scholarly journals Inverse cascade anomalies in fourth-order Leith models

2021 ◽  
Author(s):  
Simon Thalabard ◽  
Sergey Medvedev ◽  
Vladimir Grebenev ◽  
Sergey Nazarenko
Keyword(s):  
Fourth Order ◽  
Field Model ◽  
Kinetic Equations ◽  
Vacuum Field ◽  
Wave Turbulence ◽  
Anomalous Scaling ◽  
Time Singularity ◽  
Linear Diffusion ◽  
Local Approximations ◽  
Finite Time Singularity

Abstract We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with an infrared finite-time singularity associated to inverse transfer of waveaction. This case is relevant for wave turbulence arising in the Nonlinear Schrödinger model and for the gravitational waves in the Einstein’s vacuum field model. We show that inverse transfer is not described by a scaling of the constant-flux solution but has an anomalous scaling. We compute the anomalous exponents and analyze their origin using the theory of dynamical systems.

scholarly journals Finite-time singularity versus global regularity for hyper-viscous Hamilton–Jacobi-like equations

Nonlinearity ◽  
2003 ◽  
Vol 16 (6) ◽  
pp. 1967-1989 ◽  
Author(s):  
Hamid Bellout ◽  
Said Benachour ◽  
Edriss S Titi
Keyword(s):  
Finite Time ◽  
Global Regularity ◽  
Time Singularity ◽  
Finite Time Singularity

scholarly journals A fluid mechanic’s analysis of the teacup singularity

2020 ◽  
Vol 476 (2240) ◽  
pp. 20200348
Author(s):  
Dwight Barkley
Keyword(s):  
Euler Equations ◽  
Pressure Field ◽  
Meridional Flow ◽  
Cylinder Wall ◽  
Time Singularity ◽  
Pressure Poisson Equation ◽  
Velocity Gradients ◽  
Key Features ◽  
Finite Time Singularity ◽  
Incompressible Euler

The mechanism for singularity formation in an inviscid wall-bounded fluid flow is investigated. The incompressible Euler equations are numerically simulated in a cylindrical container. The flow is axisymmetric with the swirl. The simulations reproduce and corroborate aspects of prior studies reporting strong evidence for a finite-time singularity. The analysis here focuses on the interplay between inertia and pressure, rather than on vorticity. The linearity of the pressure Poisson equation is exploited to decompose the pressure field into independent contributions arising from the meridional flow and from the swirl, and enforcing incompressibility and enforcing flow confinement. The key pressure field driving the blowup of velocity gradients is that confining the fluid within the cylinder walls. A model is presented based on a primitive-variables formulation of the Euler equations on the cylinder wall, with closure coming from how pressure is determined from velocity. The model captures key features in the mechanics of the blowup scenario.

scholarly journals Interacting vacuum at infinity

2019 ◽  
Vol 16 (04) ◽  
pp. 1950052
Author(s):  
G. Kittou
Keyword(s):  
Finite Time ◽  
Central Extension ◽  
Vacuum Model ◽  
Time Singularity ◽  
Attractor Solution ◽  
The One ◽  
Finite Time Singularity

We apply the central extension technique of Poincaré to dynamics involving an interacting mixture of pressureless matter and vacuum near a finite-time singularity. We show that the only attractor solution on the circle of infinity is the one describing a vanishing matter-vacuum model at early times.

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