermal cloud development and the resulting displacement and mixing of older and newer hydrometeors. This view of the cloud fluid mechanics is also supported by the large spatial gradients in the velocity components (peaks exceed 0.05 s−1 in the downshear side of the cloud), comparable to those found in vertical transect analyses across congestus. Dominant structures in this velocity field are seen, subjectively, to be from about 500 m to 1 km.

4. Counterrotating vortex pairs

Pairs of vortices with opposite directions of rotation were frequently observed in the horizontal radar sections we obtained. Examples will be given here to show the character of these CVPs and to demonstrate that they remain identifiable (at a given altitude) over periods of several minutes. Arguments linking the CVPs to toroidal circulations discussed in DVH06 will be given in section 5.

Figures 4 and 5 depict horizontal flow patterns observed in turrets close to their tops, near 7900 and 7800 m MSL, respectively. The case shown in Fig. 4 had relatively weak ambient wind (7 m s−1 from 242° at flight level), and southwesterly shear >0.005 s−1 in the cloud layer. The second case, Fig. 5, had stronger ambient wind (17 m s−1 from the northwest), and shear, similar to the other case, lined up with the wind direction. As the figures show, the motion fields (in the air-relative frames) were dominated by flow in the middle directed opposite to the ambient wind, and by a pair of vortices bracketing that flow. The vertical vorticity averaged over regions of 500 m in diameter is 0.04 s−1 in both circulations in Fig. 4. For a 100-m-diameter region in the northern (left) vortex, the maximum vorticity was twice that value. Derived vertical vorticity for the second example is shown in the lower panel of Fig. 5, indicating values of 0.15 and 0.1 s−1 for the western (left) and eastern (right) vortices.

The centers of the vortices are identified based on a combined, and somewhat subjective, assessment of the location of minima in horizontal velocities, peaks in the vertical vorticity, and streamline patterns. Sketches are included next to the figures to help the visualization. Turbulence, interactions among multiple thermals, the specific location of the cross section with respect to the thermals (see section 5), and low radar signal-to-noise ratios in some regions affect the clarity of depiction of the vortices. Vectors are also affected by the chosen (translating) reference frame velocity, which may cause streamlines not to close in certain cases. In Fig. 4, for instance, the vortex indicated by the arrow number 2 does not present streamline loops, but the vectors are clearly showing a clockwise rotation around the marked center.

Another important feature evident in Figs. 4 –5 is the indication of intrusions of dry air into the cloud. These can be seen as dents in the outer boundaries of the cloud and as tongues of clear air (no signal) or reduced reflectivity on the northeast (southeast) sides of the vortices for Fig. 4 (Fig. 5). Since the rotation centers were located close to the outer cloud boundaries, it is reasonable to think that the circulations extended into clear air, and that the intrusions formed along the cloud-inward branches of the circulations. Clearly, echo boundaries can exhibit other convolutions not associated with vortices. One possible source of such features, as for example shown by the diverging flow region at the bottom (upshear sector) of Fig. 4, is the arrival of new thermals at the observation level. The low reflectivity associated with the upshear region in Fig. 4 is also consistent with a new surge of rising air.

The persistence of the flow pattern can be demonstrated with Fig. 6, which shows results from the sampling of the same cloud region by three consecutive aircraft passes. These results are from 17 July 2003, and refer to observations near cloud top, at 8100 m MSL. In the first pass, the cloud was penetrated along an off-center path; the two subsequent passes were outside the cloud. Echo size increased between the first and second passes, and echo strength increased substantially between the second and third passes giving the impression of a new growth pulse just after the first pass. The sequence encompasses ∼4.5 min. Only one minute after the last pass, the turret subsided below the flight level. The centers of the two vortical circulations (labeled 1 and 2 in Fig. 6) forming the CVP are manifest in all three sections. In the in situ measurements relative to the first pass, the vortices are identifiable in the shift of (u, υ) components of the air velocities.

In all three scans, the centers of rotation are fairly close to the outer cloud boundaries. This may have special significance in the third pass where the circulation on the right-hand side is centered on the boundary between high and low reflectivity zones, possibly due to entrainment/detrainment within the lower part of this circulation. In contrast to the cases in Figs. 3 –5, the flow sampled in the middle of the circulations is roughly aligned with the direction of the flight-level ambient wind (∼239° at ∼10 m s−1) and of the cloud-layer shear (0.005–0.006 s−1 roughly directed northeast). Considering areas of 200–400 m in diameter, calculated vorticity values reached 0.09 s−1. This value is toward the upper range of values encountered.

The examples presented so far were from the vicinity of the tops of turrets roughly 3 km above cloud base. The following two examples show that circulations are also found in clouds of lesser vertical development.

The sequence of observations presented in Fig. 7 is from a cloud region about 1.7 km above cloud base (5000 m MSL), when cloud top was about 300 m above that level. The two upper panels show in situ data and a VPDD analysis from the first pass. A fairly uniform updraft was present along nearly the full 1.5 km length of the penetration, and descending flow was present only at the edges and outside the cloud boundaries. The low values and uniform upward gradient of reflectivity are also consistent with this description, as is the Doppler data, which, in this instance, has relatively little contribution from particle fall velocities. No ice was recorded during the penetration, though air temperature was below −10°C. In situ horizontal gust data indicate significant counterclockwise rotation on the southwest side and a similar clockwise rotation on the northeast side. Accompanying these kinematic features, the dual-Doppler data show circulations (labels 1 and 2 in Fig. 7) in the vertical plane. The rotations in the horizontal are clearly seen in the radar section obtained 3 min after the previous pass, as shown in the bottom panel of Fig. 7, despite the noise due to the weak return signal. The line connecting the CVP centers in the horizontal plane is perpendicular to the ambient wind, so that the flow in the middle is against the direction of the main environmental advection (6 m s−1 from the northwest). Patches of higher reflectivity are located on the downwind sides of the vortex centers (bottom panel of Fig. 7); they are separated by the converging flow area in the middle of the cloud. An explanation for this reflectivity pattern can be found in the vertical section through the cloud (Fig. 8) obtained 4 min later, roughly aligned with the ambient wind direction. The radar echoes in Fig. 8 are suggestive of several growth pulses, and the presence of updrafts with weak reflectivity only in the upwind/upshear portion of the cluster supports that interpretation. Thus, the reflectivity patches seen in the horizontal section in Fig. 7 likely originated in an earlier pulse of growth. It is, then, of some significance that the rotating motions in the horizontal plane transport some of this older material into the new updraft in a manner similar to what is described to occur in association with toroidal circulations in the vertical plane (DVH06).

