9 citations · 9 across the 6 of their papers we have counts for
9 papers
Number Theory of Decaying Turbulence 3: Comparing with Physical and Numerical Experiments
Alexander Migdal, Wei Wang
We compare the predictions of the Euler-ensemble solution of freely decaying incompressible turbulence with simulations and experiments: the scaling function of the energy spectrum…
Reduction of Decaying Navier--Stokes Turbulence to the Quantum Pendulum
Alexander Migdal
The statistics of a classical flow is a problem of quantum mechanics in loop space, and not by analogy: the loop functional of any flow is the loop-ordered exponential of the covar…
Number Theory of Decaying Turbulence 2: The Energy Spectrum and the Riemann Zeta Zeros
Alexander Migdal
The odd Euler ensemble, the locally stable attractor of the momentum-loop dynamics of freely decaying incompressible turbulence, has a self-similar energy spectrum \(E(k,t)=L^{-3/2…
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…
Dual theory of decaying turbulence. 2. Numerical simulation and continuum limit
Alexander Migdal
This is the second paper in a cycle investigating the exact solution of loop equations in decaying turbulence. We perform numerical simulations of the Euler ensemble, suggested in…
Quantum Solution of Classical Turbulence. Decaying Energy Spectrum
Alexander Migdal
This paper presents a recent advancement that transforms the problem of decaying turbulence in the Navier-Stokes equations in dimensions into a Number Theory challenge: findi…