From the 1 of 6 linked papers with an AI index.
6 papers
Euler Ensemble as Decaying Turbulence Attractor: Universality, Stability and Parity Classes
Alexander Migdal
The paper analyzes the local Lyapunov stability of self‑similar Euler ensemble solutions in freely decaying Navier‑Stokes turbulence, showing that only the odd‑N planar sector is a…
Decaying Turbulence and the Riemann Hypothesis: The number theory behind the infinite-time singularity
Alexander Migdal
We derive a formal statistical solution of freely decaying incompressible turbulence in arbitrary dimension \(d>1\) using Navier--Stokes loop equations. The loop Fourier transform…
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…
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…
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…
Duality of Navier-Stokes to a one-dimensional system
Alexander Migdal
The Navier--Stokes (NS) equations describe fluid dynamics through a high-dimensional, nonlinear system of partial differential equations (PDEs). Despite their fundamental importanc…