Advances in global instability computations: from incompressible to hypersonic flow

Esta tesis constituye un gran avance en el conocimiento del estudio y análisis de inestabilidades hidrodinámicas desde un punto de vista físico y teórico, como consecuencia de haber desarrollado innovadoras técnicas para la resolución computacional eficiente y precisa de la parte principal del espectro correspondiente a los problemas de autovalores (EVP) multidimensionales que gobiernan la inestabilidad de flujos con dos o tres direcciones espaciales inhomogéneas, denominados problemas de estabilidad global lineal. En el contexto del trabajo de desarrollo de herramientas computacionales presentado en la tesis, la discretización mediante métodos de diferencias finitas estables de alto orden de los EVP bidimensionales y tridimensionales que se derivan de las ecuaciones de Navier-Stokes linealizadas sobre flujos con dos o tres direcciones espaciales inhomogéneas, ha permitido una aceleración de cuatro órdenes de magnitud en su resolución. Esta mejora de eficiencia numérica se ha conseguido gracias al hecho de que usando estos esquemas de diferencias finitas, técnicas eficientes de resolución de problemas lineales son utilizables, explotando el alto nivel de dispersión o alto número de elementos nulos en las matrices involucradas en los problemas tratados. Como más notable consecuencia cabe destacar que la resolución de EVPs multidimensionales de inestabilidad global, que hasta la fecha necesitaban de superordenadores, se ha podido realizar en ordenadores de sobremesa. Además de la solución de problemas de estabilidad global lineal, el mencionado desarrollo numérico facilitó la extensión de las ecuaciones de estabilidad parabolizadas (PSE) lineales y no lineales para analizar la inestabilidad de flujos que dependen fuertemente en dos direcciones espaciales y suavemente en la tercera con las ecuaciones de estabilidad parabolizadas tridimensionales (PSE-3D). Precisamente la capacidad de extensión del novedoso algoritmo PSE-3D para el estudio de interacciones no lineales de los modos de estabilidad, desarrollado íntegramente en esta tesis, permite la predicción de transición en flujos complejos de gran interés industrial y por lo tanto extiende el concepto clásico de PSE, el cuál ha sido empleado exitosamente durante las pasadas tres décadas en el mismo contexto para problemas de capa límite bidimensional. Típicos ejemplos de flujos incompresibles se han analizado en este trabajo sin la necesidad de recurrir a restrictivas presuposiciones usadas en el pasado. Se han estudiado problemas vorticales como es el caso de un vórtice aislado o sistemas de vórtices simulando la estela de alas, en los que la homogeneidad axial no se impone y así se puede considerar la difusión viscosa del flujo. Además, se ha estudiado el chorro giratorio turbulento, cuya inestabilidad se utiliza para mejorar las características de funcionamiento de combustores. En la tesis se abarcan adicionalmente problemas de flujos compresibles. Se presenta el estudio de inestabilidad de flujos de borde de ataque a diferentes velocidades de vuelo. También se analiza la estela formada por un elemento rugoso aislado en capa límite supersónica e hipersónica, mostrando excelentes comparaciones con resultados obtenidos mediante simulación numérica directa. Finalmente, nuevas inestabilidades se han identificado en el flujo hipersónico a Mach 7 alrededor de un cono elíptico que modela el vehículo de pruebas en vuelo HIFiRE-5. Los resultados comparan favorablemente con experimentos en vuelo, lo que subraya aún más el potencial de las metodologías de análisis de estabilidad desarrolladas en esta tesis. ABSTRACT The present thesis constitutes a step forward in advancing the frontiers of knowledge of fluid flow instability from a physical point of view, as a consequence of having been successful in developing groundbreaking methodologies for the efficient and accurate computation of the leading part of the spectrum pertinent to multi-dimensional eigenvalue problems (EVP) governing instability of flows with two or three inhomogeneous spatial directions. In the context of the numerical work presented in this thesis, the discretization of the spatial operator resulting from linearization of the Navier-Stokes equations around flows with two or three inhomogeneous spatial directions by variable-high-order stable finite-difference methods has permitted a speedup of four orders of magnitude in the solution of the corresponding two- and three-dimensional EVPs. This improvement of numerical performance has been achieved thanks to the high-sparsity level offered by the high-order finite-difference schemes employed for the discretization of the operators. This permitted use of efficient sparse linear algebra techniques without sacrificing accuracy and, consequently, solutions being obtained on typical workstations, as opposed to the previously employed supercomputers. Besides solution of the two- and three-dimensional EVPs of global linear instability, this development paved the way for the extension of the (linear and nonlinear) Parabolized Stability Equations (PSE) to analyze instability of flows which depend in a strongly-coupled inhomogeneous manner on two spatial directions and weakly on the third. Precisely the extensibility of the novel PSE-3D algorithm developed in the framework of the present thesis to study nonlinear flow instability permits transition prediction in flows of industrial interest, thus extending the classic PSE concept which has been successfully employed in the same context to boundary-layer type of flows over the last three decades. Typical examples of incompressible flows, the instability of which was analyzed in the present thesis without the need to resort to the restrictive assumptions used in the past, range from isolated vortices, and systems thereof, in which axial homogeneity is relaxed to consider viscous diffusion, as well as turbulent swirling jets, the instability of which is exploited in order to improve flame-holding properties of combustors. The instability of compressible subsonic and supersonic leading edge flows has been solved, and the wake of an isolated roughness element in a supersonic and hypersonic boundary-layer has also been analyzed with respect to its instability: excellent agreement with direct numerical simulation results has been obtained in all cases. Finally, instability analysis of Mach number 7 ow around an elliptic cone modeling the HIFiRE-5 flight test vehicle has unraveled flow instabilities near the minor-axis centerline, results comparing favorably with flight test predictions.

