The asymptotic finite-dimensional character of a spectrally-hyperviscous model of 3D turbulent flow

DOI10.1007/s10884-007-9100-3zbMath1143.35348OpenAlexW1993548737MaRDI QIDQ925224

Joel D. Avrin

Publication date: 3 June 2008

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-007-9100-3

zbMATH Keywords

inertial manifoldsdegrees of freedomattractor dimension3D turbulent flow models

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Attractors (35B41) Navier-Stokes equations (35Q30) Turbulence (76F99) Inertial manifolds (35B42)

Related Items (7)

Hyperdissipative Navier–Stokes Equations Driven by Time-Dependent Forces: Invariant Manifolds ⋮ Inertial manifolds for the hyperviscous Navier-Stokes equations ⋮ Asymptotic Galerkin convergence and dynamical system results for the 3-D spectrally-hyperviscous Navier-Stokes equations on bounded domains ⋮ Reduction methods in climate dynamics -- a brief review ⋮ Convergence results for a class of spectrally hyperviscous models of 3-D turbulent flow ⋮ Convergence of Galerkin solutions and continuous dependence on data in spectrally-hyperviscous models of 3D turbulent flow ⋮ Upper semicontinuous trajectory attractors for 3D hyperviscous flow

Cites Work

• Unnamed Item
• Inertial manifolds for nonlinear evolutionary equations
• On the dimension of the attractors in two-dimensional turbulence
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations
• The anisotropic Lagrangian averaged Euler and Navier-Stokes equations
• A spectral vanishing viscosity method for large eddy simulations
• Singular initial data and uniform global bounds for the hyper-viscous Navier-Stokes equation with periodic boundary conditions.
• Level sets of the vorticity and the stream function for the 2D periodic Navier-Stokes equations with potential forces
• Large-eigenvalue global existence and regularity results for the Navier-Stokes equation
• Global attractors for the three-dimensional Navier-Stokes equations
• Attractors representing turbulent flows
• Two-Point Closure Used for a Sub-Grid Scale Model in Large Eddy Simulations
• Global lyapunov exponents, kaplan-yorke formulas and the dimension of the attractors for 2D navier-stokes equations
• Determining modes and fractal dimension of turbulent flows
• Convergence of Spectral Methods for Nonlinear Conservation Laws
• Local energy flux and subgrid-scale statistics in three-dimensional turbulence
• Spectral Viscosity Approximations to Multidimensional Scalar Conservation Laws
• Spectral and hyper eddy viscosity in high-Reynolds-number turbulence
• Length of Vorticity Nodal Sets for Solutions of the 2D Navier–Stokes Equations
• Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers
• The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory

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