Spatiotemporal Stability Research Articles

The influence of shear layer thickness on the stability of confined two-dimensional wakes

The influence of confinement onto the inviscid and incompressible linear stability of the family of wakes introduced by Monkewitz [Phys. Fluids 31, 999 (1988)] is examined. The nondimensional parameters of the model, the velocity ratio Λ, defined as ratio of the velocity gap to the mean velocity, the profile shape parameter, which controls the shear layer thickness δw, and the confinement parameter, are varied and their effect onto temporal and spatiotemporal stability properties is considered. Particularly, the limit between absolute (A) and convective (C) instability is investigated as a function of the different parameters. For a given confinement, there exists an optimal value of the shear layer thickness for which the absolute instability is maximal. The absolute frequency and complex wavenumber of the mode at the C/A transition are discussed. Furthermore, the continuous profiles are approximated by means of piecewise broken-line profile, with similar spatiotemporal properties. As a typical application, a few nonparallel base flows, computed by direct numerical simulation at Re=500, are analyzed on a weakly nonparallel basis by plotting the locus of the local velocity profile in the (δw,Λ) plane. The absolute frequency at the C/A transition point is seen to predict accurately the frequency prevailing in the nonlinear direct numerical simulations. These results further help interpreting the influence of confinement on the Strouhal number measured experimentally in the wake of confined cylinders.

Stability analysis and breakup length calculations for steady planar liquid jets

This study uses spatio-temporal stability analysis to investigate the convective and absolute instability properties of a steady unconfined planar liquid jet. The approach uses a piecewise linear velocity profile with a finite-thickness shear layer at the edge of the jet. This study investigates how properties such as the thickness of the shear layer and the value of the fluid velocity at the interface within the shear layer affect the stability properties of the jet. It is found that the presence of a finite-thickness shear layer can lead to an absolute instability for a range of density ratios, not seen when a simpler plug flow velocity profile is considered. It is also found that the inclusion of surface tension has a stabilizing effect on the convective instability but a destabilizing effect on the absolute instability. The stability results are used to obtain estimates for the breakup length of a planar liquid jet as the jet velocity varies. It is found that reducing the shear layer thickness within the jet causes the breakup length to decrease, while increasing the fluid velocity at the fluid interface within the shear layer causes the breakup length to increase. Combining these two effects into a profile, which evolves realistically with velocity, gives results in which the breakup length increases for small velocities and decreases for larger velocities. This behaviour agrees qualitatively with existing experiments on the breakup length of axisymmetric jets.

Linear and nonlinear spatio-temporal instability in laminar two-layer flows

The linear and nonlinear spatio-temporal stability of an interface separating two Newtonian fluids in pressure-driven channel flow at moderate Reynolds numbers is analysed both theoretically and numerically. A linear, Orr–Sommerfeld-type analysis shows that most of such systems are unstable. The transition to an absolutely unstable regime is investigated, and is shown to occur in an intermediate range of Reynolds numbers and ratios of the thicknesses of the two layers, for near-density matched fluids with a viscosity contrast. A critical Reynolds number is found for transition from convective to absolute instability of relatively thin films. Results obtained from direct numerical simulations (DNSs) of the Navier–Stokes equations for long channels using a diffuse-interface method elucidate that waves generated by random noise at the inlet show that, near the inlet, waves are formed and amplified strongly, leading to ligament formation. Successive waves coalesce with each other further downstream, resulting in longer larger-amplitude waves further downstream. In the linearly absolute regime, the characteristics of the spatially growing wave near the inlet agree with that of the saddle point as predicted by the linear theory. The transition point from a convective to an absolute regime predicted by linear theory is also in agreement with a sharp change in the value of a healing length obtained from the DNSs.

Complexity of the food web structure of the Ascophyllum nodosum zone evidenced by a δ13C and δ15N study

Rocky shores dominated by canopy-forming macroalgae are characterized by complex communities making it difficult to assess whether the most abundant primary producers are at the base of the food web. This difficulty is exacerbated by the seasonal- and regional-scale variations of environmental and biotic factors that can affect the main trophic pathways. The food web structure of the Ascophyllum nodosum zone was studied during three seasons and at two sites separated by several 100s of kilometers by measuring the δ 13C and δ 15N of the major food sources and the dominant consumers of the zone. Despite the variability in isotopic compositions, both sites underwent similar significant seasonal variations. The main primary producers of the zone, A. nodosum, Fucus vesiculosus and Fucus serratus, were not at the base of the main trophic pathway but part of the diverse number of basal resources supporting the food web. The use of community-wide metric indices allowed further defining the food web structure of the A. nodosum zone as one characterized by trophic redundancy and numerous major trophic pathways. Indeed, grazers were dominated by generalists, filter-feeders utilized both planktonic and benthic organic matter, and predators displayed a high degree of omnivory. The range of values in δ 15N showed a high spatiotemporal variability within and an important overlap between trophic groups. This prevented establishing distinctive trophic levels and further emphasized the complexity of the food web structure. The spatiotemporal stability of the relative isotopic composition of the dominant consumers within trophic groups and the low variability of the community-wide indices suggested a stability of the food web structure of the A. nodosum zone at a regional scale.