Vortical circulations in both the horizontal and vertical planes in an even smaller cloud than that depicted in Figs. 7 and 8 can be identified from the in situ and remote sensing data given in Fig. 14 of DVH06. The CVP in the horizontal plane is evidenced by the rotation of the horizontal gust vectors coincident with the transition from updraft to downdrafts. The horizontal flow in the updraft in that case was directed opposite to the mean ambient wind.

CVPs were observed in a number of other cases, with the majority oriented such that the flow between the circulations was directed against the main streamflow (wind) at the level of scan. Out of 33 cases investigated in HBDD mode, 19 contained well-defined vortices. Either radar retrieved velocity fields or in situ gust vectors gave at least an indication of CVPs for 23 clouds, of which 15 cases showed strong evidence. Six cases offered clear 2D depictions of CVPs through HBDD analyses.

5. Origins of counterrotating vortex pairs

The main question raised by the data presented in the foregoing sections is: what gives rise to the CVPs? A related question is: how are these CVPs maintained over periods up to 5 min?

The vortices we describe were observed at high altitudes, well above the boundary layer, at the peripheries of the ascending updraft cores, and thus were not part of strong, vertically aligned helical flows. Our data do not show any evidence for rotating updrafts. Therefore, mechanisms for vertical vorticity generation which focus on rotating, rising columns, or boundary layer confined vortices (e.g., Carroll and Ryan 1970; Hauf 1985; Cortese and Balachandar 1993; Kanak et al. 2000), cannot be responsible for the structures we observed. Flow patterns of plumes and jets in cross flow (e.g., Church et al. 1980; Kelso et al. 1996; Cunningham et al. 2005) do not fit the cases presented, in part because the observed updrafts have limited vertical extent. In addition, observations of strong vertical vorticity at high altitudes, where the jet model would predict that vorticity induced at the surface would tilt into the horizontal direction (see section 1), would not favor this type of mechanism as a source for CVPs. With stronger shear over the size of a thermal, vorticity could be created by the interaction between a puff, or deeply elongated thermal, and the transverse environmental flow, but the absence of such shear makes a contribution by this mechanism unlikely.

For the cases reported, at least two factors reduce the applicability of larger-scale models of storm vorticity development (described by Maxworthy 1973; Rotunno 1981; Klemp 1987). In supercell storms, the baroclinically generated vorticity along a frontal boundary augments the streamwise vorticity. This interaction is missing in the moderately deep convection studied here. In addition, a continuous updraft from the surface to the higher levels required for this mechanism to sustain the growth and duration of the vertical vortices was not observed, as already mentioned. From Eq. (5) in Rotunno (1981), it can be seen that vertical vorticity can only be produced by the tilting of horizontal vorticity and by subsequent stretching. For a thermal that is initially 1 km deep, taking the 0.002 s−1 vertical shear in the lowest 1 km of the atmosphere from data for 20 July 2003, as the available ambient vorticity for tilting, the stretching term can be integrated from the surface to the level of observations. Assuming 0.002 s−1 as initial value for the vertical vorticity, integrating the stretching term for the case in Fig. 7, and assuming that the initial and final speeds of the thermal are 1 and 5 m s−1 respectively, the average vertical vorticity at the level of observation would be ∼0.01 s−1. Observed values were at least 5 times larger than that, in spite of turbulent diffusion not included in the calculations. We therefore consider the tilting and stretching of ambient horizontal vorticity inadequate to explain the CVPs.

We will attempt to show in the following that the vertical vorticity described in this paper is a manifestation of the initially horizontal (azimuthal) vorticity embedded in rising toroidal thermals. If a rising, upright vortex ring encounters unidirectional shear, its axis will tilt against the cross-flow direction (e.g., Chang and Vakili 1995; Diez et al. 2003), due to the torque [see Eq. (1) below] exerted by Kutta–Joukowski lift forces (Magnus effect) that develop in opposite directions along the upshear and downshear ring arcs. This action within the thermal opposes the normal downshear bend of the ascending air, and serves as a dynamic stabilization of the trajectory of the thermal, similarly to a gyroscopic effect.

To demonstrate the importance of the above effect, we can compare the torque due to Kutta–Joukowski forces to that produced by a sheared environment. The torque due to the Magnus effect can be approximated (ignoring the effect of drag) as:
i1520-0469-64-6-2045-e1
where ρ, U are the mean density and relative airspeed at the altitude of the thermal; dr, dt are the ring and tube diameters of the toroid, and ωh is the tube (core) vorticity. Equation (1) results from integration of the moments of the Kutta–Joukowski forces [(πd2t/4)ρU||ωh||] along the azimuth of an ideal vortex ring. While there is no precise analytical expression for the drag exerted on a thermal by the sheared ambient flow, an approximation of the resulting torque can be obtained by viewing the updraft volume as a cylinder. If a cylinder of diameter ∼1.5dr (to include the outer diameter of the thermal) is exposed to a cross wind increasing linearly with height, the torque due to drag can be written as:
i1520-0469-64-6-2045-e2
where the torque Msh is calculated with respect to the center of the cylinder, CD ≈ 1 is the drag coefficient of a 2D cylinder (neglecting any end 3D effect that would reduce the torque) of height h, kz is the vertical wind shear in the layer occupied by the cylinder, and U here denotes the relative wind speed at the level of the lower base of the cylinder. Assuming dr =1000 m, dt = 500 m, ||ωh|| = 0.04 s−1, ρ = 0.55 kg m−3, a mean relative wind speed of 2 m s−1 across the height h =1000 m, and a shear kz ≈ 0.0032 s−1 (based on our data in the proximity of the sampled thermals), the ratio of the two torques becomes Mkj/Msh ≈ 15. Chang and Vakili (1995) suggest that the effective lift force exerted on the ring is likely one-half of the Kutta–Joukowski lift, which would reduce the ratio to ∼7. In general, both torques are overestimated, since no 3D effects, or drag torque in the case of the vortex ring, are considered. This result indicates that the vortex-ring torque is significant in the development of a thermal in cross flow, and, more importantly, that tilting of the toroids can be expected.

