A connection between the Camassa–Holm equations and turbulent flows in channels and pipes
From MaRDI portal
Publication:3539173
DOI10.1063/1.870096zbMath1147.76357arXivchao-dyn/9903033OpenAlexW3098137244MaRDI QIDQ3539173
Ciprian Foias, Edriss S. Titi, Shannon Wynne, Darryl D. Holm, Shiyi Chen, Eric J. Olson
Publication date: 17 November 2008
Published in: Physics of Fluids (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/chao-dyn/9903033
Related Items
Three regularization models of the Navier–Stokes equations ⋮ Existence and uniqueness of invariant measures of 3D stochastic MHD-αmodel driven by degenerate noise ⋮ Geodesic motion on groups of diffeomorphisms with H1 metric as geometric generalised Lagrangian mean theory ⋮ Large deviation for a 3D globally modified Cahn-Hilliard-Navier-Stokes model under random influences ⋮ On the convergence of 3D Leray-\(\alpha\) equations with Navier slip boundary conditions ⋮ Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics ⋮ Convergence for a Splitting-Up Scheme for the 3D Stochastic Navier-Stokes-α Model ⋮ On a regularization of a scalar conservation law with discontinuous coefficients ⋮ Bounds for some non-standard problems in porous flow and viscous Green–Naghdi fluids ⋮ The Navier-Stokes-alpha model of fluid turbulence ⋮ Convergence analysis of the Navier–Stokes alpha model ⋮ A Lagrangian approximation to the water-wave problem ⋮ Incompressibility of the Leray-α model for wall-bounded flows ⋮ Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows ⋮ Finite-dimensional global attractor for globally modified Navier–Stokes equations with fractional dissipation ⋮ Logarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equations ⋮ The reduced order NS-αmodel for incompressible flow: theory, numerical analysis and benchmark testing ⋮ Inertial Manifolds for Certain Subgrid-Scale $\alpha$-Models of Turbulence ⋮ Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics ⋮ On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation ⋮ Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data ⋮ A note on the blowup criterion of the Lagrangian averaged Euler equations ⋮ On the convergence of a stochastic 3D globally modified two-phase flow model ⋮ On 3D Lagrangian Navier-Stokes \(\alpha\) model with a class of vorticity-slip boundary conditions ⋮ On the solvability of the Jeffreys-Oldroyd-\(\alpha\) model ⋮ Stochastic parametrization of the Richardson triple ⋮ On the large time behavior of solutions of the alpha Navier-Stokes equations ⋮ New exact traveling wave solutions for the modified form of Degasperis-Procesi equation ⋮ On the rate of convergence of the 2-D stochastic Leray-\(\alpha \) model to the 2-D stochastic Navier-Stokes equations with multiplicative noise ⋮ Numerical and convergence analysis of the stochastic Lagrangian averaged Navier-Stokes equations ⋮ Unique strong and \(\mathbb {V}\)-attractor of a three-dimensional globally modified two-phase flow model ⋮ Global attractor for the regularized Bénard problem ⋮ Pullback \(\mathbb{V}\)-attractor of a three dimensional globally modified two-phase flow model ⋮ Application of the NS-\(\alpha\) model to a recirculating flow ⋮ Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations ⋮ Filtered viscous fluid equations ⋮ The attractors for the regularized Bénard problem with fractional Laplacian ⋮ Viscosity versus vorticity stretching: global well-posedness for a family of Navier-Stokes-alpha-like models ⋮ On the convergence of statistical solutions of the 3D Navier-Stokes-\(\alpha\) model as \(\alpha\) vanishes ⋮ Analysis of a general family of regularized Navier-Stokes and MHD models ⋮ Data assimilation with model error: analytical and computational study for sabra shell model ⋮ Onsager's conjecture for subgrid scale \(\alpha\)-models of turbulence ⋮ Regularity criteria for a Lagrangian-averaged magnetohydrodynamic-\(\alpha \) model ⋮ Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations ⋮ A turbulence model for smoothed particle hydrodynamics ⋮ On the 3-D stochastic magnetohydrodynamic-\(\alpha\) model ⋮ On degrees of freedom of certain conservative turbulence models for the Navier-Stokes equations ⋮ On the use of the notion of suitable weak solutions in CFD ⋮ Optimal decay rate for higher-order derivatives of the solution to the Lagrangian-averaged Navier-Stokes-\(\alpha\) equation in \(\mathbb{R}^3\) ⋮ An optimal control problem for the Navier-Stokes-\(\alpha\) system ⋮ \(\alpha \) regularization of the POD-Galerkin dynamical systems of the Kuramoto-Sivashinsky equation ⋮ On a stochastic Leray-\(\alpha\) model of Euler equations ⋮ Martingale solution to equations for differential type fluids of grade two driven by random force of Lévy type ⋮ Weak solutions to stochastic 3D Navier-Stokes-\(\alpha \) model of turbulence: \(\alpha \)-asymptotic behavior ⋮ A deconvolution enhancement of the Navier-Stokes-\({\alpha}{\beta}\) model ⋮ Continuous data assimilation algorithm for simplified Bardina model ⋮ Turbulence properties and global regularity of a modified Navier-Stokes equation ⋮ Analytical study of certain magnetohydrodynamic-α models ⋮ Regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation ⋮ Global solutions to the Navier-Stokes-\({\bar \omega}\) and related models with rough initial data ⋮ A numerical study of the Navier-Stokes-\(\alpha \beta \) model ⋮ Uniform time of existence of the smooth solution for 3D Euler-α equations with periodic boundary conditions ⋮ Going to new lengths: studying the Navier-Stokes-\(\alpha\beta\) equations using the strained spiral vortex model ⋮ Approximation of the trajectory attractor