Three-dimensional absolute and convective instabilities in mixed convection of a viscoelastic fluid through a porous medium

By using the mathematical formalism of absolute and convective instabilities we study the nature of unstable three-dimensional disturbances of viscoelastic flow convection in a porous medium with horizontal through-flow and vertical temperature gradient. Temporal stability analysis reveals that among three-dimensional (3 D) modes the pure down-stream transverse rolls are favored for the onset of convection. In addition, by considering a spatiotemporal stability approach we found that all unstable 3 D modes are convectively unstable except the transverse rolls which may experience a transition to absolute instability. The combined influence of through-flow and elastic parameters on the absolute instability threshold, wave number and frequency is then determined, and results are compared to those of a Newtonian fluid.

Analysis of the dripping–jetting transition in compound capillary jets

We examine the behaviour of a compound capillary jet from the spatio-temporal linear stability analysis of the Navier–Stokes equations. We map the jetting–dripping transition in the parameter space by calculating the Weber numbers for which the convective/absolute instability transition occurs. If the remaining dimensionless parameters are set, there are two critical Weber numbers that verify Brigg's pinch criterion. The region of absolute (convective) instability corresponds to Weber numbers smaller (larger) than the highest value of those two Weber numbers. The stability map is affected significantly by the presence of the outer interface, especially for compound jets with highly viscous cores, in which the outer interface may play an important role even though it is located very far from the core. Full numerical simulations of the Navier–Stokes equations confirm the predictions of the stability analysis.

Linear spatio-temporal instability analysis of ice growth under a falling water film

A linear spatio-temporal stability analysis is conducted for the ice growth under a falling water film along an inclined ice plane. The full system of linear stability equations is solved by using the Chebyshev collocation method. By plotting the boundary curve between the linear absolute and convective instabilities (AI/CI) of the ice mode in the parameter plane of the Reynolds number and incline angle, it is found that the linear absolute instability exists and occurs above a minimum Reynolds number and below a maximum inclined angle. Furthermore, by plotting the critical Reynolds number curves with respect to the inclined angle for the downstream and upstream branches, the convectively unstable region is determined and divided into three parts, one of which has both downstream and upstream convectively unstable wavepackets and the other two have only downstream or upstream convectively unstable wavepacket. Finally, the effect of the Stefan number and the thickness of the ice layer on the AI/CI boundary curve is investigated.

Baseline study of the spatio-temporal patterns of reef fish assemblages prior to a major mining project in New Caledonia (South Pacific)

From 2008 onwards, the coral reefs of Koné (New Caledonia) will be subjected to a major anthropogenic perturbation linked to development of a nickel mine. Dredging and sediment runoff may directly damage the reef environment whereas job creation should generate a large demographic increase and thus a rise in fishing activities. This study analyzed reef fish assemblages between 2002 and 2007 with a focus on spatio-temporal variability. Our results indicate strong spatial structure of fish assemblages through time. Total species richness, density and biomass were highly variable between years but temporal variations were consistent among biotopes. A remarkable spatio-temporal stability was observed for trophic (mean 4.6% piscivores, 53.1% carnivores, 30.8% herbivores and 11.4% planktivores) and home range structures of species abundance contributions. These results are discussed and compared with others sites of the South Pacific. For monitoring perspectives, some indicators related to expected disturbances are proposed.

Dispersive shock waves propagating in the cubic-quintic derivative nonlinear Schrödinger equation

The propagation of a dispersive shock wave is studied in a quintic-derivative nonlinear Schrödinger (Q-DNLS) equation, which may describe, for example, the wave propagation on a discrete electrical transmission line. It is shown that a physical system described by a Q-DNLS equation without a dissipative term may support the propagation of shock waves. The influence of the derivative nonlinearity terms on the shock is analyzed. Using the found exact shock solutions of the Q-DNLS equation as the initial input signal, we investigate numerically the spatiotemporal stability of the shock signal in the network.

