Minimal perturbations approaching the edge of chaos in a Couette flow

This paper provides an investigation of the structure of the stable manifold of the lower branch steady state for the plane Couette flow. Minimal energy perturbations to the laminar state are computed, which approach within a prescribed tolerance the lower branch steady state in a finite time. For small times, such minimal-energy perturbations maintain at least one of the symmetries characterizing the lower branch state. For a sufficiently large time horizon, such symmetries are broken and the minimal-energy perturbations on the stable manifold are formed by localized asymmetrical vortical structures. These minimal-energy perturbations could be employed to develop a control procedure aiming at stabilizing the low-dissipation lower branch state

Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

The present work provides an optimal control strategy, based on the nonlinear Navier–Stokes equations, aimed at hampering the rapid growth of unsteady finite-amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimization and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier–Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is also observed for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternating wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: (i) a wall-normal velocity compensation at small times; (ii) a rotation-counterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account

Numerical Study of the Effect of Freestream Turbulence on by-pass Transition in a Boundary Layer

We use direct numerical simulations in the presence of free-stream turbulence having different values of intensity, T u, and integral length scale, L, in order to determine which kind of structures are involved in the path to transition of a boundary-layer flow. The main aim is to determine under which conditions the path to transition involves structures similar to the linear or non-linear optimal perturbations. For high values of T u and L, we observe a large-amplitude path to transition characterized by localized vortical structures and patches of high- and low-momentum fluctuations. Such a scenario is found to correlate well with the L and hairpin structures resulting from the time evolution of non-linear optimal perturbations, whereas, for lower T u and L, a larger correlation is found with respect to linear optimal disturbances. This indicates that a large-amplitude path to transition exists, different from the one characterized by elongated streaks undergoing secondary instability. To distinguish between the two transition scenarios, a simple parameter linked to the streamwise localisation of high- and low-momentum zones is introduced. Finally, an accurate law to predict the transition location is provided, taking into account both T u and L, valid for both the transition scenarios

Transient growth in the flow past a three-dimensional smooth roughness element

This work provides a global optimization analysis, looking for perturbations inducing the largest energy growth at a finite time in a boundary-layer flow in the presence of smooth three-dimensional roughness elements. Amplification mechanisms are described which can bypass the asymptotical growth of Tollmien–Schlichting waves. Smooth axisymmetric roughness elements of different height have been studied, at different Reynolds numbers. The results show that even very small roughness elements, inducing only a weak deformation of the base flow, can localize the optimal disturbance characterizing the Blasius boundary-layer flow. Moreover, for large enough bump heights and Reynolds numbers, a strong amplification mechanism has been recovered, inducing an increase of several orders of magnitude of the energy gain with respect to the Blasius case. In particular, the highest value of the energy gain is obtained for an initial varicose perturbation, differently to what found for a streaky parallel flow. Optimal varicose perturbations grow very rapidly by transporting the strong wall-normal shear of the base flow, which is localized in the wake of the bump. Such optimal disturbances are found to lead to transition for initial energies and amplitudes considerably smaller than sinuous optimal ones, inducing hairpin vortices downstream of the roughness element

Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow

Recent studies have suggested that in some cases transition can be triggered by some purely nonlinear mechanisms. Here we aim at verifying such an hypothesis, looking for a localized perturbation able to lead a boundary-layer flow to a chaotic state, following a nonlinear route. Nonlinear optimal localized perturbations have been computed by means of an energy optimization which includes the nonlinear terms of the Navier- Stokes equations. Such perturbations lie on the turbulent side of the laminar-turbulent boundary, whereas, for the same value of the initial energy, their linear counterparts do not. The evolution of these perturbations toward a turbulent flow involves the presence of streamwise-inclined vortices at short times and of hairpin structures prior to breakdown

Non-linear Optimal Perturbations in the Asymptotic Suction Boundary-layer

n/

Metastatic tumors to the stomach: clinical and endoscopic features.