Once the tilted toroid configuration is accepted, the presence of CVPs in horizontal sections follows directly. Figure 9 shows how horizontal sections across a tilted toroid can have different patterns of vorticity, depending on the location of a particular horizontal level with respect to the toroid. In the figure, an ideal toroid is modeled with its axis tilted 30° from the vertical in the upwind direction (negative y). The meridional velocity increases linearly along the tube radius up to a maximum of 5 m s−1, and the average azimuthal vorticity is 0.04 s−1. As seen from the figure, sections near the toroid center (e.g., section B in Fig. 9) contain well-defined CVPs. Less denned circulations appear in more off-center sections, but with vertical vorticity still organized in regions of opposite signs. Note how this configuration leads to vorticity regions being located on either sides of the updraft core, as is the case in the observations shown in Figs. 3 –7. In addition, the size (∼500 m) and the intensity (∼0.04–0.1 s−1) of the eddies found in cloud horizontal cross sections are comparable to their counterparts in vertical planes, consistent with the hypothesis of toroid tilting by roughly 30° or more. The persistence of these patterns is also consistent with the lifetime of the toroids sampled with vertical cross sections.

The model in Fig. 9 shows that the location of a CVP can be upwind of the updraft region, as in the upper cross section, or downwind of it, as in the lower section. In our observations, the CVPs were located downwind of the updraft in all (23) but three cases, consistent with the fact that most passes were executed near the tops of rising turrets and that wind shear was roughly aligned with the mean wind direction.

The majority of the cases studied point to a tilt of the toroid against the mean wind shear direction, in accordance with the arguments given above. In two cases (e.g., Fig. 6), the toroids were tilted roughly along the mean wind shear. Those two cases correspond to days characterized by relatively strong (∼0.005 s−1) and moderate shear (∼0.001 s−1), respectively, so that the shear is unlikely to have produced the reversed tilting. It seems possible that interactions among multiple ascending bubbles could lead to the tilting of the toroids in one direction rather than into another. Interference and mutual induction between thermals could further generate more complex patterns in the vertical vorticity, as seen in the simulations of Shapiro and Kogan (1994). Even though more intricate patterns than just two vortices in a dipole arrangement were observed in some instances, no clear evidence was found for a clover-leaf pattern of vorticity. That pattern could arise if the vortex rings underwent a horse-saddle distortion, according to Shapiro and Kanak (2002).

The mechanism for vertical vorticity generation discussed herewith can be important also to explain the development of storm rotation once the vertical profile of the wind and the effective motion of the storms are considered, but these aspects go beyond the scope of this paper.

6. Updraft configuration

In cases where the mean ambient vertical shear exceeded about 0.003 s−1, a preferential organization of updrafts and downdrafts was evident. Updrafts were located on the upshear sector of the cloud, and downdrafts and collapsing turrets on the downshear side. This spatial arrangement is the same as has been noted by several authors (e.g., Malkus 1954; Ackerman 1958; Scorer 1958; Rogers et al. 1985; Perry and Hobbs 1996; Vaillancourt et al. 1997).

The horizontal radar sections, supported by the in situ data, reveal another significant characteristic of these updrafts, namely that their horizontal speed is slower than the ambient wind speed. When seen from reference frames translating with the ambient winds, in fact, horizontal components of updrafts are directed opposite to the ambient winds. This pattern is evident, for instance, in Figs. 3, 4, 5 and 7.

A qualitatively reasonable explanation for the opposing horizontal velocity is that the updrafts at the observation level still carry some of the momentum of near-surface air. However, the weak mean shears measured from surface to cloud altitudes do not make up for the observed large momentum deficits, and neither do wind shears concentrated near the sampling altitudes. For the case in Fig. 3, for example, the rate of rise of the thermal was approximately 2.5 m s−1 (consistent with the rate of rise of a buoyant vortex ring with maximum upward velocities on the order of 5 m s−1). A simple estimate of the drag force exerted by the sheared cross flow (speed increasing 3.2 m s−1 in 1000 m below the level of observation) on the thermal simulated as a kilometer-sized sphere leads to an acceleration that would bring it to near the ambient wind speed in about 4 min, or merely 600 m of rise. These values indicate that the horizontal speed of the thermal should be much closer to the ambient wind after the full 1000 m rise, especially if mixing were considered. Analogous conclusions can be reached for the other cases.

We find a more likely explanation for the opposition of the updraft to ambient flow in that it is a consequence of the tilting of the toroidal thermal into the wind, as discussed in the preceding section and as shown in Fig. 9. The main updraft in the center of the toroid points into the wind, and the horizontal component of the air velocity is directed against the ambient flow as can be most clearly seen in the cross section B in Fig. 9 (see also Fig. 10). Further, divergence at the top of the thermal produces a radial flow from its core, so that the upshear sector has reduced momentum while the downshear sector has increased momentum with respect to the surroundings.

As an additional consequence of the tilting of the toroid into the wind, the downwind slope of a rising parcel is thwarted, so that the trajectory of the center of the tilted toroid remains nearly vertical (see Fig. 10). This stabilization of the updraft trajectory is in accord with laboratory observations (e.g., Diez et al. 2003) and with numerical simulations (e.g., Chang and Vakili 1995) illustrating how rising vortex rings can oppose and even overcome the cross-flow advection when updraft-to-cross-flow speed ratios are greater than 1.5. Based on the mean updraft speeds and the estimates of the relative air (wind) speeds (cf. section 2) for the thermals sampled, we calculated ratios in the 2 to 5 range. Higher flow ratios may lead to further toroid tilting and increased vertical straightening of the thermal trajectory. This gimbal-type stabilization mechanism is also consistent with visual observations of the evolution of cumuli we sampled. Nonetheless, a rigorous documentation of this aspect of the cloud evolution will require further work.