The seedling bank stabilizes the erratic early regeneration stages of the invasive Prunus serotina

We studied the regeneration dynamics of the semi-shade-tolerant invasive tree species Prunus serotina in the understory of 7 pine stands in its introduced range for 4 y, focusing on temporal, spatial, and spatiotemporal patterns. In each 20- × 40-m study plot, we inventoried all trees and shrubs taller than 1 m, counted seedlings in 3 age-height classes (224 subplots), trapped P. serotina seed rain (84 subplots), and identified the P serotina seed trees. The seed set, seed rain density, and seedling densities of P. sertina all varied between the years and between the study plots, but the temporal stability of the spatial regeneration patterns increased with regeneration stage. There was a clear distinction between (1) seedlings smaller than 20 cm, younger than 6 y, occurring in very high densities and (2) seedlings between 20 cm and 1 m tall, older than 6 y, showing high spatiotemporal stability. Notwithstanding the large year-to-year variation in seed input, P serotina maintained its regeneration potential in the forest understory by building up a short-lived seedling bank. The seedling bank strategy might represent an efficient way towards site occupancy of shade-tolerant non-native species in forest understories with few shade-tolerant native species.

Spatial Distribution and Temporal Stability of Prostrate Knotweed (Polygonum aviculare) and Corn Poppy (Papaver rhoeas) Seed Bank in a Cereal Field

The knowledge of weed distribution in a field is a key factor to manage weeds effectively. The feasibility of using weed distribution maps for site-specific weed control will largely depend on the stability of the spatial distribution of the populations. Seed banks are the most reliable way of telling the area's weediness, but the effect of regular herbicide applications on its stability is largely unknown. A field experiment was conducted during 3 yr in a winter wheat field under herbicide treatments with the aim of studying the seed bank's spatial distribution of prostrate knotweed and corn poppy and the spatiotemporal stability of their populations. Soil samples were taken each year on the same locations, and seed abundance was measured by germination in greenhouse. Both species accounted for more than 10% of the broad-leaved weed seed bank and they were selected for further analysis. Prostrate knotweed seed-bank density decreased 76% and corn poppy 88% in 3 yr. Spatial distribution was described by spherical isotropic semivariograms. Distance of spatial dependence (range) of prostrate knotweed and corn poppy decreased 33 and 11% respectively, and the spatial variability (sill) decreased 96 and 99%. Yearly spatial seed distribution was compared for each species and no temporal stability was observed over a 3-yr period. The lack of stability was attributed to the important decrease of seed density over time and the increase in the short-range variability (nugget). However, for prostrate knotweed, the location of minima and maxima were roughly the same between years, allowing farmers to extend the period of use of the weed distribution maps. Although spatial distribution of seed banks can be affected by processes that promote fast changes in the densities of weed populations, this fact does not mean that weed distribution maps could not be used in consecutive seasons.

Spatiotemporal evolution of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect under initial pulselike disturbances

The spatiotemporal evolution of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect is investigated by carrying out fully nonlinear two-dimensional numerical simulations initiated by a pulselike disturbance. The traveling wave packets for positive as well as negative separation factors psi are obtained numerically for ethanol-water-like mixtures (Prandtl number Pr=10 , Lewis number Le=0.01) and selected combinations of Rayleigh and Reynolds numbers at psi=0.01, 0.1 and psi=-0.1. The characteristics of the wave fronts and the transitions observed between absolute and convective instabilities when changing the parameters are compared with the results previously obtained by linear spatiotemporal stability analysis. The simulations are in very good agreement with the stability results, which confirms the validity of both approaches. Finally, in order to characterize the possible interaction between the two wave packets of the so-called downstream and upstream modes for psi<0, the spatiotemporal stability analysis is used to detect a boundary curve in the (Re, Ra) parameter region beyond which the two wave packets will never completely separate. Numerical simulations illustrate the different evolutions of the wave packets on both sides of this boundary.

