On linear instability mechanisms in incompressible open cavity flow

A theoretical study of linear global instability of incompressible flow over a rectangular spanwise-periodic open cavity in an unconfined domain is presented. Comparisons with the limited number of results available in the literature are shown. Subsequently, the parameter space is scanned in a systematic manner, varying Reynolds number, incoming boundary-layer thickness and length-to-depth aspect ratio. This permits documenting the neutral curves and leading eigenmode characteristics of this flow. Correlations constructed using the results obtained collapse all available theoretical data on the three-dimensional instabilities.

Instability Analysis of Incompressible Open Cavity Flows

El problema del flujo sobre una cavidad abierta ha sido estudiado en profundidad en la literatura, tanto por el interés académico del problema como por sus aplicaciones prácticas en gran variedad de problemas ingenieriles, como puede ser el alojamiento del tren de aterrizaje de aeronaves, o el depósito de agua de aviones contraincendios. Desde hace muchos a˜nos se estudian los distintos tipos de inestabilidades asociadas a este problema: los modos bidimensionales en la capa de cortadura, y los modos tridimensionales en el torbellino de recirculación principal dentro de la cavidad. En esta tesis se presenta un estudio paramétrico completo del límite incompresible del problema, empleando la herramienta de estabilidad lineal conocida como BiGlobal. Esta aproximación permite contemplar la estabilidad global del flujo, y obtener tanto la forma como las características de los modos propios del problema físico, sean estables o inestables. El estudio realizado permite caracterizar con gran detalle todos los modos relevantes, así como la envolvente de estabilidad en el espacio paramétrico del problema incompresible (Mach nulo, variación de Reynolds, espesor de capa límite incidente, relación altura/profundidad de la cavidad, y longitud característica de la perturbación en la dirección transversal). A la luz de los resultados obtenidos se proponen una serie de relaciones entre los parámetros y características de los modos principales, como por ejemplo entre el Reynolds crítico de un modo, y la longitud característica del mismo. Los resultados numéricos se contrastan con una campaña experimental, siendo la principal conclusión de dicha comparación que los modos lineales están presentes en el flujo real saturado, pero que existen diferencias notables en frecuencia entre las predicciones teóricas y los experimentos. Para intentar determinar la naturaleza de dichas diferencias se realiza una simulación numérica directa tridimensional, y se utiliza un algoritmo de DMD (descomposición dinámica de modos) para describir el proceso de saturación. ABSTRACT The problem of the flow over an open cavity has been studied in depth in the literature, both for being an interesting academical problem and due to the multitude of industrial applications, like the landing gear of aircraft, or the water deposit of firefighter airplanes. The different types of instabilities appearing in this flow studied in the literature are two: the two-dimensional shear layer modes, and the three-dimensional modes that appear in the main recirculating vortex inside the cavity. In this thesis a parametric study in the incompressible limit of the problem is presented, using the linear stability analysis known as BiGlobal. This approximation allows to obtain the global stability behaviour of the flow, and to capture both the morphological features and the characteristics of the eigenmodes of the physical problem, whether they are stable or unstable. The study presented here characterizes with great detail all the relevant eigenmodes, as well as the hypersurface of instability on the parameter space of the incompressible problem (Mach equal to zero, and variation of the Reynolds number, the incoming boundary layer thickness, the length to depth aspect ratio of the cavity and the spanwise length of the perturbation). The results allow to construct parametric relations between the characteristics of the leading eigenmodes and the parameters of the problem, like for example the one existing between the critical Reynolds number and its characteristic length. The numerical results presented here are compared with those of an experimental campaign, with the main conclusion of said comparison being that the linear eigenmode are present in the real saturated flow, albeit with some significant differences in the frequencies of the experiments and those predicted by the theory. To try to determine the nature of those differences a three-dimensional direct numerical simulation, analyzed with Dynamic Mode Decomposition algorithm, was used to describe the process of saturation.

