Optimal energy growth in pulsatile channel and pipe flows

Pulsatile channel and pipe flows constitute a fundamental flow configuration with significant bearing on many applications in the engineering and medical sciences. Rotating machinery, hydraulic pumps or cardiovascular systems are dominated by time-periodic flows, and their stability characteristics play an important role in their efficient and proper operation. While previous work has mainly concentrated on the modal, harmonic response to an oscillatory or pulsatile base flow, this study employs a direct–adjoint optimisation technique to assess short-term instabilities, identify transient energy-amplification mechanisms and determine their prevalence within a wide parameter space. At low pulsation amplitudes, the transient dynamics is found to be similar to that resulting from the equivalent steady parabolic flow profile, and the oscillating flow component appears to have only a weak effect. After a critical pulsation amplitude is surpassed, linear transient growth is shown to increase exponentially with the pulsation amplitude and to occur mainly during the slow part of the pulsation cycle. In this latter regime, a detailed analysis of the energy transfer mechanisms demonstrates that the huge linear transient growth factors are the result of an optimal combination of Orr mechanism and intracyclic normal-mode growth during half a pulsation cycle. Two-dimensional sinuous perturbations are favoured in channel flow, while pipe flow is dominated by helical perturbations. An extensive parameter study is presented that tracks these flow features across variations in the pulsation amplitude, Reynolds and Womersley numbers, perturbation wavenumbers and imposed time horizon.

Two-scale theory of edge state

The edge state is considered in the spectrum region where its branch splits from the bottom of a continuous conduction band. It is shown that in this region the electron wave function demonstrates two different scale behaviours: slow and fast, that enabled us to construct some simplified procedure for the analysis of the edge state. The slow wave function part obeys a simple Schrödinger equation the parameters of which are insensitive to the peculiarities of the electron dynamics, while the fast part that describes the details of electron behaviour in the primitive cell reveals itself only at the edge. The equation for this fast part was transformed into the boundary condition for the slow part equation. The proposed method is illustrated considering the simplest continuous model for a topological insulator and a tight binding model for graphene.

Analysis of a model describing stage-structured population dynamics using hawk-dove tactics

International audience The purpose of this paper is to investigate the effects of conflicting tactics of resource acquisition on stage structured population dynamics. We present a population subdivided into two distinct stages (immature and mature). We assume that immature individual survival is density dependent. We also assume that mature individuals acquire resources required to survive and reproduce by using two contrasted behavioral tactics (hawk versus dove). Mature individual survival thus is assumed to depend on the average cost of fights while individual fecundity depends on the average gain in the competition to access the resource. Our model includes two parts: a fast part that describes the encounters and fights involves a game dynamic model based upon the replicator equations, and a slow part that describes the long-term effects of conflicting tactics on the population dynamics. The existence of two time scales let us investigate the complete system from a reduced one, which describes the dynamics of the total immature and mature densities at the slow time scale. Our analysis shows that an increase in resource value may decrease total population density, because it promotes individual (i.e. selfish) behavior. Our results may therefore find practical implications in animal conservation or biological control for instance. Le but de cet article est d'étudier les effets de comportements agressifs dans l'acquisition de ressources sur la dynamique d'une population structurée en deux classes d'âge. Nous considérons une population divisée en deux sous populations distinctes (immatures et adultes matures). Nous supposons que la survie individuelle de la population immature est densité dépendante. Nous supposons également que les individus matures sont en compétition pour acquérir les ressources nécessaires pour leur survie et leur reproduction. Les adultes utilisent deux tactiques comportementales (faucon et colombe). Lors de confrontations entre adultes, la survie d'un individu mature est supposée être affectée par le coût moyen des combats alors que la fécondité dépend du gain moyen obtenu en accédant à la ressource. Notre modèle comprend deux parties : une partie rapide qui décrit les rencontres et les combats basée sur les équations du réplicateur, et une partie lente qui décrit les effets à long terme des tactiques conflictuelles sur la dynamique de la population. L'existence de deux échelles de temps nous permet d'étudier le système complet à partir d'un système réduit, qui décrit la dynamique des densités totales des immatures et des adultes à l'échelle de temps lente. Notre analyse montre que le taux de croissance global de la population dépend de la valeur de la ressource et du coût des combats entre adultes. Nos résultats trouvent des implications pratiques dans la conservation des espèces et le contrôle biologique.