Primary instability mechanisms on the magnetohydrodynamic boundary layer flow over a rotating disk subject to a uniform radial flow

This paper is devoted to the investigation of three primary linear instability mechanisms due to the resonating disturbance waves present in the three-dimensional incompressible viscous/inviscid rotating disk boundary layer flow, extending our earlier still outer fluid work [M. Turkyilmazoglu, “Resonance instabilities on the boundary layer flow over a rotating-disk under the influence of a uniform magnetic field,” J. Eng. Math. 59, 337 (2007)] to a uniform nonzero radial flow. A spatiotemporal linear stability analysis is conducted to search for the influences of physical parameters on the possible important mechanisms of resonances leading to, respectively, the absolute instability, the direct spatial instability, and the direct temporal instability. The radial flow is shown to act in the way of stabilizing all the possible mechanisms considered, more pronouncedly as the magnetic field gets strengthened. The onset of absolute instability and convective temporal instability is found to be more sensitive to the variations in the radial flow than is the onset of convective direct spatial instability. Although a considerable delay of the onset of absolute instability as well as temporal instability can be achieved by increasing the magnitude of the radial flow, the direct spatial resonance instability mechanism persists to occur for low Reynolds numbers, while the flow is still in the laminar regime, which is expected to trigger nonlinearity just prior to transition to turbulence.

Spatial variation and temporal stability of littoral water temperature relative to lakeshore morphometry: environmental analysis from the view of fish thermal ecology

Lakeshore developments change the physicochemical properties of the underwater environment by altering shore morphometry, which may have significant effects on spatial variation and temporal stability in water temperature. Spatiotemporal temperature changes are costly to fish in terms of subsequent thermoregulatory behavior and acclimation; therefore, thermal conditions have a heavy impact on the biological function of fishes. Spatiotemporal variation and stability of water temperatures along cross-shore transects in the littoral zone (within 100 m from shore) were monitored and compared on two lakeshores with different cross-shore depth profiles. One shore was associated with a retaining wall and a relatively deep, flat bottom (steep shore), whereas the other extended offshore at a gentle gradient (gentle shore). Water temperature was more spatially variable on the gentle shore than the steep shore [1.44 ± 0.47 and 0.20 ± 0.14°C (mean ± SD), respectively], but a stable temperature range (i.e., the range of temperatures continuously observed on each shore for 48 h) was maintained only on the gentle shore during seasonal temperature decline. These results suggest that gentle shores have higher potential to provide a wider range of thermal options, allowing fish to fine-tune thermoregulatory behavior and acclimate more efficiently to temperature changes.

Nearby rainforest promotes coffee pollination by increasing spatio-temporal stability in bee species richness

Natural tropical forests are highly diverse and are known to contribute to forest-based services such as pollination of nearby crops. Landscape changes cause spatial and temporal bee community changes, but consequences how the community changes affect pollination is not well analyzed. This paper addresses the effects of rainforest distance and on site flower resources in agro-forests on spatial and temporal variation in pollinator communities and the consequences for coffee pollination. The study was conducted in 24 agro-forests dominated by coffee and cacao in Sulawesi, Indonesia differing in their distance to rainforest margin of the Lore-Lindu National Park and in flower density and its temporal variation. In all agro-forests, (1) transect surveys of the understory were obtained over a five-month period to assess bee community compositional similarity, bee diversity, and the temporal variation in bee diversity; and (2) coffee flower visitors were observed and open and bagged pollination treatments conducted over one week of coffee blooming to assess bee diversity and the spatial variation in bee diversity and coffee pollination. Mean number of shared species of the understory ranged between 40 and 60% per agro-forest and was higher in agro-forests nearby the rainforest than in agro-forests with a minimal distance of 500 m isolated from the rainforest. Mean species richness in the understory and in coffee flowers decreased with rainforest isolation and increased with flower resource availability. Temporal variation in bee species richness of the understory and spatial variation of the coffee flower-visiting bee species richness per agro-forest increased with forest distance. The variation in bee species richness decreased the mean and increased the spatial variation in bee-pollinated coffee fruit set per agro-forest. In conclusion, crops grown near intact rainforests and which profit from the pollination by many species may fluctuate less in bee-pollinated fruit set across crop plants than crop plants in isolated agriculture that receive low or even single species pollination services.

Dominant frequency differences in atrial fibrillation patients with and without left ventricular systolic dysfunction

The aim of this study was to determine the mechanisms of atrial fibrillation (AF) in patients with left ventricular systolic dysfunction (LVSD). Dominant frequency (DF) spatiotemporal stability was studied in 15 patients with persistent AF (PEAF) and LVSD (Group I), 15 with PEAF without LVSD (Group II), and 10 with paroxysmal AF (PAAF) without LVSD (Group III). Dominant frequencies were analysed at 536 sites at baseline (DF1) and 26 +/- 12 min later (DF2). A DF1-DF2 difference of <or=0.5 Hz was found in 77, 70, and 48% of sites in Groups I, II, and III (P < 0.001). Maximal DF1 and DF2 were recorded at the same site in 12/15, 11/15, and 0/10 patients in Groups I, II, and III, respectively (P < 0.01). Gradient differences: Group I, DFs were higher at left atrium appendage (LAA) than at anterior (A) LA (ALA), pulmonary vein-left atrial junction (PV-LAJ), and posterior (P) LA (PLA) (7.4 +/- 1.1 vs. 6.6 +/- 1 vs. 6.8 +/- 0.8 vs. 6.8 +/- 0.7 Hz, P < 0.05); Group II, no differences; Group III, DF was higher at PV-LAJ than at LAA, AL, and PLA (6 +/- 1.2 vs. 5.3 +/- 1.1 vs. 5.2 +/- 0.9 vs. 5.4 +/- 1.1 Hz, P < 0.05). Dominant frequency stability supports stable arrhythmia sources as the mechanism of PEAF with (without) LVSD, but not of PAAF.

