The concept of vortex convective storms

It is proposed a method of analyzing the effects of the environmental vertical wind shear on the structure and dynamics of convective storms, the conditions for the occurrence of vortex storms based on the hydrodynamic laws of flow around of solid body in the Lagrangian coordinate system. There is described an example of the evolution of a supercell based on radar observations with the updated information of 3 minutes. It is shown the unity of the complex structure and dynamics, which allows proposing a typical model of vortex storms. The method of analysis affords to explain the sequential continuity of the types of storms, the prevalence of the right-propagation (in the Northern Hemisphere). It is proposed a classification of convective storms based on the interaction of the internally associated ascending flow and rotation with the environmental dynamic factor of wind shear.


Introduction
Many authors, both in Russia [1] and especially in the West (many works are summarized in [2], [3]), attach great importance to the influence of the environmental wind and, in particular, wind shear when studying the structure and dynamics of Cb. The article considers the mechanism of formation and the model of vortex convective storms based on elementary hydrodynamic laws of flow around a solid body.

Methods and results of research
For the convenience and visibility, the analysis of the dynamic effect of the environmental wind on the Convective Object (CO) -the Convective Cell (CC) or a storm, all processes will be considered in the Lagrangian Coordinate System (LCS). The LSC moves with the CO placed in its center along the mainstream V (the average wind in the layer occupied by the CO, or the wind at the level of 600 hPa, along which the CC moves). For the transferring the usual hodograph (in the Euler Coordinate System -ECS) of the environmental wind into the Dynamic Hodograph (DH) in the LCS [4], [5], it is enough to connect by vectors C of hodograph points with the mainstream point (figure 1-I) , since C LCS = C ECS -V. The obtained vectors -dynamic winds (CO-relative) -show from which direction and with what speed the horizontal streams flow to the CO. From the point of view of the physics phenomena associated to convection, on the vertical section of a linear DH (figure 1-II.1 and III b), the following tropospheric layers and the role of dynamic winds can be distinguished: the lower, sub-cloud, 0-2 km (G), containing the main share of the resource -humid, heated air -the source of mass of water vapor and energy of phases transitions; the feeder, 2-4 km (F), in which feeder clouds form and move; the average, 4-9км (M), in which main formation of hydrometeors takes place; the upper, > 9 km (H), in which there is a flow around the CO from above and blowing off of passive cloud masses. There is stand out two main layers -M and G (which are separated by an intermediate layer 3-4 km thick of relatively weak dynamic winds) according to the physical importance and dynamic strength of the winds: M separates the forming hydrometeors at the early stage of the CO development, flows around it in the mature stage with the possibility of the formation of the main stationary vortices and Stationary Convergent Zones (SCZ, figure 1-IVа,b and Va), dynamic pressure on the CO; G provides the rate of resource recovery in the area of the CO evolution and thereby its intensity and durability, the formation of stationary and Mobile Convergent Zones (MCZ) as a result of the collision of the flowing around CO flows with the counter flows of its rotation (figure 1-Vb), the formation behind the rotating main vortices of the vortex-satellites (figure 1-IVc and Vb), the dynamic pressure on the CO. By mutual orientation of the vectors M and G, 3 types of dynamic hodograph can be distinguished: linearly, with a left turn, with a right turn above the level of the mainstream (figure 1-II).
The stable vortices can be formed in the middle troposphere for flow around modes within the limits of critical values of the Reynolds number Re: Re* < Re < Re**, wherein Re = ρ·(ν·d)/η, ρ is the density of air in the middle layer; νthe wind speed in this layer; d -the size of the obstacle; η -the dynamic air viscosity. Considering the values of ρ and η are constants, the condition for the existence 3 of stable vortices is K 1 < M·d < K 2 . The presence of such conditions and processes in the lower troposphere has been proven, e.g. by the photographs of the Karman vortices formed with horizontal air flows around islands (size 5-6 km) in the ocean. The glider pilots discover stationary vortices and the specific circulation of flows around mountainous arrays (of the same scale) on land. The air density in the middle troposphere is about 2 times less and to achieve the desired mode requires high speeds or the size of the obstacle (ν·d)*, which is quite possible.
