Linear global instability of non-orthogonal incompressible swept attachment-line boundary layer flow

Instability of the orthogonal swept attachment line boundary layer has received attention by local1, 2 and global3–5 analysis methods over several decades, owing to the significance of this model to transition to turbulence on the surface of swept wings. However, substantially less attention has been paid to the problem of laminar flow instability in the non-orthogonal swept attachment-line boundary layer; only a local analysis framework has been employed to-date.6 The present contribution addresses this issue from a linear global (BiGlobal) instability analysis point of view in the incompressible regime. Direct numerical simulations have also been performed in order to verify the analysis results and unravel the limits of validity of the Dorrepaal basic flow7 model analyzed. Cross-validated results document the effect of the angle _ on the critical conditions identified by Hall et al.1 and show linear destabilization of the flow with decreasing AoA, up to a limit at which the assumptions of the Dorrepaal model become questionable. Finally, a simple extension of the extended G¨ortler-H¨ammerlin ODE-based polynomial model proposed by Theofilis et al.4 is presented for the non-orthogonal flow. In this model, the symmetries of the three-dimensional disturbances are broken by the non-orthogonal flow conditions. Temporal and spatial one-dimensional linear eigenvalue codes were developed, obtaining consistent results with BiGlobal stability analysis and DNS. Beyond the computational advantages presented by the ODE-based model, it allows us to understand the functional dependence of the three-dimensional disturbances in the non-orthogonal case as well as their connections with the disturbances of the orthogonal stability problem.

Effect of Aspect Ratio on the Three-Dimensional Global Instability Analysis of Incompressible Open Cavity Flows

The stability analysis of open cavity flows is a problem of great interest in the aeronautical industry. This type of flow can appear, for example, in landing gears or auxiliary power unit configurations. Open cavity flows is very sensitive to any change in the configuration, either physical (incoming boundary layer, Reynolds or Mach numbers) or geometrical (length to depth and length to width ratio). In this work, we have focused on the effect of geometry and of the Reynolds number on the stability properties of a threedimensional spanwise periodic cavity flow in the incompressible limit. To that end, BiGlobal analysis is used to investigate the instabilities in this configuration. The basic flow is obtained by the numerical integration of the Navier-Stokes equations with laminar boundary layers imposed upstream. The 3D perturbation, assumed to be periodic in the spanwise direction, is obtained as the solution of the global eigenvalue problem. A parametric study has been performed, analyzing the stability of the flow under variation of the Reynolds number, the L/D ratio of the cavity, and the spanwise wavenumber β. For consistency, multidomain high order numerical schemes have been used in all the computations, either basic flow or eigenvalue problems. The results allow to define the neutral curves in the range of L/D = 1 to L/D = 3. A scaling relating the frequency of the eigenmodes and the length to depth ratio is provided, based on the analysis results.

Computation of nonlinear streaky structures in boundary layer flow

En esta tesis se integran numéricamente las ecuaciones reducidas de Navier Stokes (RNS), que describen el flujo en una capa límite tridimensional que presenta también una escala característica espacial corta en el sentido transversal. La formulación RNS se usa para el cálculo de “streaks” no lineales de amplitud finita, y los resultados conseguidos coinciden con los existentes en la literatura, obtenidos típicamente utilizando simulación numérica directa (DNS) o nonlinear parabolized stability equations (PSE). El cálculo de los “streaks” integrando las RNS es mucho menos costoso que usando DNS, y no presenta los problemas de estabilidad que aparecen en la formulación PSE cuando la amplitud del “streak” deja de ser pequeña. El código de integración RNS se utiliza también para el cálculo de los “streaks” que aparecen de manera natural en el borde de ataque de una placa plana en ausencia de perturbaciones en la corriente uniforme exterior. Los resultados existentes hasta ahora calculaban estos “streaks” únicamente en el límite lineal (amplitud pequeña), y en esta tesis se lleva a cabo el cálculo de los mismos en el régimen completamente no lineal (amplitud finita). En la segunda parte de la tesis se generaliza el código RNS para incluir la posibilidad de tener una placa no plana, con curvatura en el sentido transversal que varía lentamente en el sentido de la corriente. Esto se consigue aplicando un cambio de coordenadas, que transforma el dominio físico en uno rectangular. La formulación RNS se integra también expresada en las correspondientes coordenadas curvilíneas. Este código generalizado RNS se utiliza finalmente para estudiar el flujo de capa límite sobre una placa con surcos que varían lentamente en el sentido de la corriente, y es usado para simular el flujo sobre surcos que crecen en tal sentido. Abstract In this thesis, the reduced Navier Stokes (RNS) equations are numerically integrated. This formulation describes the flow in a three-dimensional boundary layer that also presents a short characteristic space scale in the spanwise direction. RNS equations are used to calculate nonlinear finite amplitude “streaks”, and the results agree with those reported in the literature, typically obtained using direct numerical simulation (DNS) or nonlinear parabolized stability equations (PSE). “Streaks” simulations through the RNS integration are much cheaper than using DNS, and avoid stability problems that appear in the PSE when the amplitude of the “streak” is not small. The RNS integration code is also used to calculate the “streaks” that naturally emerge at the leading edge of a flat plate boundary layer in the absence of any free stream perturbations. Up to now, the existing results for these “streaks” have been only calculated in the linear limit (small amplitude), and in this thesis their calculation is carried out in the fully nonlinear regime (finite amplitude). In the second part of the thesis, the RNS code is generalized to include the possibility of having a non-flat plate, curved in the spanwise direction and slowly varying in the streamwise direction. This is achieved by applying a change of coordinates, which transforms the physical domain into a rectangular one. The RNS formulation expressed in the corresponding curvilinear coordinates is also numerically integrated. This generalized RNS code is finally used to study the boundary layer flow over a plate with grooves which vary slowly in the streamwise direction; and this code is used to simulate the flow over grooves that grow in the streamwise direction.

