Phenomenology of Wall Bounded Newtonian Turbulence

Abstract

We construct a simple analytic model for wall-bounded turbulence, containing only four adjustable parameters. Two of these parameters characterize the viscous dissipation of the components of the Reynolds stress-tensor and other two parameters characterize their nonlinear relaxation. The model offers an analytic description of the profiles of the mean velocity and the correlation functions of velocity fluctuations in the entire boundary region, from the viscous sub-layer, through the buffer layer and further into the log-layer. As a first approximation, we employ the traditional return-to-isotropy hypothesis, which yields a very simple distribution of the turbulent kinetic energy between the velocity components in the log-layer: the streamwise component contains a half of the total energy whereas the wall-normal and the cross-stream components contain a quarter each. In addition, the model predicts a very simple relation between the von-Kármán slope $\kappa$ and the turbulent velocity in the log-law region $v^{+}$ (in wall units): $v^{+}=6\kappa$. These predictions are in excellent agreement with DNS data and with recent laboratory experiments.

arXiv comment15 pages, 11 figs, included, PRE, submitted

References in corpus (7)

• Drag Reduction by Polymers in Wall Bounded Turbulence
• Drag Reduction by a Linear Viscosity Profile
• Identification and Calculation of the Universal Maximum Drag Reduction Asymptote by Polymers in Wall Bounded Turbulence
• Drag Reduction by Microbubbles in Turbulent Flows: the Limit of Minute Bubbles
• The Polymer Stress Tensor in Turbulent Shear Flows
• Additive Equivalence in Turbulent Drag Reduction by Flexible and Rodlike Polymers
• Saturation of Turbulent Drag Reduction in Dilute Polymer Solutions

Cited by in corpus (5)

• Energy- and flux-budget (EFB) turbulence closure model for the stably stratified flows. Part I: Steady-state, homogeneous regimes
• Universal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes
• Turbulent Fluxes in Stably Stratified Boundary Layers
• Energy Conservation and Second-Order Statistics in Stably Stratified Turbulent Boundary Layers
• An extension of the momentum transfer model to time-dependent pipe turbulence