The transport of passive scalar in turbulent flows remains a challenging and important problem for several reasons. First, the passive scalar spectra exhibit various behaviors depending on the molecular Schmidt number value (see [3]). The passive scalar spectrum with a high Schmidt number exhibits thus a k−1 scaling between the Kolmogorov scale and the Batchelor scale [1]. This suggests that it...

The robustness of Nakamura’s effective diffusivity diagnostic for quantifying eddy diffusivities of tracers within a streamwise-average framework is carefully examined in an oceanographic context, and the limits of its applicability are detailed. The near-surface Southern Ocean geostrophic flow, obtained from altimetric observations, is chosen for particular examination since it exhibits strong...

Duchenne muscular dystrophy (DMD) is caused by the absence of functional dystrophin (Blake et al. 2002). Dystrophin is a cytoskeleton protein normally expressed in the inner face of the plasma membrane (Ahn and Kunkel 1993). In normal skeletal muscle, dystrophin is associated with a complex of glycoproteins known as dystrophin-associated proteins (DAPs), providing a linkage between the extracel...

This study considers numerical methods for computation of optimal boundary and initial perturbations to incompressible flows. Similar to previous work, constrained Lagrangian functionals are built and gradient optimisation methods are applied to optimise perturbations that maximise the energy of perturbations in the computational domain at a given time horizon. Unlike most of the previous work ...

A direct numerical simulation of a Batchelor vortex has been carried out in the presence of freely-decaying turbulence, using both periodic and symmetric boundary conditions; the latter most closely approximates typical experimental conditions, while the former is often used in computational simulations for the purposes of numerical convenience. The higher-order velocity statistics were shown t...

1 Overview In the previous lecture we emphasized that the destruction of tracer variance by molecular diffusivity relies on the increase of ∇c by stirring. Thus the term κ∇c ·∇c in the variance budget eventually becomes important, even though the molecular diffusivity κ is very small. One goal of this lecture is to understand in more detail how tracer gradients in a moving fluid are amplified b...

The transport properties of a random velocity field with Kolmogorov spectrum and time correlations defined along Lagrangian trajectories are analyzed. The analysis is carried out in the limit of short correlation times, as a perturbation theory in the ratio, scale by scale, of the eddy decay and turnover time. Various quantities such as the Batchelor constant and the dimensionless constants ent...

A well-known problem in low Reynolds number hydrodynamics 1) is to calculate the hydrodynamic interactions between spherical particles moving in a fluid, as its solution is necessary for understanding the properties of suspensions. While the first treatment of such hydrodynamic interactions dates from 1911 when Smoluchowski 2) analysed the hydrodynamic friction between two spherical particles, ...

We study the dual cascade scenario for two-dimensional turbulence driven by a spectrally localized forcing applied over a finite wavenumber range [kmin, kmax] (with kmin > 0) such that the respective energy and enstrophy injection rates and η satisfy k2 min ≤ η ≤ k 2 max . The classical Kraichnan–Leith–Batchelor paradigm, based on the simultaneous conservation of energy and enstrophy and the sc...

This paper outlines our recent attempts to model the growth and form of microbialites from the perspective of the statistical physics of evolving surfaces. Microbialites arise from the environmental interactions of microbial communities (microbial mats). The mats evolve over time to form internally laminated organosedimentary structures (stromatolites). Modern day stromatolites exist in only a ...