Experimental Investigation of Turbulence Diffusion — A Factor in Transportation of Sediment in Open-Channel Flow

Turbulence diffusion in open-channel flow was investigated experimentally by photographing the spread of globules formed by the injection of an immiscible fluid into water. The mean-square transverse deviations of the globules at various distances downstream from the source were computed and analyzed in an effort to determine the shape of the velocity-correlation curve. Comparison was made between two types of curve which fitted the deviation data, one corresponding to a power-correlation law and the other to an exponential-correlation law

A simple eddy viscosity formulation for turbulent boundary layers near smooth walls

The aim of this study is to improve the prediction of near-wall mean streamwise velocity profile $U^+$ by using a simple method. The $U^+$ profile is obtained by solving the momentum equation which is written as an ordinary differential equation. An eddy viscosity formulation based on a near-wall turbulent kinetic energy $k^+$ function (R. Absi, Analytical solutions for the modeled $k$-equation, ASME J. Appl. Mech. \textbf{75}, 044501, 2008) and the van Driest mixing length equation (E.R. van Driest, On turbulent flow near a wall, J. Aero. Sci. \textbf{23}, 1007, 1956) is used. The parameters obtained from the $k^+$ profiles are used for the computation of $U^+$ (variables with the superscript of + are those nondimensionalized by the wall friction velocity $u_\tau$ and the kinematic viscosity $\nu$). Comparisons with DNS data of fully-developed turbulent channel flows for $109 < Re_{\tau} < 2003$ show good agreement (where $Re_{\tau}$ denotes the friction Reynolds number defined by $u_\tau$, $\nu$ and the channel half-width $\delta$)

Anomalous relaxation kinetics of biological lattice-ligand binding models

We discuss theoretical models for the cooperative binding dynamics of ligands to substrates, such as dimeric motor proteins to microtubules or more extended macromolecules like tropomyosin to actin filaments. We study the effects of steric constraints, size of ligands, binding rates and interaction between neighboring proteins on the binding dynamics and binding stoichiometry. Starting from an empty lattice the binding dynamics goes, quite generally, through several stages. The first stage represents fast initial binding closely resembling the physics of random sequential adsorption processes. Typically this initial process leaves the system in a metastable locked state with many small gaps between blocks of bound molecules. In a second stage the gaps annihilate slowly as the ligands detach and reattach. This results in an algebraic decay of the gap concentration and interesting scaling behavior. Upon identifying the gaps with particles we show that the dynamics in this regime can be explained by mapping it onto various reaction-diffusion models. The final approach to equilibrium shows some interesting dynamic scaling properties. We also discuss the effect of cooperativity on the equilibrium stoichiometry, and their consequences for the interpretation of biochemical and image reconstruction results.Comment: REVTeX, 20 pages, 17 figures; review, to appear in Chemical Physics; v2: minor correction