7. Conclusions

Detailed analyses of horizontal motion fields across active, continental Cumulus congestus led us to propose that tilted toroidal circulations within rising thermals can explain dominant features such as the counterrotating vortex pairs (CVPs) and the nature of the horizontal component of the updraft velocity. Conclusions drawn from motion fields observed in vertical transects (DVH06) back up these deductions. The near-instantaneous kinematic depictions at a resolution of ∼40 m derive from dual-Doppler analyses of data collected with the airborne Wyoming Cloud Radar (Damiani and Haimov 2006), and in situ measurements from the University of Wyoming King Air.

The clouds studied had bases at temperatures between 0° and −5°C. Measured updraft speeds reached 10 m s−1, and liquid water contents 2 g m−3. Ice crystals and small graupel developed in the upper reaches of the clouds (temperatures −15° to −20°C), and produced radar reflectivities of up to about 10 dBZ. Ambient wind shear was modest in magnitude and with nearly no changes in wind direction across the cloud layer. Data presented in this paper was selected from observations of roughly sixty clouds, many with multiple penetrations.

The CVPs reported in this paper were ∼500 m in diameter, and had vertical vorticity magnitudes of 0.04 to 0.1 s−1. Their orientation, the spacing and location of their centers with respect to the updraft core, and their vorticity values suggested a linkage to comparable vortices detected in vertical sections; the combined kinematic patterns are well predicted by a model of a toroidal thermal tilted into the (ambient) wind cross flow as shown in Fig. 9. The tilting of a rising toroid into the wind is also predicted by theory and laboratory experiments (cf. section 5).

The tilted toroid configuration also provides an explanation for the finding that, in reference frames translating with the ambient wind velocities, the horizontal components of updrafts are directed against the ambient winds (cf. section 6). Forces acting on the toroid lead to a stabilization of the updraft trajectory toward the vertical, providing a better explanation than simply transport of lower level momentum.

The following additional points can be made based on our analyses:

  1. Magnitudes (in frames relative to the mean ambient winds), gradients, and the variability of in-cloud velocities in the horizontal were comparable to those measured in vertical cloud transects. Expressed in terms of 2D mean turbulent kinetic energy per unit mass, observed values range to roughly 6–7 m2 s−2 in both planes.

  2. Local divergence in the horizontal planes was mostly associated with regions of low reflectivity, in accord with expectations for updrafts. Cases of divergence coinciding with high reflectivities result from thermals penetrating older cloud regions (at the tops of thermals).

  3. There is direct evidence in the data of entrainment and recirculation of hydrometeors as a consequence of the toroidal circulations. Dry-air intrusions were evidenced by inward velocities and reduced reflectivities near the cloud boundaries. These occurred most frequently in association with the inflow quadrants of the vortices. Reflectivity gradients at cloud edges in regions with velocity components normal to the boundaries were about 0.1–0.2 dBZ m−1, whereas in regions with velocities tangential to the boundaries the gradients were twice those values. This difference is consistent with small-scale entrainment and mixing where velocities indicate that possibility. The location of vortices at the periphery of the updrafts, and hence in proximity of the downdrafts, also favors the recycling of precipitating hydrometeors in more mature clouds.

  4. The clouds evolved through a series of ascending thermals, often leading to mixing of cloud mass from different growth pulses. This aspect of cloud evolution and inhomogeneity has specific examples in our data, but was not studied thoroughly in this work. The variance of the reflectivity across horizontal sections is almost twice that measured in vertical counterparts. Many of the vertical sections were deliberately obtained across the major updrafts, and that provides a degree of organization and stratification in the VPDD data that has no complete equivalent in the HBDD data. The horizontal scans inevitably covered larger regions occupied by both descending and ascending cloudy parcels. The multithermal nature of the cumuli as well as the turbulent and vortical flow visible from the horizontal scans, plus the recirculation of hydrometeors, dramatically influence the distribution of hydrometeors in the cloud. For this reason, mature clouds as that in Fig. 4, where new thermals are rising into an older congestus, can give rise to radar echo fields with variances in excess of 50 dBZ2. On the other hand, vertical transects in young clouds, or emerging turrets, as for instance the turret in Fig. 7a, present a more uniform reflectivity field and the variance can be as low as 4 dBZ2.

Motions consistent with tilted toroidal circulations provide an interpretation of our observations. These observations came from a fairly restrictive set of conditions, so that the range of applicability of this model to cumulus evolution remains to be determined.

Acknowledgments

The author would like to thank Dr. Samuel Haimov and colleagues in the Department of Atmospheric Science at the University of Wyoming, and the UWKA facility team involved in the HiCu03 experiment. This study was supported by NSF Grant ATM-0094956.

REFERENCES

  • Ackerman, B., 1958: Turbulence around tropical cumuli. J. Meteor., 15 , 6974.

  • Bluestein, H. W., and C. C. Weiss, 2004: Doppler radar observations of dust devils in Texas. Mon. Wea. Rev., 132 , 209224.

  • Blyth, A. M., 1993: Entrainment in cumulus clouds. J. Appl. Meteor., 32 , 626641.

  • Blyth, A. M., W. A. Cooper, and J. B. Jensen, 1988: A study of the source of entrained air in Montana cumuli. J. Atmos. Sci., 45 , 39443964.

    • Search Google Scholar
    • Export Citation
  • Carpenter, R. L. J., K. K. Droegemeier, and A. M. Blyth, 1998: Entrainment and detrainment in numerically simulated cumulus congestus clouds. Part III: Parcel analysis. J. Atmos. Sci., 55 , 34403455.

    • Search Google Scholar
    • Export Citation
  • Carroll, J. J., and J. A. Ryan, 1970: Atmospheric vorticity and dust devil rotation. J. Geophys. Res., 75 , 51795184.

  • Chang, Y. K., and A. D. Vakili, 1995: Dynamics of vortex rings in crossflow. Phys. Fluids, 7 , 15831597.

  • Church, C. R., J. T. Snow, and J. Dessens, 1980: Intense atmospheric vortices associated with a 1000 MW fire. Bull. Amer. Meteor. Soc., 61 , 682694.