for a 3D model of incompressible two-phase-flows ⋮ A phase field \(\alpha\)-Navier-Stokes vesicle-fluid interaction model: existence and uniqueness of solutions ⋮ A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows ⋮ Pullback attractor of a three dimensional globally modified Cahn–Hilliard-Navier–Stokes model ⋮ Global regularity for a Birkhoff-Rott-\(\alpha \) approximation of the dynamics of vortex sheets of the 2D Euler equations ⋮ An alternative interpretation for the Holm “alpha model” ⋮ Numerical simulations of the Lagrangian averaged Navier–Stokes equations for homogeneous isotropic turbulence ⋮ Existence and uniqueness of weak solution to a three-dimensional stochastic modified-Leray-alpha model of fluid turbulence ⋮ Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the two-dimensional Euler equations ⋮ Space-time decay estimates of solutions to 3D incompressible viscous Camassa-Holm equations ⋮ Convergence of the solution of the stochastic 3D globally modified Cahn-Hilliard-Navier-Stokes equations ⋮ On questions of decay and existence for the viscous Camassa-Holm equations ⋮ Lagrangian averaging with geodesic mean ⋮ Introduction to special issue: ``Nonlinear partial differential equations in mathematical fluid dynamics ⋮ Global Cauchy problem for a Leray-\(\alpha\) model ⋮ Stochastic phase field \(\alpha \)-Navier-Stokes vesicle-fluid interaction model ⋮ On the global boundary stabilization of the Camassa-Holm equation ⋮ On the stochastic 3D Navier-Stokes-\(\alpha\) model of fluids turbulence ⋮ On the convergence rate of the Euler-\(\alpha \), an inviscid second-grade complex fluid, model to the Euler equations ⋮ Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations ⋮ Convergence analysis and computational testing of the finite element discretization of the Navier-Stokes alpha model ⋮ Global regularity of the 4D restricted Euler equations ⋮ The Camassa-Holm equations and turbulence ⋮ Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion ⋮ Existence and linear approximation for the stochastic 3D magnetohydrodynamic-alpha model ⋮ On an accurate \(\alpha\) model for coarse mesh turbulent channel flow simulation ⋮ Modeling error of \(\alpha\)-models of turbulence on a two-dimensional torus ⋮ Data assimilation for the Navier-Stokes-\(\alpha \) equations ⋮ Optimal control of the viscous Camassa-Holm equation ⋮ Asymptotic behavior of the solutions of the generalized globally modified Navier-Stokes equations ⋮ Camassa-Holm cuspons, solitons and their interactions via the dressing method ⋮ A continuum mechanical theory for turbulence: a generalized Navier-Stokes-\(\alpha\) equation with boundary conditions ⋮ On the emergence of the Navier-Stokes-α model for turbulent channel flows ⋮ Regularity and convergence results of the velocity-vorticity-Voigt model of the 3D Boussinesq equations ⋮ Onsager's conjecture with physical boundaries and an application to the vanishing viscosity limit ⋮ On the Rate of Convergence of the Two-Dimensional α-Models of Turbulence to the Navier–Stokes Equations ⋮ Finite dimensional uniform attractors for the nonautonomous Camassa-Holm equations ⋮ APPROXIMATE SOLUTION OF MODIFIED CAMASSA–HOLM AND DEGASPERIS–PROCESI EQUATIONS USING WAVELET OPTIMIZED FINITE DIFFERENCE METHOD ⋮ The pullback attractors for the nonautonomous Camassa-Holm equations ⋮ Modelling the climate and weather of a 2D Lagrangian-averaged Euler-Boussinesq equation with transport noise ⋮ Lagrangian averaged stochastic advection by Lie transport for fluids ⋮ On the construction of suitable solutions to the Navier-Stokes equations and questions regarding the definition of large eddy simulation ⋮ Nonlinear dispersion in wave-current interactions ⋮ Geometric Lagrangian averaged Euler–Boussinesq and primitive equations ⋮ Residual stress of approximate deconvolution models of turbulence ⋮ A study of the Navier–Stokes-α model for two-dimensional turbulence ⋮ Regularization-based sub-grid scale (SGS) models for large eddy simulations (LES) of high-Redecaying isotropic turbulence ⋮ A derivation of the NS-α model and preliminary application to plane channel flow ⋮ Recent advances on the numerical modelling of turbulent flows ⋮ An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization ⋮ Turbulent boundary layer equations ⋮ Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary PDE ⋮ Multiscale turbulence models based on convected fluid microstructure ⋮ WELL-POSEDNESS AND GLOBAL ATTRACTORS FOR LIQUID CRYSTALS ON RIEMANNIAN MANIFOLDS ⋮ Convergence of the 2D Euler-\(\alpha\) to Euler equations in the Dirichlet case: indifference to boundary layers
Cites Work
- Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade
- The Euler-Poincaré equations and semidirect products with applications to continuum theories
- Geometry and curvature of diffeomorphism groups with \(H^1\) metric and mean hydrodynamics
- Generalized fluid flows, their approximation and applications
- Fluids of differential type: Critical review and thermodynamic analysis
- Self-consistent Hamiltonian dynamics of wave mean-flow interaction for a rotating stratified incompressible fluid
- The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids
- Nonlinear Reynolds stress models and the renormalization group
- Statistical analysis of the deviation of the Reynolds stress from its eddy-viscosity representation
- An integrable shallow water equation with peaked solitons
- Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow
- Turbulence statistics in fully developed channel flow at low Reynolds number
- Upper bounds on functions of the dissipation rate in turbulent shear flow