A variational derivation of the geostrophic momentum approximation

This paper demonstrates that the shallow water semigeostrophic equations arise from a degenerate second-order Hamilton principle of very special structure. The associated Euler–Lagrange operator factors into a fast and a slow first-order operator; restricting to the slow part yields the geostrophic momentum approximation as balanced dynamics. While semigeostrophic theory has been considered variationally before, this structure appears to be new. It leads to a straightforward derivation of the geostrophic momentum approximation and its associated potential vorticity law. Our observations further affirm, from a different point of view, the known difficulty in generalizing the semigeostrophic equations to the case of a spatially varying Coriolis parameter.

Rapid and Slow Decomposition in Large Eddy Simulation of Scalar Turbulence

In large eddy simulation of turbulent flow, because of the spatial filter, inhomogeneity and anisotropy affect the subgrid stress via the mean flow gradient. A method of evaluating the mean effects is to split the subgrid stress tensor into “rapid” and “slow” parts. This decomposition was introduced by Shao et al. (1999) and applied to A Priori tests of existing subgrid models in the case of a turbulent mixing layer. In the present work, the decomposition is extended to the case of a passive scalar in inhomogeneous turbulence. The contributions of rapid and slow subgrid scalar flux, both in the equations of scalar variance and scalar flux, are analyzed. A Priori numerical tests are performed in a turbulent Couette flow with a mean scalar gradient. Results are then used to evaluate the performances of different popular subgrid scalar models. It is shown that existing models can not well simulate the slow part and need to be improved. In order to improve the modeling, an extension of the model proposed by Cui et al. (2004) is introduced for the slow part, whereas the Scale-Similarity model is used reproduce the rapid part. Combining both models, A Priori tests lead to a better performance. However, the remaining problem is that none eddy-diffusion model can correctly represent the strong scalar dissipation near the wall. This problem will be addressed in future work.

Meteoroid velocity distribution derived from head echo data collected at Arecibo during regular world day observations

We report the observation and analysis of ionization flashes associated with the decay of meteoroids (so-called head echos) detected by the Arecibo 430 MHz radar during regular ionospheric observations in the spring and autumn equinoxes. These two periods allow pointing well-above and nearly-into the ecliptic plane at dawn when the event rate maximizes. The observation of many thousands of events allows a statistical interpretation of the results, which show that there is a strong tendency for the observed meteoroids to come from the apex as has been previously reported (Chau and Woodman, 2004). The velocity distributions agree with Janches et al. (2003a) when they are directly comparable, but the azimuth scan used in these observations allows a new perspective. We have constructed a simple statistical model which takes meteor velocities as input and gives radar line of sight velocities as output. The intent is to explain the fastest part of the velocity distribution. Since the speeds interpreted from the measurements are distributed fairly narrowly about nearly 60 km s-1, double the speed of the earth in its orbit, is consistent with the interpretation that many of the meteoroids seen by the Arecibo radar are moving in orbits about the sun with similar parameters as the earth, but in the retrograde direction. However, it is the directional information obtained from the beam-swinging radar experiment and the speed that together provide the evidence for this interpretation. Some aspects of the measured velocity distributions suggest that this is not a complete description even for the fast part of the distribution, and it certainly says nothing about the slow part first described in Janches et al. (2003a). Furthermore, we cannot conclude anything about the entire dust population since there are probably selection effects that restrict the observations to a subset of the population.

Meteor science from regular incoherent scatter radar ionospheric observations at Arecibo

We report the observation and analysis of ionization flashes associated with the decay of meteoroids (so-called head echos) detected by the Arecibo 430 MHz radar during regular ionospheric observations in the spring and autumn equinoxes. These two periods allow pointing well-above and nearly-into the ecliptic plane at dawn when the event rate maximizes. The observation of many thousands of events allows a statistical interpretation of the results, which show that there is a strong tendency for the observed meteoroids to come from the apex as has been previously reported (Chau and Woodman, 2003). The velocity distributions agree with Janches et al. (2003) when they are directly comparable, but the azimuth scan used in these observations allows a new perspective. We have constructed a simple statistical model which takes meteor velocities as input and gives radar line of sight velocities as output. The intent is to explain the fastest part of the velocity distribution. Since the speeds interpreted from the measurements are distributed fairly narrowly about nearly 60 km/s−1, double the speed of the earth in its orbit, the obvious interpretation is that many of the meteoroids seen by the Arecibo radar are moving in orbits about the sun with similar parameters as the earth, but in the retrograde direction. However, some aspects of the measured velocity distributions suggest that this is not a complete description even for the fast part of the distribution, and it certainly says nothing about the slow part first described in Janches et al. (2003). Furthermore, we cannot conclude anything about the entire dust population since there are probably selection effects that restrict the observations to a subset of the population.