    • Search Google Scholar
    • Export Citation
  • Cortese, T., and S. Balachandar, 1993: Vortical nature of thermal plumes in turbulent convection. Phys. Fluids, 5 , 32263232.

  • Cunningham, P., S. L. Goodrick, M. Y. Hussaini, and R. R. Linn, 2005: Coherent vortical structures in numerical simulations of buoyant plumes from wildland fires. Int. J. Wildland Fire, 14 , 6175.

    • Search Google Scholar
    • Export Citation
  • Damiani, R., and S. Haimov, 2006: A high-resolution dual-Doppler technique for fixed multi-antenna airborne radar. IEEE Trans. Geosci. Remote Sens., 42 , 34753489.

    • Search Google Scholar
    • Export Citation
  • Damiani, R., S. Haimov, and G. Vali, 2005: High-resolution airborne radar dual-Doppler technique. Preprints, 32d Conf. on Radar Meteorology, Albuquerque, NM, Amer. Meteor. Soc., CD-ROM, P1R.4.

  • Damiani, R., G. Vali, and S. Haimov, 2006: The structure of thermals in cumulus from airborne dual-Doppler radar observations. J. Atmos. Sci., 63 , 14321450.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 1984: Streamwise vorticity: The origin of updraft rotation in supercell storms. J. Atmos. Sci., 41 , 29913006.

  • Diez, F. J., L. P. Bernal, and G. M. Faeth, 2003: Round turbulent thermals, puffs, starting plumes and starting jets in uniform crossflow. ASME J. Heat Transfer, 125 , 10461057.

    • Search Google Scholar
    • Export Citation
  • Emmitt, G. D., 1978: Tropical cumulus interaction with and modification of the subcloud region. J. Atmos. Sci., 35 , 14851502.

  • Etling, D., 1985: Some aspects of helicity in atmospheric flows. Beitr. Phys. Atmos., 58 , 88100.

  • Fernando, H. J. S., and D. C. I. Smith, 2001: Vortex structure in geophysical convection. Eur. J. Mech., 20B , 437470.

  • Fric, T. F., and A. Roshko, 1994: Vortical structure in the wake of a transverse jet. J. Fluid Mech., 279 , 147.

  • Hauf, T., 1985: Rotating clouds within cloud streets. Beitr. Phys. Atmos., 58 , 380398.

  • Kanak, K. M., D. K. Lilly, and J. T. Snow, 2000: The formation of vertical vortices in the convective boundary layer. Quart. J. Roy. Meteor. Soc., 126 , 27892810.

    • Search Google Scholar
    • Export Citation
  • Kelso, R. M., T. T. Lim, and A. E. Perry, 1996: An experimental study of round jets in cross-flow. J. Fluid Mech., 306 , 111144.

  • Kitchen, M., and S. J. Caughey, 1981: Tethered-balloon observations of the structure of small cumulus clouds. Quart. J. Roy. Meteor. Soc., 107 , 853874.

    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., 1987: Dynamics of tornadic thunderstorms. Annu. Rev. Fluid Mech., 19 , 369402.

  • Lilly, D. K., 1986: The structure, energetics, and propagation of rotating convective storms. Part II: Helicity and storm stabilization. J. Atmos. Sci., 43 , 126140.

    • Search Google Scholar
    • Export Citation
  • Lim, T. T., T. H. New, and S. C. Luo, 2001: On the development of large-scale structures of a jet normal to a cross flow. Phys. Fluids, 13 , 770775.

    • Search Google Scholar
    • Export Citation
  • Malkus, J. S., 1954: Some results of a trade-cumulus cloud investigation. J. Atmos. Sci., 11 , 220237.

  • Maxworthy, T., 1973: A vorticity source for large-scale dust devils and other comments on naturally occurring columnar vortices. J. Atmos. Sci., 30 , 17171722.

    • Search Google Scholar
    • Export Citation
  • Morton, B. R., 1997a: Discrete dry convective entities. I: Review. The Physics and Parameterization of Moist Atmospheric Convection, Series C: Mathematical and Physical Sciences, Vol. 505, Kluwer Academic, 143–173.

    • Search Google Scholar
    • Export Citation
  • Morton, B. R., 1997b: Discrete dry convective entities. II: Thermals and deflected jets. The Physics and Parameterization of Moist Atmospheric Convection, Series C: Mathematical and Physical Sciences, Vol. 505, Kluwer Academic, 175–210.

    • Search Google Scholar
    • Export Citation
  • Perry, K. D., and P. V. Hobbs, 1996: Influences of isolated cumulus clouds on the humidity of their surroundings. J. Atmos. Sci., 53 , 159174.

    • Search Google Scholar
    • Export Citation
  • Rogers, D. P., J. W. Telford, and S. K. Chai, 1985: Entrainment and the temporal evolution of the microphysics of convective clouds. J. Atmos. Sci., 42 , 18461858.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., 1981: On the evolution of thunderstorm rotation. Mon. Wea. Rev., 109 , 577586.

  • Scorer, R. S., 1958: Natural Aerodynamics. Vol. 1, International Series of Monographs in Aeronautics and Astronautics, Pergamon, 312 pp.

    • Search Google Scholar
    • Export Citation
  • Scorer, R. S., and F. H. Ludlam, 1953: Bubble theory of penetrative convection. Quart. J. Roy. Meteor. Soc., 79 , 94103.

  • Shapiro, A., and Y. L. Kogan, 1994: On vortex formation in multicell convective clouds in a shear-free environment. Atmos. Res., 33 , 125136.

    • Search Google Scholar
    • Export Citation
  • Shapiro, A., and M. Kanak, 2002: Vortex formation in ellipsoidal thermal bubbles. J. Atmos. Sci., 59 , 22532269.

  • Vaillancourt, P. A., M. K. Yau, and W. W. Grabowski, 1997: Upshear and downshear evolution of cloud structure and spectral properties. J. Atmos. Sci., 54 , 12031217.

    • Search Google Scholar
    • Export Citation
  • Woodward, B., 1959: The motion in and around isolated thermals. Quart. J. Roy. Meteor. Soc., 85 , 144151.

