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Numerical Pattern of 3D Tornado Rise with Account for Mirror Asymmetry
Abstract and Figures
Authors are returning to the basic concepts of turbulence – homogeneity and symmetry principles. It is shown that the homogeneity in the sense of constant mean velocity gradient (instead of constant velocity) permits to introduce mirror asymmetry. This way is corresponding to stratified atmosphere and to differential volume in any continuum model. The basic ideas of A. N. Kolmogorov do not contradict to such an approach. Moreover, the use of the intrinsic eddy angular velocity (so-called spin or mesovorticity) as the internal thermodynamic parameter becomes necessary for adequate description of tornado (and intensive atmospheric vortices, in general) dynamics. The continuum description is formulated with standard introducing of stresses averaged over a cross-section, and now motivated asymmetry leads to the vortices moment of momentum balance. The set of nonlinear 3D partial differential equations is suggested for the problem of tornado generation from a cloud of initial vortices. The dependence of turbulent rotation viscosity on the spin permits to localize the tornado body due to the nonlinear diffusion effect. Numerical calculations are performed at two different clusters using Parjava program environment. The growth of typical tornado structure is shown by a sequence of pictures. A visual comparison with the Hurricane Isabel, 2003, is represented.
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Purpose
The purpose of the study is to evaluate the effect of different animal product wastes and plant compost on survival and growth of earthworm (Eisenia fetida).
Methods
The study is realized in a vermibin for a duration of 90 days. The initial physico-chemical parameters (pH, humidity, ash, organic matter, carbon, nitrogen, phosphorus and C:N ratio) were determined in each waste of the different substrates before the study. Six waste products (pig, poultry, rabbit, cattle, sheep and vegetal compost) in triplicate (6 × 3) were used for earthworm production. In each 12-l content vermibin, 2 kg of substrate and 30 g of mature earthworms were sown. Each month, the growth control was realized by earthworms harvest and weighing. The earthworms were put back in substrate in vermibin and 500 g of substrate were completed. The pH was measured every week.
Results
The physico-chemical parameters (pH, ash, organic matter, carbon, phosphorus, nitrogen and C:N ratio) varied (P < 0.05) according to different substrate. The C:N ratio of different organic substrates are in the range of 8.46 in vegetable compost to 19.39 in pig dung. At the end of study the biomass gain and mortality varied (P < 0.05) according to different treatments. The growth rate varied according to different organic waste (P < 0.05) and ranged between −0.06 ± 0.02 (vegetable compost) and 1.34 ± 0.11 (cow dung). Maximum weight gain and highest growth rate were attained with cow dung. Earthworm biomass gain in different animal wastes is in the order of: cow > pig > rabbit > poultry > sheep > compost vegetable.
Conclusion
The animal wastes (cow, sheep, pig, rabbit and poultry) and vegetable compost can be used to produce the earthworm. But the growth and produce depend on the biochemical quality of the substrates and the availability and facility for using a nutritive element.
Mesovortices in the eyewall region of a hurricane are intriguing elements of the hurricane engine. In-situ measurements of them are sparse, however, and our understanding of their overall role in the physics of a hurricane is incomplete. To further understand their dynamics an experimental apparatus using a homogeneous fluid (water) has been constructed to emulate the lower tropospheric flow of the hurricane eye/eyewall region. For experimental configurations possessing a central aspect ratio less than unity, a primary and secondary circulation similar to the inflow layer of an intense hurricane, and a similar radius-to-width ratio of the curvilinear shear layer bordering the eye and eyewall region, the flow supports two primary quasi-steady vortices and secondary intermittent vortices. The vortices form through Kelvin–Helmholtz instability of the curvilinear shear layer bordering the slowly upwelling fluid in the centre and the converging fluid from the periphery. The primary vortices are maintained by convergence of circulation from the periphery and merger of secondary vortices spawned along the shear layer. The horizontal flow field is measured using a particle image velocimeter. Despite the relatively strong secondary circulation through the parent vortex the horizontal flow is found to be approximately uniform in the direction parallel to the rotation axis. The peak tangential velocity is found to occur in the mesovortices and is roughly 50% greater than the parent vortex that supports them. The measurements provide insight into recent observations of excessive wind damage in landfalling storms and support the hypothesis that intense storms contain coherent vortex structures in the eyewall region with higher horizontal wind speeds locally than the parent hurricane.
Turbulence theory is one of the most intriguing parts of fluid mechanics and many outstanding scientists have tried to apply their knowledge to the development of the theory and to offer useful recommendations for solution of some practical problems. In this monograph the author attempts to integrate many specific approaches into the unified theory. The basic premise is the simple idea that a small eddy, that is an element of turbulent meso-structure, possesses its own dynamics as an object rotating with its own spin velocity and obeying the Newton dynamics of a finite body. A number of such eddies fills a coordinate cell, and the angular momentum balance has to be formulated for this spatial cell. If the cell coincides with a finite difference element at a numerical calculation and if the external length scale is large, this elementary volume can be considered as a differential one and a continuum parameterization has to be used. Nontrivial angular balance is a consequence of the asymmetrical Reynolds stress action at the oriented sides of an elementary volume. At first glance, the averaged dyad of velocity components is symmetrical, == However, if averaging is performed over the plane with normal nj, the principle of commutation is lost. As a result, the stress tensor asymmetry j is determined by other factors that participate in the angular momentum balance. This is the only possibility to determine a stress in engineering.
The problem of hurricanes and tornadoes is one of the most intriguing geophysical phenomena and its consideration is based on a nonlinear variant of the theory under consideration. Possible dependency of turbulent viscosities on spin eddy rotation rate leads to nonlinear diffusion equations and this means the localization of turbulent object by a front, slowly spreading in the atmosphere. Two variants are considered — with constant [119] and changing eddy moment of inertia [120]. The latter gives the solution with internal core (“eye”) rotating in a solid manner. The coincidence with hurricane David is shown.
Eringen's theory of micropolar fluids is adopted as a possible description of turbulent flow. Since micropolar fluids can undergo microrotations but not micro stretching, motions of this type of fluids should resemble turbulent motions. Examples of spherically symmetric microrotations without micromotion and microrotations are described.
Mesovortives that formed in hurricane Isabel is discussed. Due to the presence of six mesovortices, Isabel's eye represented a pentagonal pattern resembling a starfish. It is suggested that the mesovortices that form in hurricanes play an essential role in hurricane intensification. It is also suggested that the hurricane Isabel helped in understanding the turbulent dynamics of the hurricane inner core and helped to validate previous predictions based on the equation of motion.