Tailwind turbulence: a possible bound on energy available from turbulence for transit

We investigate the unconstrained minimum energy performance of vehicles moving through turbulence that interact with their environment through thrust, weight and drag forces, such as rotorcraft or submersibles. Using a turbulence model, we find that for such vehicles there exists a speed that minimizes energy requirements, which depends on the turbulence intensity level. For intermediate turbulence intensities the energy required for transit can be substantially smaller than what is required in quiescent fluid. We describe a simple, analytically tractable, picture for how a flight trajectory could preferentially put vehicles in tailwinds rather than headwinds, predicated on the organization of turbulence around vortices. Supported by computer optimizations of flight trajectories in a model of turbulence, we find a bound on energy reduction by turbulence, which contains no free parameters and which we expect is most useful for low to intermediate turbulence levels. Furthermore, we predict the existence of an optimum level of turbulence for which the energy use is minimized. Thus, favorable trajectories are available to maneuverable vehicles if they have sufficient knowledge of the flow and computational resources for path planning. This work strengthens previous findings that turbulence can always reduce energy use, even for power-limited vehicles.