AIM: To evaluate the clinical and endoscopic patterns in a large series of patients with metastatic tumors in the stomach. METHODS: A total of 64 patients with gastric metastases from solid malignant tumors were retrospectively examined between 1990 and 2005. The clinicopathological findings were reviewed along with tumor characteristics such as endoscopic pattern, location, size and origin of the primary sites. RESULTS: Common indications for endoscopy were anemia, bleeding and epigastric pain. Metastases presented as solitary (62.5%) or multiple (37.5%) tumors were mainly located in the middle or upper third of stomach. The main primary metastatic tumors were from breast and lung cancer and malignant melanoma. CONCLUSION: As the prognosis of cancer patients has been improving gradually, gastrointestinal (GI) metastases will be encountered more often. Endoscopic examinations should be conducted carefully in patients with malignancies, and endoscopic biopsies and information on the patient's clinical history are useful for correct diagnosis of gastric metastases

Minimal-energy perturbations rapidly approaching the edge state in Couette flow

Transition to turbulence in shear flows is often subcritical, thus the dynamics of the flow strongly depends on the shape and amplitude of the perturbation of the laminar state. In the state space, initial perturbations which directly relaminarize are separated from those that go through a chaotic trajectory by a hypersurface having a very small number of unstable dimensions, known as the edge of chaos. Even for the simple case of plane Couette flow in a small domain, the edge of chaos is characterized by a fractal, folded structure. Thus, the problem of determining the threshold energy to trigger subcritical transition consists in finding the states on this complex hypersurface with minimal distance (in the energy norm) from the laminar state. In this work we have investigated the minimal-energy regions of the edge of chaos, by developing a minimization method looking for the minimal-energy perturbations capable of approaching the edge state (within a prescribed tolerance) in a finite target time T. For sufficiently small target times, the value of the minimal energy has been found to vary with T following a power law, whose best fit is given by E T-1.75. For large values of T, the minimal energy achieves a constant value which corresponds to the energy of the minimal seed, namely the perturbation of minimal energy asymptotically approaching the edge state (Rabin et al., J. Fluid Mech., vol. 738, 2012, R1). For T\geqslant 40, all of the symmetries of the edge state are broken and the minimal perturbation appears to be localized in space with a basic structure composed of scattered patches of streamwise velocity with inclined streamwise vortices on their flanks. Finally, we have found that minimal perturbations originate in a small low-energy zone of the state space and follow very fast similar trajectories towards the edge state. Such trajectories are very different from those of linear optimal disturbances, which need much higher initial amplitudes to approach the edge state. The time evolution of these minimal perturbations represents the most efficient path to subcritical transition for Couette flow

Analysis of the environmental sustainability component, applied to medium-sized companies in the textile sector of the city of Bogotá

Como resultado del proceso de investigación se entrega un documento de referencia orientado principalmente a las medianas empresas del sector textil de la ciudad de Bogotá, de manera que les sirva para orientar el diseño y establecimiento de estrategias de sostenibilidad ambiental en los proyectos de sus organizaciones, con base en el análisis del componente de sostenibilidad ambiental, desde la revisión de los reportes GRI (Global Reporting Initiative) presentados por medianas empresas del sector textil, teniendo como referencia la línea base ambiental del estándar P5 de GPM para Gerencia de Proyectos Sostenibles. En este sentido las medianas empresas tendrán una herramienta de análisis vista como una oportunidad de crecimiento, competitividad, rentabilidad y perdurabilidad en el mercado.As a result of the research process, a reference document is delivered mainly aimed at medium-sized companies in the textile sector in the city of Bogotá, so that it helps them to guide the design and establishment of environmental sustainability strategies in the projects of their organizations. Based on the analysis of the environmental sustainability component, from the review of the GRI (Global Reporting Initiative) reports presented by medium-sized companies in the textile sector, taking as a reference the environmental baseline of the GPM P5 standard for Sustainable Project Management. In this sense, medium-sized companies will have an analysis tool seen as an opportunity for growth, competitiveness, profitability and durability in the market.Magíster en Gerencia de ProyectosMaestrí