Reduced order modeling of three dimensional external aerodynamic flows

A method is presented to construct computationally efficient reduced-order models (ROMs) of three-dimensional aerodynamic flows around commercial aircraft components. The method is based on the proper orthogonal decomposition (POD) of a set of steady snapshots, which are calculated using an industrial solver based on some Reynolds averaged Navier-Stokes (RANS) equations. The POD-mode amplitudes are calculated by minimizing a residual defined from the Euler equations, even though the snapshots themselves are calculated from viscous equations. This makes the ROM independent of the peculiarities of the solver used to calculate the snapshots. Also, both the POD modes and the residual are calculated using points in the computational mesh that are concentrated in a close vicinity of the aircraft, which constitute a much smaller number than the total number of mesh points. Despite these simplifications, the method provides quite good approximations of the flow variables distributions in the whole computational domain, including the boundary layer attached to the aircraft surface and the wake. Thus, the method is both robust and computationally efficient, which is checked considering the aerodynamic flow around a horizontal tail plane, in the transonic range 0.4?Mach number?0.8, ?3°?angle of attack?3°.

Low-dimensional modeling of streaks in a wedge flow boundary layer

This paper is concerned with the low dimensional structure of optimal streaks in a wedge flow boundary layer, which have been recently shown to consist of a unique (up to a constant factor) three-dimensional streamwise evolving mode, known as the most unstable streaky mode. Optimal streaks exhibit a still unexplored/unexploited approximate self-similarity (not associated with the boundary layer self-similarity), namely the streamwise velocity re-scaled with their maximum remains almost independent of both the spanwise wavenumber and the streamwise coordinate; the remaining two velocity components instead do not satisfy this property. The approximate self-similar behavior is analyzed here and exploited to further simplify the description of optimal streaks. In particular, it is shown that streaks can be approximately described in terms of the streamwise evolution of the scalar amplitudes of just three one-dimensional modes, providing the wall normal profiles of the streamwise velocity and two combinations of the cross flow velocity components; the scalar amplitudes obey a singular system of three ordinary differential equations (involving only two degrees of freedom), which approximates well the streamwise evolution of the general streaks.

Laminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layer

The linear instability and breakdown to turbulence induced by an isolated roughness element in a boundary layer at Mach 2:5, over an isothermal flat plate with laminar adiabatic wall temperature, have been analysed by means of direct numerical simulations, aided by spatial BiGlobal and three-dimensional parabolized (PSE-3D) stability analyses. It is important to understand transition in this flow regime since the process can be slower than in incompressible flow and is crucial to prediction of local heat loads on next-generation flight vehicles. The results show that the roughness element, with a height of the order of the boundary layer displacement thickness, generates a highly unstable wake, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer and is able to sustain the rapid growth of a number of instability modes. The most unstable of these modes are associated with varicose or sinuous deformations of the low-velocity streak; they are a consequence of the instability developing in the three-dimensional shear layer as a whole (the varicose mode) or in the lateral shear layers (the sinuous mode). The most unstable wake mode is of the varicose type and grows on average 17% faster tan the most unstable sinuous mode and 30 times faster than the most unstable boundary layer mode occurring in the absence of a roughness element. Due to the high growthrates registered in the presence of the roughness element, an amplification factor of N D 9 is reached within 50 roughness heights from the roughness trailing edge. The independently performed Navier–Stokes, spatial BiGlobal and PSE-3D stability results are in excellent agreement with each other, validating the use of simplified theories for roughness-induced transition involving wake instabilities. Following the linear stages of the laminar–turbulent transition process, the roll-up of the three-dimensional shear layer leads to the formation of a wedge of turbulence, which spreads laterally at a rate similar to that observed in the case of compressible turbulent spots for the same Mach number.

