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pro vyhledávání: '"Migdal, Alexander"'
Autor:
Migdal, Alexander
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 the previous work, as a solution to the loop equations. We designed no
Externí odkaz:
http://arxiv.org/abs/2312.16584
Autor:
Migdal, Alexander
Publikováno v:
Physics of Fluids 36, 095161 (2024)
This paper presents a recent advancement that transforms the problem of decaying turbulence in the Navier-Stokes equations in $3+1$ dimensions into a Number Theory challenge: finding the statistical limit of the Euler ensemble. We redefine this ensem
Externí odkaz:
http://arxiv.org/abs/2312.15470
Autor:
Migdal, Alexander
Publikováno v:
Fractal Fract. 2023, 7, 754
We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This solution family is equivalent to a fractal curve in complex space $\ma
Externí odkaz:
http://arxiv.org/abs/2304.13719
Autor:
Migdal, Alexander
Publikováno v:
MDPI:Fractal and Fractional, vol 7, # 5 (2023)
We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing
Externí odkaz:
http://arxiv.org/abs/2212.13356
Autor:
Migdal, Alexander
We are investigating the inviscid limit of the Navier-Stokes equation, and we find previously unknown anomalous terms in Hamiltonian, Dissipation, and Helicity, which survive this limit and define the turbulent statistics. We find various topological
Externí odkaz:
http://arxiv.org/abs/2209.12312
Autor:
Migdal, Alexander
We find a new family of exact solutions of the Confined Vortex Surface equations (The Euler equations with extra boundary conditions coming from the stability of the Navier-Stokes equations in the local tangent plane). This family of solutions has an
Externí odkaz:
http://arxiv.org/abs/2106.05103
Autor:
Migdal, Alexander
We continue the study of Confined Vortex Surfaces (\CVS{}) that we introduced in the previous paper. We classify the solutions of the \CVS{} equation and find the analytical formula for the velocity field for arbitrary background strain eigenvalues i
Externí odkaz:
http://arxiv.org/abs/2105.12719
Autor:
Migdal, Alexander
We revise the steady vortex surface theory following the recent finding of asymmetric vortex sheets (AM,2021). These surfaces avoid the Kelvin-Helmholtz instability by adjusting their discontinuity and shape. The vorticity collapses to the sheet only
Externí odkaz:
http://arxiv.org/abs/2103.02065
Autor:
Migdal, Alexander
We present a steady analytical solution of the incompressible Navier-Stokes equation for arbitrary viscosity in an arbitrary dimension $d$ of space. It represents a $d-1$ dimensional vortex "sheet" with an asymmetric profile of vorticity as a functio
Externí odkaz:
http://arxiv.org/abs/2101.06918
Autor:
Migdal, Alexander
We study steady vortex sheet solutions of the Navier-Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a functional of the
Externí odkaz:
http://arxiv.org/abs/2011.09030