Time development of small disturbances to plane Couette Flow

The question of linear sheared-disturbance evolution in constant-shear parallel flow is here reexamined with regard to the temporary-amplification phenomenon noted first by Orr in 1907. The results apply directly to Rossby waves on a beta-plane, and are also relevant to the Eady model of baroclinic instability. It is shown that an isotropic initial distribution of standing waves maintains a constant energy level throughout the shearing process, the amplification of some waves being precisely balanced by the decay of the others. An expression is obtained for the energy of a distribution of disturbances whose wavevectors lie within a given angular wedge and an upper bound derived. It is concluded that the case for ubiquitous amplification made in recent studies may have been somewhat overstated: while carefully-chosen individual Fourier components can amplify considerably before they decay. a general distribution will tend to exhibit little or no amplification.

Cylindrically symmetric flows in a Lagrangian frame

An approximate Riemann solver, in a Lagrangian frame of reference, is presented for the compressible flow equations with cylindrical and spherical symmetry, including flow in a duct of variable cross section. The scheme is applied to a cylindrically symmetric problem involving the interaction of shocks.

Spectroscopic signatures of an Fmoc–tetrapeptide, Fmoc and fluorene

The hydrophobic Fmoc [N-(fluorenyl)-9-methoxycarbonyl] unit is often conjugated to peptides to confer amphiphilicity on the molecules, and to introduce the potential for aromatic stacking interactions. In this paper we report spectroscopic data for fluorene, Fmoc and Fmoc conjugated to a small peptide (GRDS in this case) to enable interpretation of spectroscopic data collected on complex structures that can be created with Fmoc–peptide molecules. We report absorbance data (ultra violet and infrared), circular dichroism, linear dichroism (both film and Couette flow orientation) and Raman spectra. Orientations of the Fmoc chromophores in the linear dichroism studies are deduced.

Gene flow, risk assessment and the environmental release of transgenic plants

The release of genetically modified plants is governed by regulations that aim to provide an assessment of potential impact on the environment. One of the most important components of this risk assessment is an evaluation of the probability of gene flow. In this review, we provide an overview of the current literature on gene flow from transgenic plants, providing a framework of issues for those considering the release of a transgenic plant into the environment. For some plants gene flow from transgenic crops is well documented, and this information is discussed in detail in this review. Mechanisms of gene flow vary from plant species to plant species and range from the possibility of asexual propagation, short- or long-distance pollen dispersal mediated by insects or wind and seed dispersal. Volunteer populations of transgenic plants may occur where seed is inadvertently spread during harvest or commercial distribution. If there are wild populations related to the transgenic crop then hybridization and eventually introgression in the wild may occur, as it has for herbicide resistant transgenic oilseed rape (Brassica napus). Tools to measure the amount of gene flow, experimental data measuring the distance of pollen dispersal, and experiments measuring hybridization and seed survivability are discussed in this review. The various methods that have been proposed to prevent gene flow from genetically modified plants are also described. The current "transgenic traits'! in the major crops confer resistance to herbicides and certain insects. Such traits could confer a selective advantage (an increase in fitness) in wild plant populations in some circumstances, were gene flow to occur. However, there is ample evidence that gene flow from crops to related wild species occurred before the development of transgenic crops and this should be taken into account in the risk assessment process.

Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re-U), axial flow Reynolds number (Re-W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers. (c) 2006 Elsevier Ltd. All rights reserved.

Shallow water flow with cylindrical symmetry

A numerical scheme is presented tor the solution of the shallow water equations in a single radial coordinate. This can prove useful when testing codes for the two-dimensional shallow water equations. The scheme is applied with success to problems involving converging and diverging bores.

WAXS studies of global molecular orientation induced in nematic liquid crystals by simple shear flow

Global molecular orientation function coefficients for the nematic liquid crystal 4-cyano 4'-nn -pentylbiphenyl (5CB) in shear flow are presented, being extracted from 2-dimensional Wide-Angle X-ray Scattering data. A linear increase in orientation parameter P2 is observed with a logarithmic increase in shear rate. It is proposed that this arises from an increased number of LC directors aligning to the shear axis. Upon cessation of shear flow, the anisotropy is seen to relax away completely, over a time scale which is inversely proportional to the previously applied shear rate.

On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.