As the result, represents the following mechanism for the formation of a vortex system, with which such concepts as «superсell» and «mesocyclone» are associated. It is considered the linear DH and quasi-perpendicularly orient to the vector M obstacle (dense elongated cloud masses of CO) on the middle layer. At the beginning of the next stage of development in the process of periodic selfoscillations of the CO intensity (which occur due to the fact that the CO assimilates the resource faster than it is restored [6], [7]), reaching of critical flow around mode, a vortex couplet is born: cycloneanticyclone. When the elongated obstacle is located at an angle to M, the birth of one vortex is possible -cyclone or anticyclone (figure 1-IVd). When the couplet is downing into the lower layer G («dynamic tube effect»), it is flown around by counter flows of this layer with the formation of satellite vortices on the opposite side, rationalizing the flow around regime. Eventually, a system of four connected stationary vortices is formed (figure 1-Vb). In this system are formed the corridorsthe sections of joint rotation of neighboring vortices: the main resource collection is between cyclonic and anticyclonic vortices, cyclonic propagation -between cyclonic vortex and its satellite, anticyclonic -between anticyclonic vortex and its satellite, satellite -between satellite vortices. The main and satellite corridors form the storm convergence line (frontal and rear inflows of air and cloud masses of developing cells) and cyclonic and anticyclonic -the storm divergence line (removal of cloud mass and precipitation of dissipating cells). In this case, the SCZs with increased pressure forms (figure 1-Vb): basic (1), rear (2), propagation (3), anticyclonic (4) and central (5). It will be used the concept of the propagation of the СO -the increase in its mass (area) at Zm> 45dBZ in the middle layer. The propagation is manifested in varying degrees of contiguity of the feeder CC (the Footh coefficient -K F ), which reached the specific reflectivity in this layer -the signal CC (shows the storm propagation area), to the main mass (area) of the CO. On the ASU-MRL radar maps, this is referred in the form of radio-echo canopies or file-by-file increments in the LCS of the CO area. The direction of the propagation of the CO depends both on the development stage of the CO and on the dynamic vectors G, M and Wm -the maximum speed of updraft.
It is examined an example of supercell data from 05/25/2008 based on archived materials of the radar ASU-MRL, Kornesti village, SSAI, RM. The DH (figure 2-C) can be considered linear, almost coinciding with the mainstream V, the dynamic winds G ≈ 9 m·s -1 , M ≈ 7 m·s -1 are relatively small. The value of Re is: Re = 0.6kg·m -3 7m·c -1 6000m / 18000000Pa·c ≈ 0.001. In the time period from 15:00 to 16:10, the reflectivity in the layer of 6-8 km exceeded 55 dBZ (therefore, presumably as a condition for the occurrence of vortices can be taken K 1 < M · d 55 < K 2 ), and the CO was in the supercell, vortex state during which there are three stages of development with periods of about 20-25 minutes ( figure 2-A). The first stage (15:05-15:25) is associated with the formation of a complete vortex storm, which appears at the beginning in the formation from (amplifying from 14:50 to 15:05) the main cell of the initial storm of the main corridor, as well as a rapidly developing a new «cell» -a cyclonic vortex of the south of the corridor on the leeward side of the obstacle relative to M (figure 2-D).
