Turbulent diffusion in rapidly rotating flows with and without stable stratification

In this work, three different approaches are used for evaluating some Lagrangian properties of homogeneous turbulence containing anisotropy due to the application of a stable stratification and a solid-body rotation. The two external frequencies are the magnitude of the system vorticity, chosen vertical here, and the Brunt–Väisälä frequency, which gives the strength of the vertical stratification. Analytical results are derived using linear theory for the Eulerian velocity correlations (single-point, two-time) in the vertical and the horizontal directions, and Lagrangian ones are assumed to be equivalent, in agreement with an additional Corrsin assumption used by Kaneda (2000). They are compared with results from the kinematic simulation model (KS) by Nicolleau & Vassilicos (2000), which also incorporates the wave–vortex dynamics inherited from linear theory, and directly yields Lagrangian correlations as well as Eulerian ones. Finally, results from direct numerical simulations (DNS) are obtained and compared We address the question of the validity of Corrsin's simplified hypothesis, which states the equivalence between Eulerian and Lagrangian correlations. Vertical correlations are found to follow this postulate, but not the horizontal ones. Consequences for the vertical and horizontal one-particle dispersion are examined. In the analytical model, the squared excursion lengths are calculated by time integrating the Lagrangian (equal to the Eulerian) two-time correlations, according to Taylor's procedure. These quantities are directly computed from fluctuating trajectories by both KS and DNS. In the case of pure rotation, the analytical procedure allows us to relate Brownian asymptotic laws of dispersion in both the horizontal and vertical directions to the angular phase-mixing properties of the inertial waves. If stratification is present, the inertia–gravity wave dynamics, which affects the vertical motion, yields a suppressed vertical diffusivity, but not a suppressed horizontal diffusivity, since part of the horizontal velocity field escapes wavy motion

Anisotropy in Homogeneous Rotating Turbulence

The effective stress tensor of a homogeneous turbulent rotating fluid is anisotropic. This leads us to consider the most general axisymmetric four-rank ``viscosity tensor'' for a Newtonian fluid and the new terms in the turbulent effective force on large scales that arise from it, in addition to the microscopic viscous force. Some of these terms involve couplings to vorticity and others are angular momentum non conserving (in the rotating frame). Furthermore, we explore the constraints on the response function and the two-point velocity correlation due to axisymmetry. Finally, we compare our viscosity tensor with other four-rank tensors defined in current approaches to non-rotating anisotropic turbulence.Comment: 14 pages, RevTe

Quasi-static magnetohydrodynamic turbulence at high Reynolds number

We analyse the anisotropy of homogeneous turbulence in an electrically conducting fluid submitted to a uniform magnetic field, for low magnetic Reynolds number, in the quasi- static approximation. We interpret disagreeing previous predictions between linearized theory and simulations: in the linear limit, the kinetic energy of transverse velocity components, normal to the magnetic field, decays faster than the kinetic energy of the axial component, along the magnetic field (Moffatt (1967)); whereas many numerical studies predict a final state characterised by dominant energy of transverse velocity components. We investigate the corresponding nonlinear phenomenon using Direct Numerical Simulations of freely-decaying turbulence, and a two-point statistical spectral closure based on the Eddy Damped Quasi-Normal Markovian model. The transition from the three-dimensional turbulent flow to a "two-and-a-half-dimensional" flow (Montgomery & Turner (1982)) is a result of the combined effects of short-time linear Joule dissipation and longer time nonlinear creation of polarisation anisotropy. It is this combination of linear and nonlinear effects which explains the disagreement between predictions from linearized theory and results from numerical simulations. The transition is characterized by the elongation of turbulent structures along the applied magnetic field, and by the strong anisotropy of directional two-point correlation spectra, in agreement with experimental evidence. Inertial equatorial transfers in both DNS and the model are presented to describe in detail the most important equilibrium dynamics. Spectral scalings are maintained in high Reynolds number turbulence attainable only with the EDQNM model, which also provides simplified modelling of the asymptotic state of quasi-static MHD turbulence.Comment: Journal of Fluid Mechanics, 201

Anisotropic structure of homogeneous turbulence subjected to uniform rotation

Large-eddy simulation results are used to investigate the development of anisotropies and the possible transition towards a quasi two-dimensional state in rotating turbulence at high Reynolds number. The present study demonstrates the existence of two transitions that are identified by two Rossby numbers. The first transition marks the onset of anisotropic effects and corresponds to a macro Rossby number Ro(sup L) (based on a longitudinal integral length scale) near unity. A second transition can be defined in terms of a lower bound of micro-Rossby number Ro(sup w) also near unity (defined in this work as the ratio of the rms fluctuating vorticity to background vorticity) and corresponds to a continued development of anisotropy but with an increasing emergence of those indicators based on the pure two-dimensional component of the flow, e.g., integral length scales measured along the rotation axis. Investigation of the vorticity structure shows that the second transition is also characterized by an increasing tendency for alignment between the fluctuating vorticity vector and the basic angular velocity vector with a preference for corotative vorticity

Scaling and energy transfer in rotating turbulence

The inertial-range properties of quasi-stationary hydrodynamic turbulence under solid-body rotation are studied via high-resolution direct numerical simulations. For strong rotation the nonlinear energy cascade exhibits depletion and a pronounced anisotropy with the energy flux proceeding mainly perpendicularly to the rotation axis. This corresponds to a transition towards a quasi-two-dimensional flow similar to a linear Taylor-Proudman state. In contrast to the energy spectrum along the rotation axis which does not scale self-similarly, the perpendicular spectrum displays an inertial range with $k^{-2}_\perp$-behavior. A new phenomenology gives a rationale for the observations. The scaling exponents $\zeta_p$ of structure functions up to order $p=8$ measured perpendicular to the rotation axis indicate reduced intermittency with increasing rotation rate. The proposed phenomenology is consistent with the inferred asymptotic non-intermittent behavior $\zeta_p=p/2$.Comment: to be published in Europhysics Letters (www.epletters.net), minor changes to match version in prin

