Approximate inertial manifolds and effective viscosity in turbulent flows

DOI10.1063/1.858212zbMath0732.76001OpenAlexW2063074955MaRDI QIDQ3358333

Ciprian Foias, Oscar P. Manley, Roger M. Temam

Publication date: 1991

Published in: Physics of Fluids A: Fluid Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.858212

zbMATH Keywords

iterative procedurelarge eddy simulationnonlinear Galerkin methodapproximate inertial manifoldseffective viscosity-like termsmodification of the Navier-Stokes equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Turbulence (76F99) Foundations of fluid mechanics (76A02)

Related Items (22)

Finite-dimensional behavior in dissipative partial differential equations ⋮ Influences of subgrid scale dynamics on resolvable scale statistics in large-eddy simulations ⋮ The nonlinear Galerkin method: A multiscale method applied to the simulation of homogeneous turbulent flows ⋮ Explicit small-scale velocity simulation for high-\(Re\) turbulent flows ⋮ Artificial viscosity -- then and now ⋮ Numerical convergence of the Lyapunov spectrum computed using low Mach number solvers ⋮ On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation ⋮ The subgrid-scale estimation model in the physical space representation ⋮ Preserving dissipation in approximate inertial forms for the Kuramoto- Sivashinsky equation ⋮ On the ensemble average in the study of approximate inertial manifolds ⋮ A continuity property for the inverse of Mañé's projection ⋮ The subgrid-scale estimation model applied to large eddy simulations of compressible turbulence ⋮ On the ensemble average in the study of approximate inertial manifolds. II ⋮ On the number of determining nodes for the 2D Navier-Stokes equations ⋮ A balanced atmospheric model of Lorenz ⋮ Inertial manifolds, partially space-averaged equations, and the separation of scales in turbulent flows* ⋮ Hierarchical order in wall-bounded shear turbulence ⋮ Analysis and modeling of subgrid scalar mixing using numerical data ⋮ Limiting Behavior for an Iterated Viscosity ⋮ Exponential attractors and their relevance to fluid dynamics systems ⋮ Variational approach to closure of nonlinear dynamical systems: autonomous case ⋮ On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer

Cites Work

• Unnamed Item
• Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
• A nonlinear Galerkin method for the Navier-Stokes equations
• On approximate inertial manifolds to the Navier-Stokes equations
• Approximate inertial manifolds for reaction-diffusion equations in high space dimension
• Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
• Asymptotic analysis of the Navier-Stokes equations
• Inertial manifolds for nonlinear evolutionary equations
• Renormalization group analysis of turbulence. I: Basic theory
• On the dimension of the attractors in two-dimensional turbulence
• Log-corrected energy spectrum and dimension of attractor in two-dimensional turbulence
• Physical estimates of the number of degrees of freedom in free convection
• Determining modes and fractal dimension of turbulent flows
• Nonlinear Schrödinger evolution equations
• Nonlinear Galerkin Methods

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