On the Use of Matrix-Free Shift-Invert Strategies For Global Flow Instability Analysis

A novel time-stepping shift-invert algorithm for linear stability analysis of laminar flows in complex geometries is presented. This method, based on a Krylov subspace iteration, enables the solution of complex non-symmetric eigenvalue problems in a matrix-free framework. Validations and comparisons to the classical exponential method have been performed in three different cases: (i) stenotic flow, (ii) backward-facing step and (iii) lid-driven swirling flow. Results show that this new approach speeds up the required Krylov subspace iterations and has the capability of converging to specific parts of the global spectrum. It is shown that, although the exponential method remains the method of choice if leading eigenvalues are sought, the performance of the present method could be dramatically improved with the use of a preconditioner. In addition, as opposed to other methods, this strategy can be directly applied to any time-stepper, regardless of the temporal or spatial discretization of the latter.

On the role of global flow instability analysis in closed loop flow control

Control of linear flow instabilities has been demonstrated to be an effective theoretical flow control methodology, capable of modifying transitional flows on canonical geometries such as the plane channel and the flat-plate boundary layer. Extending the well-developed theoretical flow control techniques to flows over or through complex geometries requires addressing the issue of efficient capturing of the leading members of the global eigenspectrum pertinent to such flows. The present contribution describes state-of-the-art modal global instability analysis methodologies recently developed in our group, based on matrix formation and time-stepping, respectively. The relative performance of these algorithms is assessed on the recovery of BiGlobal and TriGlobal eigenspectra in the spanwise periodic and the cubic lid-driven cavity, respectively; the adjoint eigenspectrum in the latter flow is recovered for the first time. For three-dimensional flows without any homogeneous spatial direction, the time-stepping methodology was found to outperform the matrix-forming approach and permit recovering the leading TriGlobal eigenmodes in an three-dimensional open cavity of aspect ratio L : D : W = 5 : 1 : 1; theoretical flow control of this configuration is underway.

On the role of global flow instability analysis in closed loop flow control

Control of linear flow instabilities has been demonstrated to be an effective theoretical flow control methodology, capable of modifying transitional flow on canonical geometries such as the plane channel and the flat-plate boundary layer.

Linear instability analysis of incompressible flow over a cuboid cavity

Direct numerical simulations are performed to analyze the three-dimensional instability of flows over three-dimensional cavities. The flow structures at different Reynolds numbers are investigated by using the spectral-element solver nek5000. As the Reynolds number increasing, the lateral wall effects become more important, the recirculation zone shrinks, the front vortex increases and the flow structure inside of the cavity becomes more complex. Results show that the flow bifurcates from a steady state to an oscillatory regime beyond a value of Reynolds number Re = 1100.

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.

Transient excess of MYC activity can elicit genomic instability and tumorigenesis

Overexpression of the MYC protooncogene has been implicated in the genesis of diverse human tumors. Tumorigenesis induced by MYC has been attributed to sustained effects on proliferation and differentiation. Here we report that MYC may also contribute to tumorigenesis by destabilizing the cellular genome. A transient excess of MYC activity increased tumorigenicity of Rat1A cells by at least 50-fold. The increase persisted for >30 days after the return of MYC activity to normal levels. The brief surfeit of MYC activity was accompanied by evidence of genomic instability, including karyotypic abnormalities, gene amplification, and hypersensitivity to DNA-damaging agents. MYC also induced genomic destabilization in normal human fibroblasts, although these cells did not become tumorigenic. Stimulation of Rat1A cells with MYC accelerated their passage through G1/S. Moreover, MYC could force normal human fibroblasts to transit G1 and S after treatment with N-(phosphonoacetyl)-l-aspartate (PALA) at concentrations that normally lead to arrest in S phase by checkpoint mechanisms. Instead, the cells subsequently appeared to arrest in G2. We suggest that the accelerated passage through G1 was mutagenic but that the effect of MYC permitted a checkpoint response only after G2 had been reached. Thus, MYC may contribute to tumorigenesis through a dominant mutator effect.

Instability of signaling resolution models of parent–offspring conflict

Recent signaling resolution models of parent–offspring conflict have provided an important framework for theoretical and empirical studies of communication and parental care. According to these models, signaling of need is stabilized by its cost. However, our computer simulations of the evolutionary dynamics of chick begging and parental investment show that in Godfray’s model the signaling equilibrium is evolutionarily unstable: populations that start at the signaling equilibrium quickly depart from it. Furthermore, the signaling and nonsignaling equilibria are linked by a continuum of equilibria where chicks above a certain condition do not signal and we show that, contrary to intuition, fitness increases monotonically as the proportion of young that signal decreases. This result forces us to reconsider much of the current literature on signaling of need and highlights the need to investigate the evolutionary stability of signaling equilibria based on the handicap principle.