Three-dimensional distribution of cortical synapses: a replicated point pattern-based analysis

The biggest problem when analyzing the brain is that its synaptic connections are extremely complex. Generally, the billions of neurons making up the brain exchange information through two types of highly specialized structures: chemical synapses (the vast majority) and so-called gap junctions (a substrate of one class of electrical synapse). Here we are interested in exploring the three-dimensional spatial distribution of chemical synapses in the cerebral cortex. Recent research has showed that the three-dimensional spatial distribution of synapses in layer III of the neocortex can be modeled by a random sequential adsorption (RSA) point process, i.e., synapses are distributed in space almost randomly, with the only constraint that they cannot overlap. In this study we hypothesize that RSA processes can also explain the distribution of synapses in all cortical layers. We also investigate whether there are differences in both the synaptic density and spatial distribution of synapses between layers. Using combined focused ion beam milling and scanning electron microscopy (FIB/SEM), we obtained three-dimensional samples from the six layers of the rat somatosensory cortex and identified and reconstructed the synaptic junctions. A total volume of tissue of approximately 4500μm3 and around 4000 synapses from three different animals were analyzed. Different samples, layers and/or animals were aggregated and compared using RSA replicated spatial point processes. The results showed no significant differences in the synaptic distribution across the different rats used in the study. We found that RSA processes described the spatial distribution of synapses in all samples of each layer. We also found that the synaptic distribution in layers II to VI conforms to a common underlying RSA process with different densities per layer. Interestingly, the results showed that synapses in layer I had a slightly different spatial distribution from the other layers.

Three-dimensional spatial distribution of synapses in the neocortex: A dual-beam electron microscopy study

In the cerebral cortex, most synapses are found in the neuropil, but relatively little is known about their 3-dimensional organization. Using an automated dual-beam electron microscope that combines focused ion beam milling and scanning electron microscopy, we have been able to obtain 10 three-dimensional samples with an average volume of 180 µm(3) from the neuropil of layer III of the young rat somatosensory cortex (hindlimb representation). We have used specific software tools to fully reconstruct 1695 synaptic junctions present in these samples and to accurately quantify the number of synapses per unit volume. These tools also allowed us to determine synapse position and to analyze their spatial distribution using spatial statistical methods. Our results indicate that the distribution of synaptic junctions in the neuropil is nearly random, only constrained by the fact that synapses cannot overlap in space. A theoretical model based on random sequential absorption, which closely reproduces the actual distribution of synapses, is also presented.

Global instability analysis and control of three-dimensional long open cavity flow

The three-dimensional wall-bounded open cavity may be considered as a simplified geometry found in industrial applications such as leading gear or slotted flats on the airplane. Understanding the three-dimensional complex flow structure that surrounds this particular geometry is therefore of major industrial interest. At the light of the remarkable former investigations in this kind of flows, enough evidences suggest that the lateral walls have a great influence on the flow features and hence on their instability modes. Nevertheless, even though there is a large body of literature on cavity flows, most of them are based on the assumption that the flow is two-dimensional and spanwise-periodic. The flow over realistic open cavity should be considered. This thesis presents an investigation of three-dimensional wall-bounded open cavity with geometric ratio 6:2:1. To this aim, three-dimensional Direct Numerical Simulation (DNS) and global linear instability have been performed. Linear instability analysis reveals that the onset of the first instability in this open cavity is around Recr 1080. The three-dimensional shear layer mode with a complex structure is shown to be the most unstable mode. I t is noteworthy that the flow pattern of this high-frequency shear layer mode is similar to the observed unstable oscillations in supercritical unstable case. DNS of the cavity flow carried out at different Reynolds number from steady state until a nonlinear saturated state is obtained. The comparison of time histories of kinetic energy presents a clearly dominant energetic mode which shifts between low-frequency and highfrequency oscillation. A complete flow patterns from subcritical cases to supercritical case has been put in evidence. The flow structure at the supercritical case Re=1100 resembles typical wake-shedding instability oscillations with a lateral motion existed in the subcritical cases. Also, This flow pattern is similar to the observations in experiments. In order to validate the linear instability analysis results, the topology of the composite flow fields reconstructed by linear superposition of a three-dimensional base flow and its leading three-dimensional global eigenmodes has been studied. The instantaneous wall streamlines of those composited flows display distinguish influence region of each eigenmode. Attention has been focused on the leading high-frequency shear layer mode; the composite flow fields have been fully recognized with respect to the downstream wave shedding. The three-dimensional shear layer mode is shown to give rise to a typical wake-shedding instability with a lateral motions occurring downstream which is in good agreement with the experiment results. Moreover, the spanwise-periodic, open cavity with the same length to depth ratio has been also studied. The most unstable linear mode is different from the real three-dimensional cavity flow, because of the existence of the side walls. Structure sensitivity of the unstable global mode is analyzed in the flow control context. The adjoint-based sensitivity analysis has been employed to localized the receptivity region, where the flow is more sensible to momentum forcing and mass injection. Because of the non-normality of the linearized Navier-Stokes equations, the direct and adjoint field has a large spatial separation. The strongest sensitivity region is locate in the upstream lip of the three-dimensional cavity. This numerical finding is in agreement with experimental observations. Finally, a prototype of passive flow control strategy is applied.