  • Zhao, M., and P. H. Austin, 2005: Life cycle of numerically simulated shallow cumulus clouds. Part II: Mixing dynamics. J. Atmos. Sci., 62 , 12911310.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Horizontal beam dual-Doppler operation of the Wyoming Cloud Radar.

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Fig. 2.
Fig. 2.

King Air sounding for 1750–2000 UTC 20 Jul 2003. The bar on the right of the plot denotes the cloud layer.

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Fig. 3.
Fig. 3.

Two sets of observations of a cumulus congestus from 2030 UTC 16 Jul 2003, at 7900 m MSL. (a)–(d) Up–down radar profile and in situ data, and (e) an HBDD section from a subsequent pass. (a) LWC (solid line) and IWC (dotted line); (b) gust-probe measured air vertical velocity ω, with overlaid 1-s gust vectors in the vertical [u, ω and horizontal plane (u, υ)] (deviations from a mean horizontal wind); (c),(d) Doppler velocity and reflectivity contours in the vertical plane above and below the aircraft (AC); (e) reflectivity contours [using same color bar as in (d)] and dual-Doppler retrieved velocity vectors (relative to the ambient wind); thin black lines are streamlines, thick solid lines are the AC air-relative tracks of the (top) HBDD and of the (bottom) up–down profiling passes; the arrow labeled with N indicates true north, the ambient wind (∼260° at 11.8 m s−1) is shown by the thick arrow (not to scale); vector grid resolution is ∼45 m, but only every second vector is shown for clarity; the marker (heavy white cross) points to the center of the region of horizontal divergence.

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Fig. 4.
Fig. 4.

Same as Fig. 3e but for a horizontal section showing a CVP from 2050 UTC 17 Jul 2003, at 7900 m MSL. Filled contours are reflectivity (dBZ). Labels 1 and 2 point to the centers of the CVP and label 3 to the region of horizontally diverging flow. Thick lines in the inset figure at top left are a conceptual interpretation of the CVP. Flight level ambient wind was 242° at ∼7 m s−1 (arrow not to scale for better visualization).

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Fig. 5.
Fig. 5.

Same as Fig. 4 but for an example of CVP from 1935:30 UTC 12 May 2003, at 7800 m MSL, with the bottom panel showing the derived vorticity values (s−1). Mean wind at flight altitude is 307° at 17 m s−1. Labels 1 and 2 point to the centers of the vortices. The vorticity data had to be thresholded for the errors coming from the derivative calculations at the edges of the cloud, where grid cells with valid data are adjacent to those containing data below the noise limit.

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Fig. 6.
Fig. 6.

Three consecutive horizontal sections showing persistence of CVP, from 17 Jul 2003, at 8100 m MSL; scan times: 2116, 2117:30, and 2119 UTC, respectively. The first pass (A) was made closer to the center of the cloud, whereas the other two were near its outer edge. Meaning of symbols and of filled contours for the lower panels are the same as in Fig. 4. Labels 1 and 2 denote the centers of two circulations. (top) In situ data collected during the first pass: ω (solid) air vertical velocity, T (dashed) reverse-flow temperature, LWC (dashed–dotted) from DMT probe, IWC (dotted), and horizontal plane gust vectors (relative to the mean wind at flight level; i.e., 239° at 10 m s−1).

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Fig. 7.
Fig. 7.

(middle) A vertical section with in situ data and (bottom) a horizontal section through a smaller cloud. Data are from 1903–1906 UTC 20 Jul 2003, at 6700 m MSL. Meaning of symbols and of filled contours for the lower panels are the same as in Fig. 4. (top) In situ data: w (solid) air vertical velocity, LWC (dashed–dotted) from DMT probe, and horizontal-plane gust vectors (relative to the mean wind at flight level; i.e., 314° at 6 m s−1). Labels 1 and 2 point to the centers of circulations. The thick solid lines in bottom panel represent the air-relative aircraft tracks of the top VPDD pass and of the up–down profiling pass shown in Fig. 8. Thick lines in the insets at left are conceptual interpretations of the flow.

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Fig. 8.
Fig. 8.

Contours of (a) Doppler velocity and (b) radar reflectivity in the vertical plane above and below the AC, for an up–down profiling pass revealing multiple thermals in the cloud shown in Fig. 7; time 1910:30 UTC.

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Fig. 9.
Fig. 9.

Simple model of a tilted toroid core. The meridional velocity increases linearly along the tube radius, with maximum velocity equal to 5 m s−1 and the average azimuthal vorticity is 0.04 s−1. The ratio of mean updraft to relative airspeed is assumed to be about 5 (see section 6). The toroid axis is tilted by 30° in the upwind direction (negative y). Relative wind direction is denoted by thick arrows. Filled contours of vertical vorticity (s−1) and horizontal velocity vectors are shown in three horizontal sections (A, B, C).

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Fig. 10.
Fig. 10.

Schematic of the stabilized trajectory (dash–dot–dot line) of the rising toroid. Because of an aerodynamic torque, the toroid tilts into the wind and opposes the normal cross-flow advection, which by itself would lead to a rise along the slanted dotted line. The updraft core is marked by three thick arrows in the center of the toroid. The wind shear is denoted by the arrows on the right-hand side. The hollow arrows represent the resultant Kutta–Joukowski forces mat produce the tilting torque on the toroid. The ratio of mean updraft to relative airspeed is assumed to be about 5 at all levels.

Citation: Journal of the Atmospheric Sciences 64, 6; 10.1175/JAS3941.1

Save
  • Ackerman, B., 1958: Turbulence around tropical cumuli. J. Meteor., 15 , 6974.

  • Bluestein, H. W., and C. C. Weiss, 2004: Doppler radar observations of dust devils in Texas. Mon. Wea. Rev., 132 , 209224.

  • Blyth, A. M., 1993: Entrainment in cumulus clouds. J. Appl. Meteor., 32 , 626641.

  • Blyth, A. M., W. A. Cooper, and J. B. Jensen, 1988: A study of the source of entrained air in Montana cumuli. J. Atmos. Sci., 45 , 39443964.

