Because of Coriolis forces caused by the Earth's rotation, the structure of the atmospheric boundary layer often contains wind-direction change with height, also known as wind-direction veer. Under low turbulence conditions, such as in stably stratified atmospheric conditions, this veer can be significant, even across the vertical extent of a wind turbine's rotor disk. The veer then causes the wind turbine wake to skew as it advects downstream. This wake skew has been observed both experimentally and numerically. In this work, we attempt to examine the wake skewing process in some detail, and quantify how differently a skewed wake versus a non skewed wake affects a downstream turbine. We do this by performing atmospheric large-eddy simulations to create turbulent inflow winds with and without veer. In the veer case, there is a roughly 8 degree wind direction change across the turbine rotor. We then perform subsequent large-eddy simulations using these inflow data with an actuator line rotor model to create wakes. The turbine modeled is a large, modern, offshore, multimegawatt turbine. We examine the unsteady wake data in detail and show that the skewed wake recovers faster than the non skewed wake. We also show that the wake deficit does not skew to the same degree that a passive tracer would if subject to veered inflow. Last, we use the wake data to place a hypothetical turbine 9 rotor diameters downstream by running aeroelastic simulations with the simulated wake data. We see differences in power and loads if this downstream turbine is subject to a skewed or non skewed wake. We feel that the differences observed between the skewed and nonskewed wake are important enough that the skewing effect should be included in engineering wake models.