The DNA Helicase Activity of BLM Is Necessary for the Correction of the Genomic Instability of Bloom Syndrome Cells

Bloom syndrome (BS) is a rare autosomal recessive disorder characterized by growth deficiency, immunodeficiency, genomic instability, and the early development of cancers of many types. BLM, the protein encoded by BLM, the gene mutated in BS, is localized in nuclear foci and absent from BS cells. BLM encodes a DNA helicase, and proteins from three missense alleles lack displacement activity. BLM transfected into BS cells reduces the frequency of sister chromatid exchanges and restores BLM in the nucleus. Missense alleles fail to reduce the sister chromatid exchanges in transfected BS cells or restore the normal nuclear pattern. BLM complements a phenotype of a Saccharomyces cerevisiae sgs1 top3 strain, and the missense alleles do not. This work demonstrates the importance of the enzymatic activity of BLM for its function and nuclear localization pattern.

Characterization of the instability mechanisms affecting slopes on carbonatic Flysch: Alicante (SE Spain), case study

The studied Flysch sequence of Alicante occupies a widely populated area crossed by main communication routes. The slopes existing on this area usually suffer slope instabilities that cause substantial damage and a very high maintenance cost. In order to assess the type of instability mechanisms affecting these heterogeneous carbonatic slopes, in this paper a wide inventory of 194 Flysch rock slopes has been performed, reporting the existing lithologies, their competence and their relative arrangement and the geometrical relationship between bedding and the slope and the associated instability mechanism. All these data have been jointly used for performing an instability mechanisms characterization. For systematically characterizing the wide type of complex rock exposures existing in the study area, they are divided into basic units referred as lithological pattern columns to which the different observed instability mechanisms are associated. Inventoried instability mechanisms are diverse and sometimes are combined with each other. Rockfalls are a very common instability mechanism associated to the differential weathering and sapping of the marly lithologies which are present in a wide number of geometrical combinations. The other instability mechanisms closely depend on the combination of the geometrical and lithological parameters. Therefore, this work provides a new basic tool which can be easily used during preliminary project stages for knowing the instability mechanisms which can affect rock slopes excavated on carbonatic Flysch heterogeneous geological formations.