    • Search Google Scholar
    • Export Citation
  • Carpenter, R. L. J., K. K. Droegemeier, and A. M. Blyth, 1998: Entrainment and detrainment in numerically simulated cumulus congestus clouds. Part III: Parcel analysis. J. Atmos. Sci., 55 , 34403455.

    • Search Google Scholar
    • Export Citation
  • Carroll, J. J., and J. A. Ryan, 1970: Atmospheric vorticity and dust devil rotation. J. Geophys. Res., 75 , 51795184.

  • Chang, Y. K., and A. D. Vakili, 1995: Dynamics of vortex rings in crossflow. Phys. Fluids, 7 , 15831597.

  • Church, C. R., J. T. Snow, and J. Dessens, 1980: Intense atmospheric vortices associated with a 1000 MW fire. Bull. Amer. Meteor. Soc., 61 , 682694.

    • Search Google Scholar
    • Export Citation
  • Cortese, T., and S. Balachandar, 1993: Vortical nature of thermal plumes in turbulent convection. Phys. Fluids, 5 , 32263232.

  • Cunningham, P., S. L. Goodrick, M. Y. Hussaini, and R. R. Linn, 2005: Coherent vortical structures in numerical simulations of buoyant plumes from wildland fires. Int. J. Wildland Fire, 14 , 6175.

    • Search Google Scholar
    • Export Citation
  • Damiani, R., and S. Haimov, 2006: A high-resolution dual-Doppler technique for fixed multi-antenna airborne radar. IEEE Trans. Geosci. Remote Sens., 42 , 34753489.

    • Search Google Scholar
    • Export Citation
  • Damiani, R., S. Haimov, and G. Vali, 2005: High-resolution airborne radar dual-Doppler technique. Preprints, 32d Conf. on Radar Meteorology, Albuquerque, NM, Amer. Meteor. Soc., CD-ROM, P1R.4.

  • Damiani, R., G. Vali, and S. Haimov, 2006: The structure of thermals in cumulus from airborne dual-Doppler radar observations. J. Atmos. Sci., 63 , 14321450.

    • Search Google Scholar
    • Export Citation
  • Davies-Jones, R., 1984: Streamwise vorticity: The origin of updraft rotation in supercell storms. J. Atmos. Sci., 41 , 29913006.

  • Diez, F. J., L. P. Bernal, and G. M. Faeth, 2003: Round turbulent thermals, puffs, starting plumes and starting jets in uniform crossflow. ASME J. Heat Transfer, 125 , 10461057.

    • Search Google Scholar
    • Export Citation
  • Emmitt, G. D., 1978: Tropical cumulus interaction with and modification of the subcloud region. J. Atmos. Sci., 35 , 14851502.

  • Etling, D., 1985: Some aspects of helicity in atmospheric flows. Beitr. Phys. Atmos., 58 , 88100.

  • Fernando, H. J. S., and D. C. I. Smith, 2001: Vortex structure in geophysical convection. Eur. J. Mech., 20B , 437470.

  • Fric, T. F., and A. Roshko, 1994: Vortical structure in the wake of a transverse jet. J. Fluid Mech., 279 , 147.

  • Hauf, T., 1985: Rotating clouds within cloud streets. Beitr. Phys. Atmos., 58 , 380398.

  • Kanak, K. M., D. K. Lilly, and J. T. Snow, 2000: The formation of vertical vortices in the convective boundary layer. Quart. J. Roy. Meteor. Soc., 126 , 27892810.

    • Search Google Scholar
    • Export Citation
  • Kelso, R. M., T. T. Lim, and A. E. Perry, 1996: An experimental study of round jets in cross-flow. J. Fluid Mech., 306 , 111144.

  • Kitchen, M., and S. J. Caughey, 1981: Tethered-balloon observations of the structure of small cumulus clouds. Quart. J. Roy. Meteor. Soc., 107 , 853874.

    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., 1987: Dynamics of tornadic thunderstorms. Annu. Rev. Fluid Mech., 19 , 369402.

  • Lilly, D. K., 1986: The structure, energetics, and propagation of rotating convective storms. Part II: Helicity and storm stabilization. J. Atmos. Sci., 43 , 126140.

    • Search Google Scholar
    • Export Citation
  • Lim, T. T., T. H. New, and S. C. Luo, 2001: On the development of large-scale structures of a jet normal to a cross flow. Phys. Fluids, 13 , 770775.

    • Search Google Scholar
    • Export Citation
  • Malkus, J. S., 1954: Some results of a trade-cumulus cloud investigation. J. Atmos. Sci., 11 , 220237.

  • Maxworthy, T., 1973: A vorticity source for large-scale dust devils and other comments on naturally occurring columnar vortices. J. Atmos. Sci., 30 , 17171722.

    • Search Google Scholar
    • Export Citation
  • Morton, B. R., 1997a: Discrete dry convective entities. I: Review. The Physics and Parameterization of Moist Atmospheric Convection, Series C: Mathematical and Physical Sciences, Vol. 505, Kluwer Academic, 143–173.

    • Search Google Scholar
    • Export Citation
  • Morton, B. R., 1997b: Discrete dry convective entities. II: Thermals and deflected jets. The Physics and Parameterization of Moist Atmospheric Convection, Series C: Mathematical and Physical Sciences, Vol. 505, Kluwer Academic, 175–210.

    • Search Google Scholar
    • Export Citation
  • Perry, K. D., and P. V. Hobbs, 1996: Influences of isolated cumulus clouds on the humidity of their surroundings. J. Atmos. Sci., 53 , 159174.

    • Search Google Scholar
    • Export Citation
  • Rogers, D. P., J. W. Telford, and S. K. Chai, 1985: Entrainment and the temporal evolution of the microphysics of convective clouds. J. Atmos. Sci., 42 , 18461858.

    • Search Google Scholar
    • Export Citation
  • Rotunno, R., 1981: On the evolution of thunderstorm rotation. Mon. Wea. Rev., 109 , 577586.

  • Scorer, R. S., 1958: Natural Aerodynamics. Vol. 1, International Series of Monographs in Aeronautics and Astronautics, Pergamon, 312 pp.

    • Search Google Scholar
    • Export Citation
  • Scorer, R. S., and F. H. Ludlam, 1953: Bubble theory of penetrative convection. Quart. J. Roy. Meteor. Soc., 79 , 94103.