Ultrafast diffraction of tightly focused waves with spatiotemporal stabilization

Experimental studies of ultrafast beam shaping have come about from the need to compensate diffraction-induced dispersive effects in femtosecond laser beams. From a theoretical point of view, chromatic matching of diffracted spherical waves in the vicinity of the geometrical focus is attained by applying conveniently dispersive boundary conditions in the far-field zone, a subject thoroughly analyzed in the paraxial regime. For applications demanding high spatial resolution, however, high-numerical-aperture microscope objectives may be employed instead and would lead to nonparaxiality of the focal wavefields. These circumstances have motivated our investigation. Concretely we report on prerequisites for spectral invariance extended to wide-angle geometries, which provides stabilization of the spatiotemporal response in the Fourier plane. In this context, general boundary conditions are given in the frame of the Debye representation of wavefields. Features of this sort of dynamic apodization (spatial filtering) leading to perfect achromatization are described in detail.

Limits of the existence of the Kuroshio and Gulf Stream currents owing to climate trends

Based on the variational property of the energy scattering minimum, this paper presents a model of a zonal jet current applied to the Kuroshio Extension and Gulf Stream after their separation from the western boundary and their turning to the east. The model suggests the following features: (1) the condition of jet existence is the asymmetric current shape with a sharp northern boundary; (2) the dynamic current axis is located south of the convergence axis (this is one of the mechanisms of the formation of two-(multi)front structures in the ocean represented by the Subarctic Front and Kuroshio Extension); and (3) there is a critical parameter range beyond which the current is not the jet current anymore. The modern climate warming tendency is approaching a critical state, when a change in the circulation structure is expected. 1. The object of our research is the transversal structure of a geostrophic jet current applied to the Kuroshio Extension and Gulf Stream oceanic currents after their separation from the coast between 30°–40° N and their eastward turn. Jet character, permanence, and spatiotemporal stability are the properties of these currents on a climatic scale [1, 2]. The parameters of the current are as follows: width ~100 km, depth 1 km, velocity 1 m/s, and water discharge 50 × 10 6 m 3 /s. The aim of this research is to determine the limits of conservation of the jet current under variation of the external parameters owing to possible climatic trends. 2. Variation formulation. The transversal structure of a zonally uniform geostrophic jet current is modeled on a climatic scale with consideration of the detailed structure (influence of the bottom topography and meandering). The origin of coordinates is at the ocean

수산 음향 기법을 이용한 연안 저서 어군의 시.공간 분포 및 안정성 조사

Hydroacoustic technique was used to analyze spatiotemporal stability and distribution of demersal fish aggregations in the coastal region to overcome some limitations of the existing methods such as net and diving. The survey was carried out in the Baekeum Bay on the south coast of Korea in January 2007. The bottom depth in the study site ranges from 7 to 25 m. In order to outline aggregations of demersal fish initial scanning using 200 kHz split-beam transducer was randomly conducted over the large area. Having detected fish aggregation in the specific region, intensive acoustic survey of irregular star pattern was carried out along 14 transects across the area in question. The results of the acoustic survey show that all demersal fish aggregations are concentrated about 5 m from sea bottom having a slight slope and remain steady with no spatial or temporal variations during acoustic survey. The hydroacoustic method used in this study offers a new approach to understand vertical and horizontal distribution, spatiotemporal stability, and biomass estimate of demersal fish aggregations in coastal regions. Additionally, the number of individual fish estimated from in situ acoustic target strength data can be used to understand the standing stock of demersal fish aggregation.

Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka,G,Pr,L, χ,M,B), as well as the inclination angle (β) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (χ≥0), and oscillatory for χ&lt;0. Moreover, the P-mode which is short-wave unstable for χ=0 remains so for χ&lt;0, but becomes long-wave unstable for χ&gt;0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability.