The Kolmogorov-Obukhov statistical theory of turbulence

DOI10.1007/s00332-012-9164-zzbMath1282.76112OpenAlexW2065015552MaRDI QIDQ361914

Björn Birnir

Publication date: 19 August 2013

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-012-9164-z

zbMATH Keywords

Brownian motionstochastic partial differential equationsturbulenceinvariant measureNavier-Stokes equationcentral limit theoremlarge deviationsFeynman-Kac formulastructure functionsprobability distribution functionintermittencyCameron-Martin formulafully developed turbulencehomogeneous Lévy processinertial cascadeintermittency correctionsKolmogorov-Obukhov scalinglog-Poisson processes

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Statistical turbulence modeling (76F55) Stochastic analysis applied to problems in fluid mechanics (76M35) Navier-Stokes equations (35Q30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items

Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions ⋮ On the mild Itô formula in Banach spaces ⋮ Probability density functions of vorticities in turbulent channels with effects of blowing and suction ⋮ Convergence rates for the numerical approximation of the 2D stochastic Navier-Stokes equations ⋮ Reynolds number dependence of the structure functions in homogeneous turbulence ⋮ Governing stochastic equation for a self-similar random process ⋮ From Wind-Blown Sand to Turbulence and Back ⋮ The statistical theory of the angiogenesis equations ⋮ Incremental Similarity and Turbulence ⋮ The Kolmogorov-Obukhov-She-Leveque scaling in turbulence ⋮ Gamma Kernels and BSS/LSS Processes ⋮ Exponential moments for numerical approximations of stochastic partial differential equations ⋮ Time-discretization of stochastic 2-D Navier-Stokes equations with a penalty-projection method ⋮ Strong solutions for the stochastic 3D LANS-α model driven by non-Gaussian Lévy noise ⋮ Approximation of the heat fluxes dynamics in the North Atlantic by stochastic diffusion process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems
• Applied stochastic control of jump diffusions.
• Existence, uniqueness and statistical theory of turbulent solutions of the stochastic Navier-Stokes equation, in three dimensions -- an overview
• Processes of normal inverse Gaussian type
• Turbulent flow computation.
• An introduction to infinite-dimensional analysis
• Turbulence without pressure: existence of the invariant measure
• On the velocity distribution in homogeneous isotropic turbulence: correlations and deviations from Gaussianity
• Turbulent cascade and intermittency growth
• The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers
• Some specific features of atmospheric tubulence
• A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
• Turbulent Flows
• The Kolmogorov-Obukhov Theory of Turbulence
• On Kolmogorov's inertial-range theories
• Anomalous scaling of low-order structure functions of turbulent velocity
• Stochastic differential equations. An introduction with applications.
• A basic course in probability theory