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  • American Meteorological Society  (4)
  • 2005-2009  (4)
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  • 1
    Publication Date: 2005-01-01
    Description: The collection equation is analyzed for the case of two spherical hydrometeors with collection efficiency unity and exponential size distributions. When the fall velocities are significantly different a more general form of the conventional Wisner approximation can be formulated. The accuracy of the new formula exceeds that of the Wisner approximation for all cases considered, except for the collection of a faster species by a slower species if the amount of the faster species is relatively small compared with that of the slower species. The exact solution of the collection equation is then rederived and cast into the form of a power series involving the ratio of the two characteristic fall velocities. It is shown that the new formulation is a first-order correction to the continuous collection equation for hydrometeors with finite diameters and fall velocities. Based on the analysis, the implications for the behavior of both the exact collection equation and its representation in numerical models are discussed.
    Print ISSN: 0022-4928
    Electronic ISSN: 1520-0469
    Topics: Geography , Geosciences , Physics
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  • 2
    Publication Date: 2006-04-01
    Description: An idealized supercell simulation using the Regional Atmospheric Modeling System (RAMS) produced an elongated low-level mesocyclone that subsequently collapsed into a concentrated vortex. Though vorticity continually increased in the mesocyclone due to horizontal convergence, the collapse phase was additionally characterized by rapidly decreasing pressure, closed streamlines, and the creation of a compact vorticity center isolated from the remaining vorticity. It was shown in Part I of this study that the concentration phase was not initiated by an increase in horizontal convergence, suggesting that the proximate cause resided elsewhere. In this study, the vortex concentration in Part I is examined from a vorticity dynamics perspective. It is shown that concentration occurs when inward radial velocity and vertical vorticity become more spatially correlated in the region surrounding the nascent vortex. It is also emphasized that the anisotropy of the horizontal convergence, which is nearly plane-convergent and of comparable magnitude to the mesocyclonic vorticity, is critical to an understanding of the process. The resultant evolution is intermediate between a state of purely two-dimensional nondivergent dynamics and one in which plane convergence confines vorticity to its axis of dilatation. This intermediate state produces a concentrated vortex more rapidly than either end state. The unsteady nature of the initial vorticity band also serves to increase the circulation and wind speed amplification of the final vortex. It is shown how conceptual models in the fluid dynamics literature can be applied to predicting the time and length scales of tornadic mesocyclone evolution.
    Print ISSN: 0022-4928
    Electronic ISSN: 1520-0469
    Topics: Geography , Geosciences , Physics
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  • 3
    Publication Date: 2006-04-01
    Description: An idealized simulation of a supercell using the Regional Atmospheric Modeling System (RAMS) was able to produce a low-level mesocyclone near the intersection of the forward- and rear-flank downdrafts. The creation of the low-level mesocyclone is similar to previous studies. After 3600 s, the low-level mesocyclone underwent a period of rapid intensification, during which its form changed from an elongated patch to a compact center. This transition was also accompanied by a sudden decrease in pressure (to 12 mb below that of the neighboring flow), and was found to occur even in the absence of nested grids. It is shown that the stage of strong intensification does not begin aloft, as in the dynamic pipe effect, and then descend to the surface. Rather, the vortex is initiated near the surface, and then builds upward. The process is completed in 5 min, and the final vortex can be clearly distinguished from the larger-scale mesocyclone at the cloud base. The reduction of pressure can be explained as a consequence of the evacuation of mass in the horizontal convergence equation. This is in contrast to axisymmetric models of vortex intensification, which generally rely on the evacuation of mass in the vertical divergence equation. In the latter cases a positive horizontal convergence tendency is what initiates the concentrated vortex. However, nondivergent models prove that vorticity concentration can occur in the absence of any horizontal convergence. Here the concentration is associated with a negative horizontal convergence tendency.
    Print ISSN: 0022-4928
    Electronic ISSN: 1520-0469
    Topics: Geography , Geosciences , Physics
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  • 4
    Publication Date: 2007-01-01
    Description: Past microphysical investigations, including Part I of this study, have noted that the collection equation, when applied to the interaction between different hydrometeor species, can predict large mass transfer rates, even when an exact solution is used. The fractional depletion in a time step can even exceed unity for the collected species with plausible microphysical conditions and time steps, requiring “normalization” by a microphysical scheme. Although some of this problem can be alleviated through the use of more moment predictions and hydrometeor categories, the question as to why such “overdepletion” can be predicted in the first place remains insufficiently addressed. It is shown through both physical and conceptual arguments that the explicit time discretization of the bulk collection equation for any moment is not consistent with a quasi-stochastic view of collection. The result, under certain reasonable conditions, is a systematic overprediction of collection, which can become a serious error in the prediction of higher-order moments in a bulk scheme. The term numerical bounding is used to refer to the use of a quasi-stochastically consistent formula that prevents fractional collections exceeding unity for any moments. Through examples and analysis it is found that numerical bounding is typically important in mass moment prediction for time steps exceeding approximately 10 s. The Poisson-based numerical bounding scheme is shown to be simple in application and conceptualization; within a straightforward idealization it completely corrects overdepletion while even being immune to the rediagnosis error of the time-splitting method. The scheme’s range of applicability and utility are discussed.
    Print ISSN: 1558-8424
    Electronic ISSN: 1558-8432
    Topics: Geography , Physics
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