The Strange Eigenmode in Lagrangian Coordinates

For a distribution advected by a simple chaotic map with diffusion, the "strange eigenmode" is investigated from the Lagrangian (material) viewpoint and compared to its Eulerian (spatial) counterpart. The eigenmode embodies the balance between diffusion and exponential stretching by a chaotic flow. It is not strictly an eigenmode in Lagrangian coordinates, because its spectrum is rescaled exponentially rapidly.Comment: 15 pages, 6 figures. RevTeX4 format with psfra

Stirring by swimming bodies

We consider the stirring of an inviscid fluid caused by the locomotion of bodies through it. The swimmers are approximated by non-interacting cylinders or spheres moving steadily along straight lines. We find the displacement of fluid particles caused by the nearby passage of a swimmer as a function of an impact parameter. We use this to compute the effective diffusion coefficient from the random walk of a fluid particle under the influence of a distribution of swimming bodies. We compare with the results of simulations. For typical sizes, densities and swimming velocities of schools of krill, the effective diffusivity in this model is five times the thermal diffusivity. However, we estimate that viscosity increases this value by two orders of magnitude.Comment: 5 pages, 5 figures. PDFLaTeX with RevTeX 4 macros. Final versio

Energy-Conserving Truncations for Convection with Shear Flow

A method is presented for making finite Fourier mode truncations of the Rayleigh--Benard convection system that preserve invariants of the full partial differential equations in the dissipationless limit. These truncations are shown to have no unbounded solutions and provide a description of the thermal flux that has the correct limiting behavior in a steady-state. A particular low-order truncation (containing 7 modes) is selected and compared with the 6 mode truncation of Howard and Krishnamurti (1986), which does not conserve the total energy in the dissipationless limit. A numerical example is presented to compare the two truncations and study the effect of shear flow on thermal transport.Comment: 18 pages, 5 Postscript figures, uses RevTeX and epsf. Accepted for publication in Physics of Fluid