Capillary jet instability under the influence of gravity

The focus of this paper is on the effect of gravity stretching on disturbed capillary jet instability. Break-up and droplet formation under low flows are simulated using finite difference solution of a one-dimensional approximation of disturbed capillary jet instability chosen from the work by Eggers and Dupont (J. Fluid Mech. 155 (1994) 289). Experiments were conducted using water and aqueous glycerol solutions to compare with simulations. We use a gravity parameter, G, which quantifies gravity stretching by relating flow velocity, orifice size and acceleration and is the reciprocal of the Fronde number. The optimum disturbance frequency Omega(opt) was found to be inversely proportional to G. However, this relationship appears to be complex for the range of G's investigated. At low G, the relationship between Omega(opt) and G appears to be linear but takes on a weakly decaying like trend as G increases. As flows are lowered, the satellite-free regime decreases, although experimental observation found that merging of main and satellite drops sometimes offset this effect to result in monodispersed droplet trains post break-up. Viscosity did not significantly affect the relationship between the disturbance frequency and G, although satellite drops could be seen more clearly close to the upper limit for instability at high G's. It is possible to define regimes of satellite formation under low flows by considering local wavenumbers at the point of instability. (C) 2004 Elsevier Ltd. All rights reserved.

S100A4 downregulates filopodia formation through increased dynamic instability

Cell migration requires the initial formation of cell protrusions, lamellipodia and/or filopodia, the attachment of the leading lamella to extracellular cues and the formation and efficient recycling of focal contacts at the leading edge. The small calcium binding EF-hand protein S100A4 has been shown to promote cell motility but the direct molecular mechanisms responsible remain to be elucidated. In this work, we provide new evidences indicating that elevated levels of S100A4 affect the stability of filopodia and prevent the maturation of focal complexes. Increasing the levels of S100A4 in a rat mammary benign tumor derived cell line results in acquired cellular migration on the wound healing scratch assay. At the cellular levels, we found that high levels of S100A4 induce the formation of many nascent filopodia, but that only a very small and limited number of those can stably adhere and mature, as opposed to control cells, which generate fewer protrusions but are able to maintain these into more mature projections. This observation was paralleled by the fact that S100A4 overexpressing cells were unable to establish stable focal adhesions. Using different truncated forms of the S100A4 proteins that are unable to bind to myosin IIA, our data suggests that this newly identified functions of S100A4 is myosin-dependent, providing new understanding on the regulatory functions of S100A4 on cellular migration.

Stochastically driven instability in rotating shear flows

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Stochastically driven instability in rotating shear flows

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Design of a fiber scheme for nonlinear Raman pump broadening through modulation instability

In this work we explore numerically an experimentally the dependence of the broadened spectra on the choice of fibers and we analyze a series of basic rules to be taken into account when using nonlinear broadening to reduce the gain ripple of broadband Raman amplifiers

Dual-pump Raman amplification with enhanced flatness using modulation instability

In this work, we utilize modulation instability to the broadening of the two CW-pumps of a wideband Raman amplifier. Applying nonlinear fiber process, we demonstrate a feasibility of a certain control over the broadening process, leading to clear improvements in the flatness of the amplifier gain over its operational bandwidth.