Characterising the three-dimensional ozone distribution of a tidally locked Earth-like planet

We simulate the 3D ozone distribution of a tidally locked Earth-like exoplanet using the high-resolution, 3D chemistry climate model CESM1(WACCM) and study how the ozone layer of a tidally locked Earth (TLE) (ΩTLE = 1/365 days) differs from that of our present-day Earth (PDE) (ΩPDE = 1/1 day). The middle atmosphere reaches a steady state a symptotically within the first 80 days of the simulation. An upwelling, centred on the subsolar point, is present on the day side while a downwelling, centred on the antisolar point, is present on the night side. In the mesosphere, we find similar global ozone distributions for the TLE and the PDE, with decreased ozone on the day side and enhanced ozone on the night side. In the lower mesosphere, a jet stream transitions into a large-scale vortex around a low-pressure system, located at low latitudes of the TLE night side. In the middle stratosphere, the concentration of odd oxygen is approximately equal to that of the ozone [(Ox) ≈ (O3)]. At these altitudes, the lifetime of odd oxygen is ~16 h and the transport processes significantly contribute to the global distribution of stratospheric ozone. Compared to the PDE, where the strong Coriolis force acts as a mixing barrier between low and high latitudes, the transport processes of the TLE are governed by jet streams variable in the zonal and meridional directions. In the middle stratosphere of the TLE, we find high ozone values on the day side, due to the increased production of atomic oxygen on the day side, where it immediately recombines with molecular oxygen to form ozone. In contrast, the ozone is depleted on the night side, due to changes in the solar radiation distribution and the presence of a downwelling. As a result of the reduced Coriolis force, the tropical and extratropical air masses are well mixed and the global temperature distribution of the TLE stratosphere has smaller horizontal gradients than the PDE. Compared to the PDE, the total ozone column global mean is reduced by ~19.3 %. The day side and the night side total ozone column means are reduced by 23.21 and 15.52 %, respectively. Finally, we present the total ozone column (TOC) maps as viewed by a remote observer for four phases of the TLE during its revolution around the star. The mean TOC values of the four phases of the TLE vary by up to 23 %.

(Table 2) Abundance of the main groups of planktonic animals in the 250-900 m water layer at the Broken Spur and Lost City sites according to visual counts from the Mir manned submersibles in 2002 and 2005

Three dives of the Mir manned submersibles with plankton counts and two vertical plankton hauls with a BR net were carried out above the Lost City (Atlantis underwater massif) and the Broken Spur hydrothermal fields during cruise 50 of R/V Akademik Mstislav Keldysh. Above the Atlantis seamount no significant increase in plankton concentration was found. Above the Lost City field horizontal heterogeneity of plankton distribution in the near-bottom layer and in overlying water layers was shown. Near-bottom aggregations of euphausiids and amphipods previously reported by other scientists seem to be related to attraction of these animals by the submersible's headlights rather than represent a natural phenomenon.

