Vortical and Wave Modes in 3D Rotating Stratified Flows: Random Large Scale Forcing

Utilizing an eigenfunction decomposition, we study the growth and spectra of energy in the vortical and wave modes of a 3D rotating stratified fluid as a function of $\epsilon = f/N$. Working in regimes characterized by moderate Burger numbers, i.e. $Bu = 1/\epsilon^2 < 1$ or $Bu \ge 1$, our results indicate profound change in the character of vortical and wave mode interactions with respect to $Bu = 1$. As with the reference state of $\epsilon=1$, for $\epsilon < 1$ the wave mode energy saturates quite quickly and the ensuing forward cascade continues to act as an efficient means of dissipating ageostrophic energy. Further, these saturated spectra steepen as $\epsilon$ decreases: we see a shift from $k^{-1}$ to $k^{-5/3}$ scaling for $k_f < k < k_d$ (where $k_f$ and $k_d$ are the forcing and dissipation scales, respectively). On the other hand, when $\epsilon > 1$ the wave mode energy never saturates and comes to dominate the total energy in the system. In fact, in a sense the wave modes behave in an asymmetric manner about $\epsilon = 1$. With regard to the vortical modes, for $\epsilon \le 1$, the signatures of 3D quasigeostrophy are clearly evident. Specifically, we see a $k^{-3}$ scaling for $k_f < k < k_d$ and, in accord with an inverse transfer of energy, the vortical mode energy never saturates but rather increases for all $k < k_f$. In contrast, for $\epsilon > 1$ and increasing, the vortical modes contain a progressively smaller fraction of the total energy indicating that the 3D quasigeostrophic subsystem plays an energetically smaller role in the overall dynamics.Comment: 18 pages, 6 figs. (abbreviated abstract

Finite element computation of transient dissipative double diffusive magneto-convective nanofluid flow from a rotating vertical porous surface in porous media

This paper aimed to investigate the transient dissipative MHD double diffusive free convective boundary layer flow of electrically-conducting nanofluids from a stationary or moving vertical porous surface in a rotating high permeability porous medium, considering buoyancy, thermal radiation and first order chemical reaction. Thermo-diffusion (Soret) and diffuso-thermal (Dufour) effects are also considered. Darcy’s law is employed. The mathematical model is formulated by considering water-based nanofluids containing metallic nano-particles for both stationary and moving plate cases. Three nanofluids are examined, namely copper, aluminium oxide or titanium oxide in water. The transformed non-linear, coupled, dimensionless partial differential equations describing the flow are solved with physically appropriate boundary conditions by using Galerkin weighted residual scheme. For prescribed permeability, numerical results are presented graphically for the influence of a number of emerging parameters. Validation of finite element solutions for skin friction and Nusselt number is achieved via comparison with the previously published work as special cases of the present investigation and very good correlation obtained. Increasing rotational parameter is observed to reduce both primary and secondary velocity components. Primary and secondary velocities are consistently elevated with increasing Soret, Dufour, thermal Grashof and solutal Grashof numbers. Increasing Schmidt number, chemical reaction and suction parameter both suppress nano - particle concentration whereas the converse behavior is computed with increasing Soret number. The study is relevant to high temperature rotating chemical engineering systems exploiting magnetized nanofluids and also electromagnetic nanomaterial manufacturing processes

Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis

Macroscopic transport by synthetic molecular machines

Nature uses molecular motors and machines in virtually every significant biological process, but demonstrating that simpler artificial structures operating through the same gross mechanisms can be interfaced with—and perform physical tasks in—the macroscopic world represents a significant hurdle for molecular nanotechnology. Here we describe a wholly synthetic molecular system that converts an external energy source (light) into biased brownian motion to transport a macroscopic cargo and do measurable work. The millimetre-scale directional transport of a liquid on a surface is achieved by using the biased brownian motion of stimuli-responsive rotaxanes (‘molecular shuttles’) to expose or conceal fluoroalkane residues and thereby modify surface tension. The collective operation of a monolayer of the molecular shuttles is sufficient to power the movement of a microlitre droplet of diiodomethane up a twelve-degree incline.

Does Sex Trade with Violence among Genotypes in Drosophila melanogaster?

The evolutionary forces shaping the ability to win competitive interactions, such as aggressive encounters, are still poorly understood. Given a fitness advantage for competitive success, variance in aggressive and sexual display traits should be depleted, but a great deal of variation in these traits is consistently found. While life history tradeoffs have been commonly cited as a mechanism for the maintenance of variation, the variability of competing strategies of conspecifics may mean there is no single optimum strategy. We measured the genetically determined outcomes of aggressive interactions, and the resulting effects on mating success, in a panel of diverse inbred lines representing both natural variation and artificially selected genotypes. Males of one genotype which consistently lost territorial encounters with other genotypes were nonetheless successful against males that were artificially selected for supernormal aggression and dominated all other lines. Intransitive patterns of territorial success could maintain variation in aggressive strategies if there is a preference for territorial males. Territorial success was not always associated with male mating success however and females preferred ‘winners’ among some male genotypes, and ‘losers’ among other male genotypes. This suggests that studying behaviour from the perspective of population means may provide limited evolutionary and genetic insight. Overall patterns of competitive success among males and mating transactions between the sexes are consistent with mechanisms proposed for the maintenance of genetic variation due to nonlinear outcomes of competitive interactions

A framework for the probabilistic analysis of meteotsunamis

This paper is not subject to U.S. copyright. The definitive version was published in Natural Hazards 74 (2014): 123-142, doi:10.1007/s11069-014-1294-1.A probabilistic technique is developed to assess the hazard from meteotsunamis. Meteotsunamis are unusual sea-level events, generated when the speed of an atmospheric pressure or wind disturbance is comparable to the phase speed of long waves in the ocean. A general aggregation equation is proposed for the probabilistic analysis, based on previous frameworks established for both tsunamis and storm surges, incorporating different sources and source parameters of meteotsunamis. Parameterization of atmospheric disturbances and numerical modeling is performed for the computation of maximum meteotsunami wave amplitudes near the coast. A historical record of pressure disturbances is used to establish a continuous analytic distribution of each parameter as well as the overall Poisson rate of occurrence. A demonstration study is presented for the northeast U.S. in which only isolated atmospheric pressure disturbances from squall lines and derechos are considered. For this study, Automated Surface Observing System stations are used to determine the historical parameters of squall lines from 2000 to 2013. The probabilistic equations are implemented using a Monte Carlo scheme, where a synthetic catalog of squall lines is compiled by sampling the parameter distributions. For each entry in the catalog, ocean wave amplitudes are computed using a numerical hydrodynamic model. Aggregation of the results from the Monte Carlo scheme results in a meteotsunami hazard curve that plots the annualized rate of exceedance with respect to maximum event amplitude for a particular location along the coast. Results from using multiple synthetic catalogs, resampled from the parent parameter distributions, yield mean and quantile hazard curves. Further refinements and improvements for probabilistic analysis of meteotsunamis are discussed