Normal law of distribution of wind velocity vector in polar coordinates
Journal Title: Український гідрометеорологічний журнал - Year 2017, Vol 20, Issue 20
Abstract
It is impossible to organize wind energy systems without studying of wind speed regime at the surface layer of the atmosphere within a specific area and at climatic scales. Such studies are often accompanied by approximations of probabilities of wind speed performed in the form of normal law of a system of random values presented by a zonal u and a meridional v which are components of a wind speed vector. It is suggested that, for the purposes of wind energy, display of a wind speed vector in polar coordinates (r,a) where r is a module of wind speed and a is a polar angle appears to be more preferable. The article shows a transform from a normal law of distribution of probabilities with density f(u,v) to a normal law distribution with density f(r,a) completed by means of functional transformation with elliptic dispersion in place. Based on a normal law of distribution f(r,a) and through integration with respect to corresponding variables (r,a) individual distributions of probabilities f(r) and f(a) as well as conditional distributions of probabilities f(r/a) and f(a/r) were obtained in the areas of their existence. The article shows individual distributions in case of circular and elliptic dispersion of a wind speed vector. It shows that an individual distribution of a wind speed probability in case of circular dispersion and in the absence of correlated dependence turns into the Rayleigh's distribution and a conditional distribution of a polar angle degenerates in an even distribution. The cases of distributions with dispersions of a wind speed module having elliptic properties subject to availability of correlated connection between wind speed components were also studied. Calculation of probabilities of a polar angle being within different sections of the area 0≤α≤2π with set values of a wind speed module also took place. Numerical experiments proved the advantage of such modeling of distributions of wind speed vector.
Authors and Affiliations
E. P. Shkolnyy
Keywords
Related Articles
- EP ID EP327539
- DOI 10.31481/uhmj.20.2017.01
- Views 84
- Downloads 0
Description of artificial reservoirs within the catchment area of the Great Kuyalnik River and regulation of their operation at the present time and in future
The paper presents the results of surveys of artificial reservoirs of the Great Kuyalnik River and its tributaries which, due to their considerable number and filling volumes, significantly reduce the runoff of the river...
Calculation of wind speed in the 300-meter lower layer of the atmosphere based on the meteorological observations taking account of temperature stratification and surface roughness
Introduction. Taking into account relationship of wind profile power-law exponent (m) from hydrostatic stability of the layer and surface roughness the calculation method of wind speed and direction in the lower 300-mete...
Current distribution of wind in Morocco
Information about wind is widely used in many sectors of the economy. Wind also causes many dangerous and extreme weather events. Modern climate changes require a certain revision of weather patterns previously accepted...
Effect of forestry of the southern Ukraine on the regulation of carbon dioxide in the atmosphere
The article describes Tsyurupinsk Forest Hunting Range as the most powerful natural ecosystem having an effect on regulation of technology-related processes, namely on reduction of carbon dioxide stress on the environmen...
Modeling of sunflower’s productivity under future climate changes in Ukraine considering the scenarios of RCP anthropogenic impact
Climate change is one of the major global issues. Climate is one of the most significant factors determining the level of crop yields, including sunflower crops. Currently the sunflower planting acreage in Ukraine has al...