  • Shapiro, A., and Y. L. Kogan, 1994: On vortex formation in multicell convective clouds in a shear-free environment. Atmos. Res., 33 , 125136.

    • Search Google Scholar
    • Export Citation
  • Shapiro, A., and M. Kanak, 2002: Vortex formation in ellipsoidal thermal bubbles. J. Atmos. Sci., 59 , 22532269.

  • Vaillancourt, P. A., M. K. Yau, and W. W. Grabowski, 1997: Upshear and downshear evolution of cloud structure and spectral properties. J. Atmos. Sci., 54 , 12031217.

    • Search Google Scholar
    • Export Citation
  • Woodward, B., 1959: The motion in and around isolated thermals. Quart. J. Roy. Meteor. Soc., 85 , 144151.

  • Zhao, M., and P. H. Austin, 2005: Life cycle of numerically simulated shallow cumulus clouds. Part II: Mixing dynamics. J. Atmos. Sci., 62 , 12911310.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Horizontal beam dual-Doppler operation of the Wyoming Cloud Radar.

  • Fig. 2.

    King Air sounding for 1750–2000 UTC 20 Jul 2003. The bar on the right of the plot denotes the cloud layer.

  • Fig. 3.

    Two sets of observations of a cumulus congestus from 2030 UTC 16 Jul 2003, at 7900 m MSL. (a)–(d) Up–down radar profile and in situ data, and (e) an HBDD section from a subsequent pass. (a) LWC (solid line) and IWC (dotted line); (b) gust-probe measured air vertical velocity ω, with overlaid 1-s gust vectors in the vertical [u, ω and horizontal plane (u, υ)] (deviations from a mean horizontal wind); (c),(d) Doppler velocity and reflectivity contours in the vertical plane above and below the aircraft (AC); (e) reflectivity contours [using same color bar as in (d)] and dual-Doppler retrieved velocity vectors (relative to the ambient wind); thin black lines are streamlines, thick solid lines are the AC air-relative tracks of the (top) HBDD and of the (bottom) up–down profiling passes; the arrow labeled with N indicates true north, the ambient wind (∼260° at 11.8 m s−1) is shown by the thick arrow (not to scale); vector grid resolution is ∼45 m, but only every second vector is shown for clarity; the marker (heavy white cross) points to the center of the region of horizontal divergence.

  • Fig. 4.

    Same as Fig. 3e but for a horizontal section showing a CVP from 2050 UTC 17 Jul 2003, at 7900 m MSL. Filled contours are reflectivity (dBZ). Labels 1 and 2 point to the centers of the CVP and label 3 to the region of horizontally diverging flow. Thick lines in the inset figure at top left are a conceptual interpretation of the CVP. Flight level ambient wind was 242° at ∼7 m s−1 (arrow not to scale for better visualization).

  • Fig. 5.

    Same as Fig. 4 but for an example of CVP from 1935:30 UTC 12 May 2003, at 7800 m MSL, with the bottom panel showing the derived vorticity values (s−1). Mean wind at flight altitude is 307° at 17 m s−1. Labels 1 and 2 point to the centers of the vortices. The vorticity data had to be thresholded for the errors coming from the derivative calculations at the edges of the cloud, where grid cells with valid data are adjacent to those containing data below the noise limit.

  • Fig. 6.

    Three consecutive horizontal sections showing persistence of CVP, from 17 Jul 2003, at 8100 m MSL; scan times: 2116, 2117:30, and 2119 UTC, respectively. The first pass (A) was made closer to the center of the cloud, whereas the other two were near its outer edge. Meaning of symbols and of filled contours for the lower panels are the same as in Fig. 4. Labels 1 and 2 denote the centers of two circulations. (top) In situ data collected during the first pass: ω (solid) air vertical velocity, T (dashed) reverse-flow temperature, LWC (dashed–dotted) from DMT probe, IWC (dotted), and horizontal plane gust vectors (relative to the mean wind at flight level; i.e., 239° at 10 m s−1).

  • Fig. 7.

    (middle) A vertical section with in situ data and (bottom) a horizontal section through a smaller cloud. Data are from 1903–1906 UTC 20 Jul 2003, at 6700 m MSL. Meaning of symbols and of filled contours for the lower panels are the same as in Fig. 4. (top) In situ data: w (solid) air vertical velocity, LWC (dashed–dotted) from DMT probe, and horizontal-plane gust vectors (relative to the mean wind at flight level; i.e., 314° at 6 m s−1). Labels 1 and 2 point to the centers of circulations. The thick solid lines in bottom panel represent the air-relative aircraft tracks of the top VPDD pass and of the up–down profiling pass shown in Fig. 8. Thick lines in the insets at left are conceptual interpretations of the flow.

  • Fig. 8.

    Contours of (a) Doppler velocity and (b) radar reflectivity in the vertical plane above and below the AC, for an up–down profiling pass revealing multiple thermals in the cloud shown in Fig. 7; time 1910:30 UTC.

  • Fig. 9.

    Simple model of a tilted toroid core. The meridional velocity increases linearly along the tube radius, with maximum velocity equal to 5 m s−1 and the average azimuthal vorticity is 0.04 s−1. The ratio of mean updraft to relative airspeed is assumed to be about 5 (see section 6). The toroid axis is tilted by 30° in the upwind direction (negative y). Relative wind direction is denoted by thick arrows. Filled contours of vertical vorticity (s−1) and horizontal velocity vectors are shown in three horizontal sections (A, B, C).

  • Fig. 10.

    Schematic of the stabilized trajectory (dash–dot–dot line) of the rising toroid. Because of an aerodynamic torque, the toroid tilts into the wind and opposes the normal cross-flow advection, which by itself would lead to a rise along the slanted dotted line. The updraft core is marked by three thick arrows in the center of the toroid. The wind shear is denoted by the arrows on the right-hand side. The hollow arrows represent the resultant Kutta–Joukowski forces mat produce the tilting torque on the toroid. The ratio of mean updraft to relative airspeed is assumed to be about 5 at all levels.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1748 722 46
PDF Downloads 240 67 3