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physics.flu-dyn2025
Geometric Solution of Turbulence as Diffusion in Loop Space
Alexander Migdal
Strongly nonlinear dynamics, from fluid turbulence to quantum chromodynamics, have long constituted some of the most challenging problems in theoretical physics. This review descri…
physics.flu-dyn2025
Geometric Solution of Turbulent Mixing
Alexander Migdal
We derive an analytical solution for the one-point distribution of a passive scalar in decaying homogeneous turbulence, in the limit of strong turbulence (high Re, fixed Schmidt nu…
physics.flu-dyn2025
Dual Theory of MHD Turbulence
Alexander Migdal
We present an exact analytic solution for decaying incompressible magnetohydrodynamic (MHD) turbulence. Our solution reveals a dual formulation in terms of two interacting Euler en…