Turbulent Couette Flow:An analytical solution

A simple analytical solution for turbulent plane Couette flow is obtained from a subset of the Navier-Stokes equations. This approach analyses the effect of the unsteady state Lagrangian diffusion of viscous momentum on the smoothed phase velocity. Three initial velocity profiles at the start of a turbulent wall cycle are considered. The predictions adequate identify the existence of three layers usually observed in turbulent flow fields, in particular a viscosity dominated wall layer and a log-law layer. Experimental measurements of time-averaged velocity are also well correlated. Key words: Couette flow, turbulent, attractors, analytical solution, Lagrangian partial derivative, time scale, initial conditions

• Publication year

  2010

• Venue

  arXiv: Fluid Dynamics

• Publication date

  2010-09-06

• Fields of study

  Physics, Engineering

• Identifiers
  arXiv 1009.0969
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• A Zonal Similarity Analysis Of Friction Factors: Case Study 1: Pipe Flow Of Power Law Fluids

  2010influential reference
• On the Non Specific Nature of Classical Turbulence Statistics

  2010influential reference
• A Theoretical Closure for Turbulent Flows Near Walls

  2010influential reference
• The Fourth Partial Derivative In Transport Dynamics

  2010cited by this paper
• A Zonal Similarity Analysis of Velocity Profiles in Wall-Bounded Turbulent Shear Flows

  2010influential reference
• Additive Layers: An Alternate Classification of Flow Regimes

  2010influential reference
• Formation of turbulent patterns near the onset of transition in plane Couette flow

  2010cited by this paper
• The Instantaneous Wall Viscosity in Pipe Flow of Power Law Fluids: Case Study for a Theory of Turbulence in Time-Independent Non-Newtonian Fluids

  2009influential reference
• A theory of turbulence. Part 1:Towards solutions of the Navier-stokes equations

  2009influential reference
• Scaling of torque in turbulent Taylor-Couette flow with background rotation

  2009cited by this paper
• On the Effect of the Internal Friction of Fluids on the Motion of Pendulums

  2009cited by this paper
• Hairpin vortex solution in planar couette flow: a tapestry of knotted vortices.

  2009cited by this paper
• A Four Component Decomposition of the Instantaneous Velocity in Turbulent Flow

  2009influential reference
• Direct numerical simulation of turbulent Taylor–Couette flow

  2007cited by this paper
• Turbulence transition in pipe flow

  2007cited by this paper
• Mean flow of turbulent–laminar patterns in plane Couette flow

  2007cited by this paper
• Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders

  2007cited by this paper
• Turbulence structure in a Taylor–Couette apparatus

  2007cited by this paper
• Visualizing the geometry of state space in plane Couette flow

  2007influential reference
• Recurrent motions within plane Couette turbulence

  2006cited by this paper
• Experimental study on mean velocity and turbulence characteristics of plane Couette flow: low-Reynolds-number effects and large longitudinal vortical structure

  2005cited by this paper
• Formulation of turbulence mechanics.

  2004cited by this paper
• Similarity laws of velocity profiles and turbulence characteristics of Couette–Poiseuille turbulent flows

  2004cited by this paper
• Transition in boundary layers subject to free-stream turbulence

  2004cited by this paper
• Smooth and rough boundaries in turbulent Taylor-Couette flow.

  2003cited by this paper
• Scaling of the turbulence transition threshold in a pipe.

  2003cited by this paper
• Coherent structure generation in near-wall turbulence

  2002cited by this paper
• Models for Turbulent Plane Couette Flow Using the Proper Orthogonal Decomposition: Minimal Flow Unit

  2001cited by this paper
• Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst

  2001cited by this paper
• Stability and bifurcations in stratified Taylor–Couette flow

  2000cited by this paper
• Interpretation of large-scale structures observed in a turbulent plane Couette flow

  1997cited by this paper
• Very large structures in plane turbulent Couette flow

  1996cited by this paper
• Effects of free stream turbulence intensity on heat and mass transfers at the surface of a circular cylinder and an elliptical cylinder, axis ratio 4

  1995cited by this paper
• Model for plane turbulent Couette flow.

  1995cited by this paper
• On the dynamical theory of incompressible viscous fluids and the determination of the criterion

  1995cited by this paper
• Modeling plane turbulent Couette flow

  1994cited by this paper
• A time-space transformation for non-Newtonian laminar boundary layers

  1992cited by this paper
• Turbulent flow between concentric rotating cylinders at large Reynolds number.

  1992cited by this paper
• A modified penetration theory and its relation to boundary layer transport

  1992cited by this paper
• Plane-Couette flow between smooth and rough walls

  1991cited by this paper
• The structure of turbulence in a simulated plane Couette flow

  1991cited by this paper
• Effect of Reynolds number on the topology of the organized motion in a turbulent boundary layer

  1990cited by this paper
• Turbulence in fluids: Stochastic and numerical modeling /2nd revised and enlarged edition/

  1990cited by this paper
• Strange attractors in weakly turbulent Couette-Taylor flow.

  1987cited by this paper
• The Strange Attractor Theory of Turbulence

  1982cited by this paper
• The Structure of Turbulent Plane Couette Flow

  1982cited by this paper
• Unsteady Viscous Flows

  1981cited by this paper
• Unsteady viscous flow

  1975cited by this paper
• Combined dye-streak and hydrogen-bubble visual observations of a turbulent boundary layer

  1974cited by this paper
• Mean period of fluctuations near the wall in turbulent flows

  1972cited by this paper
• An introduction to turbulence and its measurement

  1971cited by this paper
• Transport phenomena for engineers

  1971cited by this paper
• The periodic viscous sublayer in turbulent flow

  1970cited by this paper
• Turbulence Structure in Plane Couette Flow

  1970cited by this paper
• A visual investigation of the wall region in turbulent flow

  1969cited by this paper
• Viscous Sublayer and Adjacent Wall Region in Turbulent Pipe Flow

  1967cited by this paper
• Transition in circular Couette flow

  1965influential reference
• Hydrodynamic resistance and the heat loss of rotating solids

  1963cited by this paper
• The Viscous Sublayer Along a Smooth Boundary

  1956cited by this paper
• Turbulent exchange of mass and momentum with a boundary

  1956cited by this paper
• Über die Geschwindigkeitsverteilung in einer geradlinigen turbulenten Couetteströmung

  1956cited by this paper
• Boundary Layer Theory

  1955cited by this paper
• On the statistical theory of turbulence

  1937cited by this paper
• Fluid Friction between Rotating Cylinders. I. Torque Measurements

  1936cited by this paper
• Fluid Friction between Rotating Cylinders. II. Distribution of Velocity between Concentric Cylinders when Outer One Is Rotating and Inner One Is at Rest

  1936cited by this paper
• The Mechanics of Viscous Fluids

  1935cited by this paper
• Stability of a Viscous Liquid Contained between Two Rotating Cylinders

  1923cited by this paper

• Inflectional Instability of Linearized Incompressible Euler Equations via Linear Partial Inequality Tests

  2025cites this paper
• Additive layers: An alternative classification of flow regimes

  2012cites this paper
• Reflections on a Penetration Theory of Turbulent Heat Transfer

  2010cites this paper