GALCIT Colloquium

In turbulent flows, energy flux refers to the transfer of kinetic energy across different scales of motion, a concept that is a cornerstone of turbulence theory. The direction of net energy flux is prescribed by the dimensionality of the fluid system. According to Kolmogorov's 1941 scaling theory, three-dimensional turbulence has a net energy flux toward smaller length scales, while in two-dimensional turbulence, energy transfers toward larger scales, as described in Kraichnan and Batchelor's seminal works. Manipulating energy flux across different scales with localized physical perturbations in flow systems is a formidable task because the energy at any scale is not localized in physical space. In this talk, I will present a theoretical framework that enables the manipulation of energy flux direction in turbulent flows. Based on this framework, we have successfully demonstrated the manipulation of a flow system to achieve the desired directions of net energy flux through both electromagnetically driven thin-layer flow experiments and direct numerical simulations in two dimensions. Notably, we generated a type of turbulent flow that has never been produced before—two-dimensional Navier-Stokes turbulence with a net forward energy flux. Beyond theoretical interest, we will discuss how our theoretical framework can have profound applications and implications across natural and engineered systems. First, at the centimeter scale, it predicts—and we experimentally confirm—that spectral energy flux in quasi-two-dimensional flows can be enhanced by up to two orders of magnitude around a Reynolds number of order unity (defined based on linear friction). Second, at the meter scale, the framework reveals that there is no universal minimum body size required for swimmers to generate appreciable biogenic turbulence; rather, such turbulence depends jointly on organism size, the ambient flow, as well as their geometric alignment. Third, at submesoscale, we demonstrate that small-scale boundaries—three orders of magnitude smaller than the oceanic transport barrier itself—can be used to disrupt and modulate transport barriers, offering a new pathway for low-energy control of large-scale material exchange.