How transient turbulent tailwinds and updrafts reduce energy consumption in flight

We investigate the potential for environmental turbulence to reduce energy consumption relative to transit through still air or water. For vehicles that move along tortuous trajectories, rather than straight ones, we previously showed that tailwinds can substantially reduce energy consumption in a two-dimensional turbulence model, an effect captured by the Tailwind Turbulence (TT) bound (Bollt and Bewley, 2025). Here we show how transient turbulent updrafts in three dimensional (3D) turbulence can further reduce energy consumption relative to TT, especially in the technologically important regime of weak turbulence, a regime that applies to most current engineered vehicles. To do so, we optimized the trajectories of point-mass vehicles acted on by drag and thrust in one-way-coupled 3D direct numerical simulations of homogeneous and isotropic turbulence. We extend TT to include the advantages present in turbulent updrafts, and we analyze the properties of those trajectories optimized to minimize energy, and the flows along those trajectories.