We apply a modified proper orthogonal decomposition (POD) to large eddy simulation data of a wind turbine wake in a turbulent atmospheric boundary layer. The turbine is modeled as an actuator disk. Our analysis mainly focuses on the pragmatic identification of spatial modes, which yields a low order description of the wake flow. This reduction to a few degrees of freedom is a crucial first step for the development of simplified dynamic wake models based on modal decompositions. It is shown that only a few modes are necessary to capture the basic dynamical aspects of quantities that are relevant to a turbine in the wake flow. Furthermore, we show that the importance of the individual modes depends on the relevant quantity chosen. Therefore, the optimal choice of modes for a possible model could in principle depend on the application of interest. We additionally present a possible interpretation of the extracted modes by relating them to the specific properties of the wake. For example, the first mode is related to the horizontal large-scale movement.

In this work, large eddy simulation data is analysed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the large eddy simulation (LES) model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD), three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three different wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistical characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be captured by adding to our model a homogeneous turbulent field. In this way, we present a procedure to derive stochastic wake models from costly computational fluid dynamics (CFD) calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained.

We investigate the competition between two different functional groups of phytoplankton in the wake of an island close to a coastal upwelling region. We couple a simple biological model with three trophic levels and a hydrodynamic model of a von Kármán vortex street. The spatio-temporal abundance shows that the different phytoplankton groups dominate in different regions of the flow. The composition of the phytoplankton community varies e.g. for the different vortices. We study the mechanism leading to these inhomogeneous dominance patterns by investigating the nutrient transport in the flow and the interplay of hydrodynamic and biological time scales.