Signatures of two-dimensionalisation of 3D turbulence in presence of rotation

A reason has been given for the inverse energy cascade in the two-dimensionalised rapidly rotating 3D incompressible turbulence. For such system, literature shows a possibility of the exponent of wavenumber in the energy spectrum's relation to lie between -2 and -3. We argue the existence of a more strict range of -2 to -7/3 for the exponent in the case of rapidly rotating turbulence which is in accordance with the recent experiments. Also, a rigorous derivation for the two point third order structure function has been provided helping one to argue that even with slow rotation one gets, though dominated, a spectrum with the exponent -2.87, thereby hinting at the initiation of the two-dimensionalisation effect with rotation.Comment: An extended and typos-corrected version of the earlier submissio

Analysis of probe level patterns in Affymetrix microarray data

<p>Abstract</p> <p>Background</p> <p>Microarrays have been used extensively to analyze the expression profiles for thousands of genes in parallel. Most of the widely used methods for analyzing Affymetrix Genechip microarray data, including RMA, GCRMA and Model Based Expression Index (MBEI), summarize probe signal intensity data to generate a single measure of expression for each transcript on the array. In contrast, other methods are applied directly to probe intensities, negating the need for a summarization step.</p> <p>Results</p> <p>In this study, we used the Affymetrix rat genome Genechip to explore variability in probe response patterns within transcripts. We considered a number of possible sources of variability in probe sets including probe location within the transcript, middle base pair of the probe sequence, probe overlap, sequence homology and affinity. Although affinity, middle base pair and probe location effects may be seen at the gross array level, these factors only account for a small proportion of the variation observed at the gene level. A BLAST search and the presence of probe by treatment interactions for selected differentially expressed genes showed high sequence homology for many probes to non-target genes.</p> <p>Conclusion</p> <p>We suggest that examination and modeling of probe level intensities can be used to guide researchers in refining their conclusions regarding differentially expressed genes. We discuss implications for probe sequence selection for confirmatory analysis using real time PCR.</p

The Egyptian wheat cultivar Gemmeiza-12 is a source of resistance against the fungus <i>Zymoseptoria tritici</i>

Background: Wheat is one of the world’s most important cereal crops. However, the fungal pathogen Zymoseptoria tritici can cause disease epidemics, leading to reduced yields. With climate change and development of new agricultural areas with suitable environments, Z. tritici may advance into geographical areas previously unaffected by this pathogen. It is currently unknown how Egyptian wheat will perform in the face of this incoming threat. This project aimed to assess the resistance of Egyptian wheat germplasm to Z. tritici, to identify cultivars with high levels of resistance and characterise the mechanism(s) of resistance present in these cultivars. Results: Eighteen Egyptian wheat cultivars were screened against two Z. tritici model isolates and exhibited a wide spectrum of responses. This ranged from resistance to complete susceptibility to one or both isolates tested. The most highly resistant cultivars from the initial screen were then tested under two environmental conditions against modern UK field isolates. Disease levels under UK-like conditions were higher, however, symptom development on the cultivar Gemmeiza-12 was noticeably slower than on other Egyptian wheats. The robustness of the resistance shown by Gemmeiza-12 was confirmed in experiments mimicking Egyptian environmental conditions, where degree of Z. tritici infection was lower. The Kompetitive allele-specific PCR (KASP) diagnostic assay suggested the presence of an Stb6 resistant allele in several Egyptian wheats including Gemmeiza-12. Infection assays using the IPO323 WT and IPO323ΔAvrStb6 mutant confirmed the presence of Stb6 in several Egyptian cultivars including Gemmeiza-12. Confocal fluorescence microscopy demonstrated that growth of the IPO323 strain is blocked at the point of stomatal penetration on Gemmeiza-12, consistent with previous reports of Stb gene mediated resistance. In addition to this R-gene mediated resistance, IPO323 spores showed lower adherence to leaves of Gemmeiza-12 compared to UK wheat varieties, suggesting other aspects of leaf physiology may also contribute to the resistance phenotype of this cultivar. Conclusion: These results indicate that Gemmeiza-12 will be useful in future breeding programs where improved resistance to Z. tritici is a priority

The decay of Batchelor and Saffman rotating turbulence

The decay rate of isotropic and homogeneous turbulence is known to be affected by the large-scale spectrum of the initial perturbations, associated with at least two cannonical self-preserving solutions of the von K\'arm\'an-Howarth equation: the so-called Batchelor and Saffman spectra. The effect of long-range correlations in the decay of anisotropic flows is less clear, and recently it has been proposed that the decay rate of rotating turbulence may be independent of the large-scale spectrum of the initial perturbations. We analyze numerical simulations of freely decaying rotating turbulence with initial energy spectra $\sim k^4$ (Batchelor turbulence) and $\sim k^2$ (Saffman turbulence) and show that, while a self-similar decay cannot be identified for the total energy, the decay is indeed affected by long-range correlations. The decay of two-dimensional and three-dimensional modes follows distinct power laws in each case, which are consistent with predictions derived from the anisotropic von K\'arm\'an-Howarth equation, and with conservation of anisotropic integral quantities by the flow evolution