Path Lengths in Turbulence

By tracking tracer particles at high speeds and for long times, we study the geometric statistics of Lagrangian trajectories in an intensely turbulent laboratory flow. In particular, we consider the distinction between the displacement of particles from their initial positions and the total distance they travel. The difference of these two quantities shows power-law scaling in the inertial range. By comparing them with simulations of a chaotic but non-turbulent flow and a Lagrangian Stochastic model, we suggest that our results are a signature of turbulence.     

Bis-imine primary amine protection of the dialkyltriamine,norspermidine

This Letter details the particular use of salicylaldehyde (2-hydroxybenzaldehyde) for the regiospecific protection of primary amines in a representative polyamine, norspermidine (N-(3-aminopropyl)propane-1,3-diamine) under mild reaction conditions in high yield. The lack of intramolecular hexahydropyrimidine formation allowed for subsequent N²-acylation and N²-alkylation reactions, typical of polyamine synthetic strategies.     

Curvature of lagrangian trajectories in turbulence

We report measurements of the curvature of Lagrangian trajectories in an intensely turbulent laboratory water flow measured with a high-speed particle-tracking system. The probability density function (PDF) of the instantaneous curvature is shown to have robust power-law tails. We propose a model for the instantaneous curvature PDF, assuming that the acceleration and velocity are uncorrelated Gaussian random variables, and show that our model reproduces the tails of our measured PDFs. We also predict the scaling of the most probable vorticity magnitude in turbulence, assuming Heisenberg-Yaglom scaling. Finally, we average the curvature along trajectories and show that, by removing the effects of large-scale flow reversals, the filtered curvature reveals the turbulent features.