Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Two-dimensional turbulence in the inverse cascade range.

V Yakhot1

  • 1Department of Aerospace and Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Generalized Knudsen Number for Unsteady Fluid Flow.

Physical review letters·2017
Same author

Nanofluidics of Single-Crystal Diamond Nanomechanical Resonators.

Nano letters·2015
Same author

Crossover from hydrodynamics to the kinetic regime in confined nanoflows.

Physical review letters·2012
Same author

Porous superhydrophobic membranes: hydrodynamic anomaly in oscillating flows.

Physical review letters·2011
Same author

High-frequency nanofluidics: a universal formulation of the fluid dynamics of MEMS and NEMS.

Lab on a chip·2010
Same author

Measurement of local dissipation scales in turbulent pipe flow.

Physical review letters·2009

Transverse velocity differences in two-dimensional turbulence exhibit normal Kolmogorov scaling and Gaussian statistics, resolving a apparent contradiction. A new theory explains these findings using a linear Langevin-like equation and a universal random force.

Area of Science:

  • Fluid Dynamics
  • Turbulence Theory
  • Statistical Mechanics

Background:

  • Forced two-dimensional Navier-Stokes equations exhibit complex nonlinear behavior.
  • Observed normal Kolmogorov scaling and Gaussian statistics for velocity differences appear contradictory.
  • Understanding turbulence scaling and statistics is crucial for fluid dynamics.

Purpose of the Study:

  • To reconcile the apparent contradiction between Kolmogorov scaling and Gaussian statistics in 2D turbulence.
  • To develop a theoretical framework explaining the observed phenomena.
  • To provide testable predictions for experimental validation.

Main Methods:

  • Derivation of a self-consistent expression for pressure gradient contributions.
  • Formulation of a linear Langevin-like equation for transverse velocity differences.

Related Experiment Videos

  • Analysis of the probability density function (PDF) for longitudinal velocity differences.

    • Main Results:

    • Transverse velocity differences follow normal Kolmogorov scaling (<(deltav)(2n)> proportional r(2n/3)).
    • Transverse velocity differences obey Gaussian statistics.
    • A nonlocal, universal, solution-dependent Gaussian random force governs small-scale transverse velocity differences.

    Conclusions:

    • The derived theory successfully explains the observed Gaussian statistics and Kolmogorov scaling.
    • The theory posits that small-scale transverse velocity differences are governed by a linear Langevin-like equation.
    • The study offers quantitative predictions for future experimental verification in two-dimensional turbulence.