Unbalanced instabilities of rapidly rotating stratified shear flows

The linear stability of a rotating, stratified, inviscid horizontal plane Couette flow in a channel is studied in the limit of strong rotation and stratification. An energy argument is used to show that unstable perturbations must have large wavenumbers. This motivates the use of a WKB-approach which, in the first instance, provides an approximation for the dispersion relation of the various waves that can propagate in the flow. These are Kelvin waves, trapped near the channel walls, and inertia-gravity waves with or without turning points. Although, the wave phase speeds are found to be real to all algebraic orders in the Rossby number, we establish that the flow, whether cyclonic or anticyclonic, is unconditionally unstable. This is the result of linear resonances between waves with oppositely signed wave momenta. We derive asymptotic estimates for the instability growth rates, which are exponentially small in the Rossby number, and confirm them by numerical computations. Our results, which extend those of Kushner et al (1998) and Yavneh et al (2001), highlight the limitations of the so-called balanced models, widely used in geophysical fluid dynamics, which filter out Kelvin and inertia-gravity waves and hence predict the stability of the Couette flow. They are also relevant to the stability of Taylor-Couette flows and of astrophysical accretion discs.Comment: 6 figure

Elliptical instability of a rapidly rotating, strongly stratified fluid

The elliptical instability of a rotating stratified fluid is examined in the regime of small Rossby number and order-one Burger number corresponding to rapid rotation and strong stratification. The Floquet problem describing the linear growth of disturbances to an unbounded, uniform-vorticity elliptical flow is solved using exponential asymptotics. The results demonstrate that the flow is unstable for arbitrarily strong rotation and stratification; in particular, both cyclonic and anticyclonic flows are unstable. The instability is weak, however, with growth rates that are exponentially small in the Rossby number. The analytic expression obtained for the growth rate elucidates its dependence on the Burger number and on the eccentricity of the elliptical flow. It explains in particular the weakness of the instability of cyclonic flows, with growth rates that are only a small fraction of those obtained for the corresponding anticyclonic flows. The asymptotic results are confirmed by numerical solutions of Floquet problem.Comment: 17 page

Subtyping somatic tinnitus: a cross-sectional UK cohort study of demographic, clinical and audiological characteristics

Somatic tinnitus is the ability to modulate the psychoacoustic features of tinnitus by somatic manoeuvres. The condition is still not fully understood and further identification of this subtype is essential, particularly for the purpose of establishing protocols for both its diagnosis and treatment. This study aimed to investigate the characteristics of somatic tinnitus within a large UK cohort using a largely unselected sample. We believe this to be relatively unique in comparison to current literature on the topic. This was investigated by using a total of 608 participant assessments from a set of recognised tinnitus and audiology measures. Results from a set of chi-square tests of association found that amongst the individuals with somatic tinnitus, a higher proportion had pulsatile tinnitus (different from heartbeat), were under the age of 40, reported variation in the loudness of their tinnitus and reported temporomandibular joint (TMJ) disorder. The same pattern of results was confirmed using a multivariate analysis of the data based on logistic regression. These findings have strong implications towards the profiling of somatic tinnitus as a distinct subtype of general tinnitus

Exponential smallness of inertia-gravity wave generation at small Rossby number

This paper discusses some of the mechanisms whereby fast inertia-gravity waves can be generated spontaneously by slow, balanced atmospheric and oceanic flows. In the small-Rossby-number regime relevant to mid-latitude dynamics, high-accuracy balanced models, which filter out inertia-gravity waves completely, can in principle describe the evolution of suitably initialised flows up to terms that are exponentially small in the Rossby number , i.e, of the form exp(−α/) for some α> 0. This suggests that the mechanisms of inertia-gravity-wave generation, which are not captured by these balanced models, are also exponentially weak. This has been confirmed by explicit analytical results obtained for a few highly-simplified models. We review these results and present some of the exponential-asymptotic techniques that have been used in their derivation. We examine both spontaneous-generation mechanisms which generate exponentially small waves from perfectly balanced initial conditions, and unbalanced instability mechanisms which amplify unbalanced initial perturbations of steady flows. The relevance of the results to realistic flows is discussed. 2

Estimating generalized Lyapunov exponents for products of random matrices

We discuss several techniques for the evaluation of the generalised Lyapunov exponents which characterise the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorithm that performs importance sampling using a simple random resampling step is proposed as a general-purpose numerical method which is both efficient and easy to implement. Alternative techniques complementing this method are presented. These include the computation of the generalised Lyapunov exponents by solving numerically an eigenvalue problem, and some asymptotic results corresponding to high-order moments of the matrix products. Taken together, the techniques discussed in this paper provide a suite of methods which should prove useful for the evaluation of the generalised Lyapunov exponents in a broad range of applications. Their usefulness is demonstrated on particular products of random matrices arising in the study of scalar mixing by complex fluid flows.Comment: Revised version: references added to the published versio

A 3000 year chronology of North Anatolian Fault ruptures, utilizing magnetic susceptibility trench logging, near Lake Ladik, Turkey

Understanding the irregularity of seismic cycles: A case study in Turke

Strategy for the identification of micro-organisms producing food and feed products : bacteria producing food enzymes as study case

Recent European regulations require safety assessments of food enzymes (FE) before their commercialization. FE are mainly produced by micro-organisms, whose viable strains nor associated DNA can be present in the final products. Currently, no strategy targeting such impurities exists in enforcement laboratories. Therefore, a generic strategy of first line screening was developed to detect and identify, through PCR amplification and sequencing of the 16S-rRNA gene, the potential presence of FE producing bacteria in FE preparations. First, the specificity was verified using all microbial species reported to produce FE. Second, an in-house database, with 16S reference sequences from bacteria producing FE, was constructed for their fast identification through blast analysis. Third, the sensitivity was assessed on a spiked FE preparation. Finally, the applicability was verified using commercial FE preparations. Using straightforward PCR amplifications, Sanger sequencing and blast analysis, the proposed strategy was demonstrated to be convenient for implementation in enforcement laboratories

Scalar decay in a three-dimensional chaotic flow

The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow employed extensively in studies of mixing in two dimensions. It is used to show that theoretical predictions for two-dimensional flows with small diffusivity carry over to three dimensions even though the stretching properties differ significantly. The variance decay rate, scalar field structure, and time evolution of statistical moments confirm that there are two distinct regimes of scalar decay: a locally controlled regime, which applies when the domain size is comparable to the characteristic lengthscale of the velocity field, and a globally controlled regime, which when applies when the domain is larger. Asymptotic predictions for the variance decay rate in both regimes show excellent agreement with the numerical results. Consideration of both the forward flow and its time reverse makes it possible to compare the scalar evolution in flows with one or two expanding directions; simulations confirm the theoretical prediction that the decay rate of the scalar is the same in both flows, despite the very different scalar field structures