Performance of wind turbines in a turbulent atmosphere

The effect of atmospheric turbulence on the power fluctuations of large wind turbines was studied. The significance of spatial non-uniformities of the wind is emphasized. The turbulent wind with correlation in time and space is simulated on the computer by Shinozukas method. The wind turbulence is modelled according to the Davenport spectrum with an exponential spatial correlation function. The rotor aerodynamics is modelled by simple blade element theory. Comparison of the spectrum of power output signal between 1-D and 3-D turbulence, shows the significant power fluctuations centered around the blade passage frequency

Comparison between solutions of SDEs and ODEs

A ratio-limit comparison between ξt, the solution of an SDE driven by a semimartingale, and Ht, the solution of an associated ODE, is proved on the set where limt→∞ξt=∞. Sufficient conditions in terms of the driving processes and the coefficients are obtained for limt→∞ξt to be ∞. © 1988

Existence and uniqueness of solutions to the backward 2D stochastic Navier-Stokes equations

The backward two-dimensional stochastic Navier-Stokes equations (BSNSEs, for short) with suitable perturbations are studied in this paper, over bounded domains for incompressible fluid flow. A priori estimates for adapted solutions of the BSNSEs are obtained which reveal a pathwise L∞ (H) bound on the solutions. The existence and uniqueness of solutions are proved by using a monotonicity argument for bounded terminal data. The continuity of the adapted solutions with respect to the terminal data is also established. © 2008 Elsevier B.V. All rights reserved