In-cavity pulse shaping and dissipative parametric instability mode-locking in fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral shape, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this work, we review our recent progress on the realisation of pulse shaping in passively- mode-locked fibre lasers by inclusion of an amplitude and phase spectral filter into the laser cavity. We present a fibre laser design in which pulse shaping occurs through filtering of a spectrally nonlinearly broadened pulse in the cavity. This strategy of pulse shaping is illustrated through the numerical demonstration of the laser operation in different pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [1]. As an application of this general approach, we show that the use of an in-cavity flat-top spectral filter makes it possible to directly generate sinc-shaped Nyquist pulses of high quality and of a widely tunable bandwidth from the laser [2]. We also report on a recently-developed versatile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soliton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [3]. Further, we report on our recent results on the passive mode locking of a Raman fibre laser by a recently predicted new type of parametric instability – the dissipative Faraday instability [4], where spatially periodic zig-zag modulation of spectrally dependent losses can lead to pattern formation in the temporal domain. High-order harmonic mode locking is achieved in a very simple experimental configuration, with the laser cavity including an optical fibre and two chirped fibre Bragg gratings, and no additional mode-locking elements. The results not only open up new possibilities for the design of mode-locked lasers, but extend beyond fibre optics to other fields of physics and engineering. References [1] S. Boscolo, C. Finot, H. Karakuzu, P. Petropoulos, “Pulse shaping in mode-locked fiber laser by in-cavity spectral filter,” Opt. Lett., vol. 39, pp. 438–441, 2014. [2] S. Boscolo, C. Finot, S. K. Turitsyn, “Bandwidth programmable optical Nyquist pulse generation in passively mode-locked fiber laser,” IEEE Photon. J., vol. 7, 7802008(8), 2015. [3] J. Peng, S. Boscolo, “Filter-based dispersion-managed versatile ultrafast fibre laser,” Sci. Rep., 2016, In press. [4] A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett., vol. 116, 028701, 2016.

Earnings Variability and Earnings Instability of Women and Men in Canada: How Do the 1990's Compare to the 1980's (Working Paper 25)

It seems to be generally assumed that earnings instability has increased in the last decade or so, as earnings inequality has widened, but is this indeed the case, and if so, to what degree? This paper builds on earlier U.S. work to look at the total variance in individuals’ earnings with a focus on the distinction between permanent earnings variation associated with factors such as human capital investments or other persistent worker attributes, and transitory earnings variation or instability for a given individual from one year to another. We find that there was an increase in overall earnings variability, especially for men, but that the greatest part of this increase was driven by the permanent component – that is, by a widening dispersion of (life-cycle) earnings differentials across workers. The increased volatility of workers’ earnings about their life-cycle earnings profiles played a secondary role in the overall increase in men’s earnings variability, whereas for women this effect was very small or even worked in the opposite direction (depending on the particular age group). Patterns by age and region are also investigated.

Combustion Instability and Active Control: Alternative Fuels, Augmentors, and Modeling Heat Release

Experimental and analytical studies were conducted to explore thermo-acoustic coupling during the onset of combustion instability in various air-breathing combustor configurations. These include a laboratory-scale 200-kW dump combustor and a 100-kW augmentor featuring a v-gutter flame holder. They were used to simulate main combustion chambers and afterburners in aero engines, respectively. The three primary themes of this work includes: 1) modeling heat release fluctuations for stability analysis, 2) conducting active combustion control with alternative fuels, and 3) demonstrating practical active control for augmentor instability suppression. The phenomenon of combustion instabilities remains an unsolved problem in propulsion engines, mainly because of the difficulty in predicting the fluctuating component of heat release without extensive testing. A hybrid model was developed to describe both the temporal and spatial variations in dynamic heat release, using a separation of variables approach that requires only a limited amount of experimental data. The use of sinusoidal basis functions further reduced the amount of data required. When the mean heat release behavior is known, the only experimental data needed for detailed stability analysis is one instantaneous picture of heat release at the peak pressure phase. This model was successfully tested in the dump combustor experiments, reproducing the correct sign of the overall Rayleigh index as well as the remarkably accurate spatial distribution pattern of fluctuating heat release. Active combustion control was explored for fuel-flexible combustor operation using twelve different jet fuels including bio-synthetic and Fischer-Tropsch types. Analysis done using an actuated spray combustion model revealed that the combustion response times of these fuels were similar. Combined with experimental spray characterizations, this suggested that controller performance should remain effective with various alternative fuels. Active control experiments validated this analysis while demonstrating 50-70\% reduction in the peak spectral amplitude. A new model augmentor was built and tested for combustion dynamics using schlieren and chemiluminescence techniques. Novel active control techniques including pulsed air injection were implemented and the results were compared with the pulsed fuel injection approach. The pulsed injection of secondary air worked just as effectively for suppressing the augmentor instability, setting up the possibility of more efficient actuation strategy.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.