ИСТИНА

The problem of description of the wind field between spatially heterogeneous vegetation cover and the atmospheric surface layer leads to the solution of the system of the Navier-Stokes equation and a continuity equation. As usually the system is averaged before solving. To construct the mathematical model describing the process of the air flow interaction with vegetation we used the description that is appropriate for dissipative contrast structures in active environments. Such environments include multi-stable and excitable elements. Multi-stable elements have more than one stable state. We use the following analogy: the X component of the wind velocity plays the role of a multi-stable element. It has two stable states: the wind speed $u_{open}$ in open area and the wind speed $u_{forest}$ inside the vegetation (forest). The other two components of the wind velocity play the role of an excitable element and have one zero stable state. The initial condition is specified as external factor that switches the state of multi-stable element from level $u_{forest}$ to level $u_{open}$ . The continuity equation defines the feedback. The dissipative contrast structures are commonly described by parabolic equations with cubic nonlinearity. That is why we choose such a nonlinearity to describe the interaction of horizontal air flow with vegetation in the proposed model. We should note that the use of contrast structures allows to obtain a stable solution of the considered system of equations.