In the white isolines of radar reflectivity Zm = 55 dBZ of surface precipitations on the leeward side, the characteristic notches associated with the centers of the vortices of the couplet are visible. Then, the precipitations began to separate into two areas of maxima ("RFD" and "FFD" [2], [3]) due to the impact on them of two adjacent opposite vortices with the creation of two hail fallouts streaks ( figure 2-B). Wherein, the largest hail, due to centrifugal forces, is concentrated on the outer side of the cyclonic vortex in the main corridor and is retrieved by the anticyclonic vortex (and then by the satellite of the cyclonic vortex). There is a gradual transformation of the horizontal field of the radar reflectivity Zm of the cyclonic vortex: from the maximum in the center of the circle to its distribution In the period 15: 25-15: 50, the 1 st CC of the main storm, being in the mean layer with the reflectivity of more than 45 dBZ and being carried away by the flows around and the rotation in this layer, is partially drawn into the cyclonic vortex, and partially is carried away beyond its limits and dissipated. This is manifested in the rotation of the canopy and the increments in the LCS around the vortex circumference. At the same time, the 2 nd CC of the main storm appears and grows. In the period 15: 50-16: 15, a similar process of carrying away of the 2 nd CC and the inception and growth of the 3 rd CC takes place, which at 16:06 gave an absolute maximum reflectivity of 72.6 dBZ. At 15:18 on the A1 map in figure 3, a «trident» is visible at the exit of the propagation corridor, formed by two descending branches of diverging vortices and the main storm between them. On maps A6 and C6, hail-dangerous chains are visible (according to Н 45 ) in the ascending branch of the anticyclonic vortex. Figure 4 shows the vertical sections of the radio-echo on the influences map at 15:18 along the three indicated contours. In the first two, they manifest the natural cycle of gradual development of cells rotating around the circumference of a cyclonic vortex, as well as carried away from the MCZ. It can be seen that having dropped precipitation in the main and propagation corridors, rather dense residual cloud masses continue to rotate in the circumference and rising in the ascending branch of the vortex. The pool of cold air from dropouts spreading at high speed along the propagation corridor stimulates the main storm. Figure 5 shows CCs at different stages of development, rotating in a circumference 6 km in diameter around the axis of the cyclonic vortex (exact correspondence [2] [3]; the diameter of the vortices should probably be equal to half the length of the obstacle, i.e., ≈ d/2).
It can be seen that the region of maximum ascending flows is located not in center of vortex, but in the ascending branches of the main vortices in the SCZ-1. The dissipation of a vortex storm begins when the conditions for its occurrence disappear: the value of Re of the flow around regime in the middle layer M becomes less than the critical Re* with a decrease in the size/density of the obstacle d in this layer due to the weakening of the convection intensity. The anticyclonic vortex begins to weaken and blur, its satellite disappears. The cyclonic vortex, decreasing in size, shifts to the driving edge of the storm, strengthening, together with its satellite, as a result of which Zm even reaches its maximum. After the collapse of the cyclonic vortex, its satellite remains the leader: figure 2-E shows that the last chain of the CCs drowns into it from the cyclonic vortex. In the final stage of storm dissipation, after the destruction of all vortices, the storm is elongated similar to the starting line. The remnants of three storms/CCs are visible in it (respectively, three former SCZ on the storm divergence  figure 2-F), more powerful in SCZ-3. During the entire evolution period, the presented full vortex storm did not divide into right-and left-propagation halves. During the stage of development of a vortex storm, there is a gradual increase of the velocity of the updraft and, accordingly, the speed of rotation of the vortex, then a decrease. It looks like turning the entire vortex system counterclockwise, then back (row C versus row A, figure 3). This corresponds to the deflection of the upper hail fall band and the approach of the lower band with it in the period up to 15:40 ( figure 2-B), followed by a return to the previous position. This phenomenon determines the zigzag direction of the storm propagation in the LCS (figure 4-E, [4]). Figure 6, based on the results of the presented analysis, as well as the analysis of other vortex storms, presents the generalized structural-dynamic model of the vortex storm (for the Northern Hemisphere, with a more active cyclonic vortex), on which can be seen its main structural elements (features).
The actual development of the considered processes and the particularities of the structure and dynamics of the vortex system depend on the mutual ratio of the modules and orientation of the vectors M and G, as well as the size and orientation of the obstacle relative to them. The degree of visibility of the structure of the storm and its transformation in time on radar maps strongly depends on the orientation of the storm relative to the radar. Taking the main thing in the CO (its inner essence) is the presence of coupled updraft W and rotation R, which are realized in environmental shear circumstances (G and M), and the other qualities are external manifestations of this process, it is possible to propose a classification of convective storms on the example of a linear DH (figure 7).