# The research of the evolution of the wind profile over the underlying surface

### Аuthors

Kudrov M. A.*, Zudov K. A.**, Yudin M. A.***, Kharchilava Y. E.****

Moscow Institute of Physics and Technology (State University) (MIPT), 16, Gagarin St., Zhukovsky,140180, Russia

*e-mail: mkudrov@phystech.edu
**e-mail: xzudov@mail.ru
***e-mail: mikleudin@yandex.ru
****e-mail: harchilava.yurii@gmail.com

### Abstract

The basic idea of this scientific work was the study of the evolution of the velocity profiles over the underlying surface. The purpose of the work was to obtain the vision of change in the velocities distribution in the flow over the surface with the adhesion condition in relation to a given initial velocity profile. The initial profile of the wind around the boundary layer. It also presents physical and mathematical explanation of the derivation of the velocity profile of wind on the basis a two-layer model of the boundary layer. The conclusion was based on the theory of M.I. Yudin and M.E. Shvets for the coefficient of turbulence. Moreover, in this work we simulate the wind profile evolution for flowing over flat surface with the length of 10 km, obtained on the basis of two-layer model. The modelling was carried out by the numerical integration of the Reynolds equations with the closure of turbulence model SST. It was verified by means of numerical calculations that the resulting profile of the wind speed based on a two-layer model has evolved significantly at fluxion over a smooth surface, which is caused by not taking into account the rotation of the Earth, and the temperature profile in the course of the calculations. Whereas the logarithmic profile of wind velocity, which is a characteristic of the surface sublayer, does not change in the course of calculations.

### Keywords:

profile velocity, boundary conditions, turbulence coefficient

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