Identification of a 2D turbulent wind spectrum

Turbulent wind spectrum models usually involve nonrational terms. For such models the development of a Markovian time simulator relies on a rational approximation obtained by the way of an identification stage. This paper presents a general method to manage this identification stage, that provides us with a family of stable rational approximations which is proved to converge towards the true model as the dimension increases. We first give an exact but infinite dimensional state space representation of the spectrum. It is based on the use of a diffusive equation. For bi-dimensional (2D) signals it also uses decoupling by spatial Fourier transformation. Then the discretization of this exact model leads easily to stable finite dimensional approximations over a prescribed frequency range. This approach is applied to the identification of a theoretical 2D turbulent wind spectrum, and of a 1D turbulent wind spectrum estimated from in flight recorded data.