Justin Beroz: A closed-form mathematical framework for modeling turbulent fluids скачать в хорошем качестве

Justin Beroz: A closed-form mathematical framework for modeling turbulent fluids

Despite significant advances over the past two centuries, a complete general mathematical framework for turbulent fluid motion has yet to be put forth, and remains the longest standing unsolved problem in classical physics. I will present such a framework, which is based on constructing a spectral decomposition for the fluid’s kinetic energy from first principles. The approach departs from the usual Reynolds decomposition and yields a set of closed and solvable ordinary differential equations in matrix form. Within this prescription, the linear terms in the Navier-Stokes equations correspond to a symmetric matrix operator, and the nonlinear convective term enters as an anti-symmetric operator that provides coupling between eigenstates of turbulent fluctuation. Specifically, I will present a derivation for the turbulent energy spectrum, including the Kolmogorov energy cascade; elucidate instability mechanisms for the transition to turbulence; and detail the analytical solution for turbulence in a box. Careful attention will be given to the physical picture and scaling, in addition to the rigorous mathematical program. The talk will conclude with a forward look into current efforts implementing the model into a numerical simulation within my company, ReynKo Inc.