Convex integration (CI) has been developed in the past 10 years as a constructive technique for the incompressible Euler equations in connection with Onsager’s conjecture. The goal of this project is to transform the theoretical CI algorithm into a computational algorithm, enabling us for the first time to directly compute weak solutions of the Euler equations with small-scale structure compatible with Kolmogorov’s K41 theory and whose existence has been first conjectured by L. Onsager in 1949. More specifically, our aim is to 

• develop a numerical implementation of the construction of weak solutions with the ability to go beyond temporal scales currently available in HPC turbulence simulations.
• compare numerical convergence rates to available theoretical bounds.
• study for the first time Lagrangian properties of K41 and intermittent weak solutions.
• explore the numerical construction of weak solutions with multifractal properties, with an eye towards new, HPC-informed bounds on structure function exponents.

The project requires both theoretical and computational expertise.