(Table 1) Comparison of three chronologies for the sapropel series of cores KC01-KC01b

The Quaternary climate of southern Europe (south Italy and Greece) is investigated by pollen analysis of the sapropels which were deposited in the deep eastern Mediterranean Sea during the last 1 million year (Ma). The time-scale of core KC01b in the Ionian Sea has been established by tuning its oxygen isotopic record to the ice volume model of Imbrie and Imbrie (1980, doi:10.1126/science.207.4434.943). For the last 250,000 year (250 ka), the previous pollen studies and astronomical tuning have been confirmed. Sapropels were deposited under a large range of Mediterranean climates: fully interglacial, fully glacial, and intermediary, as revealed mainly by the balance between the respective pollen abundances of oak (Quercus) and sage-brush (Artemisia). The high value of the oak reveals the warm and wet climate of an Interglacial, and the high value of the sage-brush, the dry and cold climate of a Glacial. Whereas the Mediterranean climate is directly related to the variation of the high-latitude ice sheets, the deposition of sapropels is not so. In contrast with the wide climatic range, sapropels were deposited only when summer insolation in the low latitudes reached its highest peaks. However, between 250 ka and 1 Ma, that stable pattern is not yet established. Only six sapropels are observed, many expected ones do not appear, even as ghosts signalled by peaks of barium abundance, that remain after the post-deposition oxidation of organic matter. The pattern of sapropel formation in stable and direct relationship to highest insolation does not seem to apply. For five of those sapropels, neither climate extremes are observed; they mainly formed during intermediary types of Mediterranean climate. In contrast, one sapropel (and one ghost) relates to a relatively low peak of insolation, and its climate is of a unique, composite type not seen later. This might suggest an unsuspected, more complex pattern linking the formation of Mediterranean sapropels to the astronomical configuration.

(Table 1) Conditions of vertical near-bottom profiling and the main parameters of the benthic boundary layer in several regions of the Black Sea shelf

Measurements of 14 vertical profiles of currents and hydrological parameters in the near-bottom layer with depth resolution of 0.1 m were carried out in several regions of the Black Sea shelf, at five points over the continental slope, and in three deep water regions. The upper boundary of the benthic boundary layer (BBL) was reliably determined at a point at distance from 5-7 to 35-40 m from the bottom where the gradients of density and current velocity changed. Experimental data obtained were used to determine the coefficient of bottom friction, friction velocity, coefficients of vertical diffusion of momentum and density, and vertical fluxes of temperature and salinity in the BBL.

Raw data of SCADCP (self-contained Acoustic Doppler Current Profiler) from three moorings in the Eastern Weddell Sea, 2005-2008

The success of any efforts to determine the effects of climate change on marine ecosystems depends on understanding in the first instance the natural variations, which contemporarily occur on the interannual and shorter time scales. Here we present results on the environmental controls of zooplankton distribution patterns and behaviour in the eastern Weddell Sea, Southern Ocean. Zooplankton abundance and vertical migration are derived from the mean volume backscattering strength (MVBS) and the vertical velocity measured by moored acoustic Doppler current profilers (ADCPs), which were deployed simultaneously at 64°S, 66.5°S and 69°S along the Greenwich Meridian from February, 2005, until March, 2008. While these time series span a period of full three years they resolve hourly changes. A highly persistent behavioural pattern found at all three mooring locations is the synchronous diel vertical migration (DVM) of two distinct groups of zooplankton that migrate between a deep residence depth during daytime and a shallow depth during nighttime. The DVM was closely coupled to the astronomical daylight cycles. However, while the DVM was symmetric around local noon, the annual modulation of the DVM was clearly asymmetric around winter solstice or summer solstice, respectively, at all three mooring sites. DVM at our observation sites persisted throughout winter, even at the highest latitude exposed to the polar night. Since the magnitude as well as the relative rate of change of illumination is minimal at this time, we propose that the ultimate causes of DVM separated from the light-mediated proximal cue that coordinates it. In all three years, a marked change in the migration behaviour occurred in late spring (late October/early November), when DVM ceased. The complete suspension of DVM after early November is possibly caused by the combination of two factors: (1) increased availability of food in the surface mixed layer provided by the phytoplankton spring bloom, and (2) vanishing diurnal enhancement of the threat from visually oriented predators when the illumination is quasi-continuous during the polar and subpolar summer. Zooplankton abundance in the water column, estimated as the mean MVBS in the depth range 50-300 m, was highest end of summer and lowest mid to end winter on the average annual cycle. However, zooplankton abundance varied several-fold between years and between locations. Based on satellite and in situ data of chlorophyll and sea ice as well as on hydrographic measurements, the interannual and spatial variations of zooplankton mean abundance can be explained by differences in the magnitude of the phytoplankton spring bloom, which develops during the seasonal sea ice retreat. Whereas the vernal ice melt appears necessary to stimulate the blooming of phytoplankton, it is not the determinator of the blooms magnitude, its areal extent and duration. A possible explanation for the limitation of the phytoplankton bloom in some years is top-down control. We hypothesise that the phytoplankton spring development can be curbed by grazing when the zooplankton had attained high abundance by growth during the preceding summer.

Three Generations of FPGA DAQ Development for the ATLAS Pixel Detector

Thesis (Master's)--University of Washington, 2016-06