An analytical wake deflection model for wind farms including secondary wake steering

Abstract. Wake interactions between turbines are a major source of power loss in wind farms, which yaw-based wake steering seeks to mitigate. Existing steering models commonly superpose single-turbine deficit and deflection models, which can struggle with non-linear phenomena such as secondary wake steering; momentum-conserving models that do capture it rely on iteration or proxies such as effective yaw angles. This paper extends an approximate "conservation of momentum deficit" solution to the lateral direction, giving an analytical, non-iterative model of the cumulative streamwise and lateral velocity deficits in a wind farm of yawed turbines. Distinguishing the streamwise from the lateral wake makes the spatial distribution of lateral momentum induced by yaw misalignment explicit, and wake deflection follows diagnostically by integrating the local skew angle. The framework yields physical insight into secondary wake steering: the wake of an unyawed downstream turbine is deflected not only by the cross-flow of the upstream wakes, but also, for about a third of its deflection, by the turbine's own streamwise deficit slowing the flow that carries that cross-flow. Against wind-tunnel measurements of single- and multi-turbine configurations, the model reproduces the far-wake deflection and lateral velocity distributions, and is more accurate than established engineering models in most configurations; over the full hub-height velocity field – which needs no wake centre and remains well defined where wakes merge – it is the more accurate in every configuration tested. The main discrepancies are confined to the near wake, where the simplified treatment underpredicts the streamwise velocity deficit. Being analytical and non-iterative, the formulation suits wind farm control and optimisation applications that require low-order models.