Induction of microsatellite instability by oxidative DNA damage

Instability of repetitive sequences, both in intronic sequences and within coding regions, has been demonstrated to be a hallmark of genomic instability in human cancer. Understanding how these mutational events arise may provide an opportunity for prevention or early intervention in cancer development. To study the source of this instability, we have identified a region of the β-lactamase gene that is tolerant to the insertion of fragments of exogenous DNA as large as 1,614 bp with minimal loss of enzyme activity, as determined by antibiotic resistance. Fragments inserted out-of-frame render Escherichia coli sensitive to antibiotic, and compensatory frameshift mutations that restore the reading frame of β-lactamase can be selected on the basis of antibiotic resistance. We have utilized this site to insert a synthetic microsatellite sequence within the β-lactamase gene and selected for mutations yielding frameshifts. This assay provides for detection of one frameshift mutation in a background of 106 wild-type sequences. Mismatch repair deficiency increased the observed frameshift frequency ≈300-fold. Exposure of plasmid containing microsatellite sequences to hydrogen peroxide resulted in frameshift mutations that were localized exclusively to the microsatellite sequences, whereas DNA damage by UV or N-methyl-N′-nitro-N-nitrosoguanidine did not result in enhanced mutagenesis. We postulate that in tumor cells, endogenous production of oxygen free radicals may be a major factor in promoting instability of microsatellite sequences. This β-lactamase assay may provide a sensitive methodology for the detection and quantitation of mutations associated with the development of cancer.

The human XRCC9 gene corrects chromosomal instability and mutagen sensitivities in CHO UV40 cells

The Chinese hamster ovary (CHO) mutant UV40 cell line is hypersensitive to UV and ionizing radiation, simple alkylating agents, and DNA cross-linking agents. The mutant cells also have a high level of spontaneous chromosomal aberrations and 3-fold elevated sister chromatid exchange. We cloned and sequenced a human cDNA, designated XRCC9, that partially corrected the hypersensitivity of UV40 to mitomycin C, cisplatin, ethyl methanesulfonate, UV, and γ-radiation. The spontaneous chromosomal aberrations in XRCC9 cDNA transformants were almost fully corrected whereas sister chromatid exchanges were unchanged. The XRCC9 genomic sequence was cloned and mapped to chromosome 9p13. The translated XRCC9 sequence of 622 amino acids has no similarity with known proteins. The 2.5-kb XRCC9 mRNA seen in the parental cells was undetectable in UV40 cells. The mRNA levels in testis were up to 10-fold higher compared with other human tissues and up to 100-fold higher compared with other baboon tissues. XRCC9 is a candidate tumor suppressor gene that might operate in a postreplication repair or a cell cycle checkpoint function.

Minisatellite instability in severe combined immunodeficiency mouse cells

We have recently found that okadaic acid, which shows strong inhibitory activity on protein serine/threonine phosphatases and tumor-promoting activity in vivo and in vitro, induces minisatellite mutation (MSM). Human tumors and chemically induced counterparts in experimental animals are also sometimes associated with MSM. In the present study, we demonstrated minisatellite (MS) instability in severe combined immunodeficiency (SCID) cells in which the DNA-dependent protein kinase catalytic subunit (DNA-PKcs) is impaired. Cells from a SCID fibroblast cell line transformed by simian virus 40 large tumor antigen, SC3VA2, and from an embryonal SCID fibroblast cell line, SC1K, were cloned and propagated to 107 to 108 cells, and then subjected to subcloning. After propagation of each subclone to 107 to 108 cells, DNA samples were digested with HinfI and analyzed by Southern blotting using the Pc-1 MS sequence as a probe. Under low-stringency conditions, about 40 MS bands were detected, with 45% ± 6% and 37% ± 3% of SC3VA2 and SC1K cells, respectively, having MSM. In contrast, cells from the RD13B2 cell line, which was established from SCVA2 by introducing human chromosome 8q fragments, on which DNA-PKcs is known to reside, to complement the SCID phenotype, showed a very low frequency of MSM (3% ± 3%). The high frequencies of MSM in SC3VA2 and SC1K were significant, with no difference between the two. The present study clearly demonstrates that MS instability exists in SCID fibroblasts, suggesting that DNA-PKcs might be involved in the stable maintenance of MS sequences in the genome.

