С помощью новой двумерной модели мезомасштабных процессов оценивается влияние неоднородности температуры и влажности на образование вихревых структур в нижнем слое атмосферы. Вывод модели осуществляется на основе локально-равновесного подхода путем усреднения поперек слоя исходных трехмерных уравнений, описывающих мезомасштабные атмосферные процессы. Для замыкания системы, заключающегося в определении нелинейных слагаемых и значений на границах полей скорости, температуры и влажности через усредненные поля, используется точное решение исходной задачи, описывающее однородное по горизонтальным координатам течение. Это решение находится для бесконечного горизонтального вращающегося слоя в предположении несжимаемости воздуха в нижнем слое атмосферы и линейного распределения температуры и влажности подстилающей поверхности. Численные расчеты проводились методом сеток с помощью явной конечно-разностной схемы на сетке 200×200 узлов. Рассматривалась площадка 40 на 40 километров в северо-западной части города Перми и прилежащих окрестностях. Расчеты показали, что на фоне значительных горизонтальных градиентов температуры воздуха и влажности в нижнем слое атмосферы возникают вихревые структуры с вертикальной осью вращения. Появление вихревых структур обуславливается также конфигурацией зон значительных градиентов и их расположением относительно движущегося воздуха.Ключевые слова: моделирование пограничного слоя атмосферы, неоднородность температуры и влажности, численные расчеты TWO-DIMENSIONAL MODEL OF MESOSCALE PROCESSES IN THE LOWER ATMOSPHERE WITH ALLOWANCE FOR INHOMOGENEITY OF TEMPERATURE AND AIR HUMIDITY K.G. Shvarts, Yu.A. Shvarts and V.A. Shklyaev Perm State University, Perm, Russian FederationA new two-dimensional model of mesoscale processes is used to estimate the influence of temperature and air humidity heterogeneities on the formation of vortex structures in the lower atmosphere. The model has been developed on the basis of the local equilibrium approach by averaging the original three-dimensional equations for mesoscale atmospheric processes across the layer. To close the system of equations, an exact solution of the original problem describing the flow homogeneous with respect to horizontal coordinates is applied. The closure consists in determining the nonlinear terms and the values at the boundaries of velocity, temperature and humidity fields via the averaged field. The solution is obtained for an infinite horizontal rotating layer under the assumption of air incompressibility in the lower atmosphere and linear distribution of the temperature and humidity of the underlying surface. Numerical calculations were performed using a grid method, in which an explicit finite difference scheme is applied to a grid of 200×200 nodes. Computations were carried out for the 40×40 km area in the North-Western part of the city of Perm and its immediate vicinity with account for the underlying surface roughness. It has been found that the vortex structure with a vertical axis of rotation arises at significant horizontal...
Abstract. Within the framework of block self-organizing of geological bodies with use of deformation theory the mathematical solution of a problem for effective final speed is proposed. The analytical and numerical integrated solutions of Navier-Stokes equation for deformable porous space were obtained. The decisions of multi-scaled regional problems «on a flow basis» were also presented: from lithology of rock space -to a well and from a well -to petro-physics. The evolutionary transformation of the linear solution of the equation on mass conservation up to the energetically stable non-linear solution of the equation on preserving the number of movements is also offered. Basing upon the analytical solution of Navier-Stokes equation and model of A.N. Kolmogorov we have obtained the energy model of turbulence pulsing controlled chaos, conjugated with risk stability of average well inflow and cluster structure of Earth de fluidization. IntroductionRevolution with shale has brightly illustrated the possibilities of theoretical solutions for NavierStokes equation in the burning issue of the century -global geology correlated with global mathematics, geo-physics, geo-dynamics and global economy. Multi-scaled solutions for continuous medium of porous micro-structure, the equations based upon the conservation laws and phase trajectories of micro-world pulse moment are correlated by energy with conjugated solutions of Navier-Stokes equation and conditions of system equilibrium (porous matrix). Physical and mathematical solutions of inflow profiles with due consideration of geological risks in development of the reservoir with complex structure are well coordinated with geo-physical, seismic experiments, actual well production rates and cluster structure of the economics.
The authors present the hydro-geological basin-type model of global energetics with hydro-dynamic potential showing the interaction of inland platforms of the Earth. The authors propose the new cluster-type approach towards the asymmetric multi-scaled modeling at the basis of integral solution within the quadrature of Navier-Stokes equation for deformed micro-structure of Earth's porous space. We have studied the effect of poor local tectonic faults upon the arrangement of hydrocarbon traps in lithosphere, shale tight fields, that is based upon the interconnected methods in geophysics, hydro-geology and geo-mechanics, tectono-physics and structural geology. The authors also present the scientific concept of new principles to increase the level of geo-informatics while searching exploring and developing the hydro-carbon reserves, geo-physical studies of seismic emissions, micro-seismic and seismology of mega-scales in geological ages of stresses with transition to predictable man-induced time for geological/technological events. Basing upon the conjugation of Navier-Stokes equation and due consideration of deforming relaxation we have built the energy self-arranged model of Earth's lithosphere de-fluidization, have found inherent energy delayed spectra for the dynamic contacts of stratified structure. We have obtained the energy conjugated solution of micro-structure porous media interaction for hydro-geological decompression of subduction channel in seabed and saturation of generalized Middle Oceanic Ridge with self-organization of classic sedimentological hydro-carbon traps and complexly organized shale reservoirs with compacted depositions of Allochthon structures in Domanik and Bazhenov formations. The authors present the energy stable mean filtration profile as per Darcy, conjugated with stress-deformed status of porous geo-media micro-structure at various boundary conditions: closed-type or capillary jammed boundaries of filtration blocks and free-type -with phase filtration front and diffusive displacement of fluids by saturated porous media and smart technologies of multi-stage hydro-fracture in dense shale reservoirs. Analytically, in quadrature, there is the dissipation velocity, potential and kinetic energy potentials of mean outflow and shear layer of filtration dissipative structure, like a generalized model of viscous elasticity that depends upon the wave number, phase velocity, thickness of the layer and geo-mechanical parameters that reflect the geo-media heterogeneity.
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