The onset and extent of genomic instability in sporadic colorectal tumor progression

Cancer cell genomes contain alterations beyond known etiologic events, but their total number has been unknown at even the order of magnitude level. By sampling colorectal premalignant polyp and carcinoma cell genomes through use of the technique inter-(simple sequence repeat) PCR, we have found genomic alterations to be considerably more abundant than expected, with the mean number of genomic events per carcinoma cell totaling approximately 11,000. Colonic polyps early in the tumor progression pathway showed similar numbers of events. These results indicate that, as with certain hereditary cancer syndromes, genomic destabilization is an early step in sporadic tumor development. Together these results support the model of genomic instability being a cause rather than an effect of malignancy, facilitating vastly accelerated somatic cell evolution, with the observed orderly steps of the colon cancer progression pathway reflecting the consequences of natural selection.

Genetic instability of cancer cells is proportional to their degree of aneuploidy

Genetic and phenotypic instability are hallmarks of cancer cells, but their cause is not clear. The leading hypothesis suggests that a poorly defined gene mutation generates genetic instability and that some of many subsequent mutations then cause cancer. Here we investigate the hypothesis that genetic instability of cancer cells is caused by aneuploidy, an abnormal balance of chromosomes. Because symmetrical segregation of chromosomes depends on exactly two copies of mitosis genes, aneuploidy involving chromosomes with mitosis genes will destabilize the karyotype. The hypothesis predicts that the degree of genetic instability should be proportional to the degree of aneuploidy. Thus it should be difficult, if not impossible, to maintain the particular karyotype of a highly aneuploid cancer cell on clonal propagation. This prediction was confirmed with clonal cultures of chemically transformed, aneuploid Chinese hamster embryo cells. It was found that the higher the ploidy factor of a clone, the more unstable was its karyotype. The ploidy factor is the quotient of the modal chromosome number divided by the normal number of the species. Transformed Chinese hamster embryo cells with a ploidy factor of 1.7 were estimated to change their karyotype at a rate of about 3% per generation, compared with 1.8% for cells with a ploidy factor of 0.95. Because the background noise of karyotyping is relatively high, the cells with low ploidy factor may be more stable than our method suggests. The karyotype instability of human colon cancer cell lines, recently analyzed by Lengnauer et al. [Lengnauer, C., Kinzler, K. W. & Vogelstein, B. (1997) Nature (London) 386, 623–627], also corresponds exactly to their degree of aneuploidy. We conclude that aneuploidy is sufficient to explain genetic instability and the resulting karyotypic and phenotypic heterogeneity of cancer cells, independent of gene mutation. Because aneuploidy has also been proposed to cause cancer, our hypothesis offers a common, unique mechanism of altering and simultaneously destabilizing normal cellular phenotypes.

Evolutionary instability of the major histocompatibility complex class I loci in New World primates

Homologues of the human major histocompatibility complex (MHC) HLA-A, -B, -E, -F, and -G loci are present in all the Catarrhini (Old World primates, apes, and humans), and some of their allelic lineages have survived several speciation events. Analysis of 26 MHC class I cDNAs from seven different genera of New World primates revealed that the Callitrichinae (tamarins and marmosets) are an exception to these rules of MHC stability. In gene trees of primate MHC class I genes, sequences from the Callitrichinae cluster in a genus-specific fashion, whereas in the other genera of New World primates, as in the Catarrhini, they cluster in a transgeneric way. The genus-specific clustering of the Callitrichinae cDNAs indicates that there is no orthology between MHC class I loci in genera of this phyletic group. Additionally, the Callitrichinae genera exhibit limited variability of their MHC class I genes, in contrast to the high variability displayed by all other primates. Each Callitrichinae genus, therefore, expresses its own set of MHC class I genes, suggesting that an unusually high rate of turnover of loci occurs in this subfamily. The limited variability of MHC class I genes in the Callitrichinae is likely the result of the recent origin of these loci.