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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
171

Arterial Response to Local Mechanical Variables: The Effects of Circumferential and Shear Stress

Wayman, Brian H. 09 April 2007 (has links)
Arteries respond to changes in global mechanical parameters (pressure, flow rate, and longitudinal stretching) by remodeling to restore local parameters (circumferential stress, shear stress, and axial strain) to baseline levels. Because a change in a single global parameter results in changes of multiple local parameters, the effects of individual local parameters on remodeling remain unknown. This study uses a novel approach to study remodeling in organ culture based on independent control of local mechanical parameters. The approach is illustrated by studying the effects of circumferential and shear stress on remodeling-related biological markers. Porcine carotid arteries were cultured for three days at a circumferential stress of 50 kPa or 150 kPa or, in separate experiments, a shear stress of 0.75 Pa or 2.25 Pa. At high circumferential stress, matrix synthesis, smooth muscle cell proliferation, and cell death are significantly greater, but matrix metalloproteinase-2 (MMP-2) and pro-MMP-2 activity are significantly less. In contrast, biological markers measured were unaffected by shear stress. Applications of the proposed approach for improved understanding of remodeling, optimizing mechanical conditioning of tissue engineered arteries, and selection of experimentally motivated growth laws are discussed.
172

Role of shear stress in angiopoietin-2-dependent neovascularization: implications in occlusive vascular disease and atherosclerosis

Tressel, Sarah Lynne 06 March 2008 (has links)
Neovascularization, or the formation of blood vessels, is important in both normal physiological processes as well as pathophysiological processes. The main players in neovascularization, endothelial cells (EC), are highly influenced by hemodynamic shear stress and this may play an important role in neovascularization. Two typical types of shear stress found in the vascular system are a unidirectional laminar shear stress (LS) found in straight regions and a disturbed, oscillatory shear stress (OS) found at branches or curves. At the cellular level, LS is thought to promote EC quiescence whereas OS is thought to promote EC dysfunction. Oscillatory sheared EC are pro-proliferative, pro-migratory, and secrete growth factors, all functions important in neovascularization. There are several diseases that involve both disturbed shear stress and neovascularization, such as atherosclerosis, aortic valve disease, and occlusive vascular disease. In these pathophysiological scenarios fluid shear stress may provide a driving force for neovascularization. Therefore, we hypothesized that oscillatory shear stress promotes greater neovascularization compared to unidirectional laminar shear stress through the secretion of angiogenic factors, which play a physiological role in neovascularization in vivo. To test this hypothesis, we first performed tubule formation and migration assays, two important functions in neovessel formation. We found that OS promotes greater tubule formation and migration of EC as compared to LS and this was mediated through secreted factors. Using gene and protein array analysis, we identified Angiopoietin-2 (Ang2) as being upregulated by OS compared to LS in EC. We found that inhibiting Ang2 blocked OS-mediated tubule formation and migration and that LS-inhibited tubule formation could be rescued by addition of Ang2. In addition, Ang2 was found to be upregulated at sites of disturbed flow in vivo, implicating a physiological role for Ang2. To further investigate the physiological role of Ang2 in neovascularization, we examined the effects of inhibiting Ang2 in a mouse model of hindlimb ischemia, which involves both disturbed flow and neovascularization. We found that Ang2 was upregulated in the ischemic adductor muscle suggesting that it plays a role in recovery during hindlimb ischemia. In addition, we found that inhibiting Ang2 decreased blood flow recovery. Ang2 inhibition resulted in decreased smooth muscle cell coverage of vessels as well as decreased macrophage infiltration. These findings suggest that Ang2 promotes blood flow recovery through the recruitment of smooth muscle cells and formation of collaterals, as well as the recruitment of macrophages that secrete important growth factors and help degrade the extracellular matrix in order for neovascularization to occur. In conclusion, this work illustrates the shear stress regulation of neovessel formation through the expression of Ang2, and the role of Ang2 in neovascularization in vivo. By understanding how angiogenic factors are regulated and what role they play in vivo, we can better understand human disease and develop important therapeutic targets.
173

Turbulent rectangular jets / Τυρβώδεις ορθογωνικές δέσμες εκροή

Alnahhal, Mohammed 11 August 2011 (has links)
Turbulent jet flows issuing from rectangular nozzles are used in many technological and practical applications. Understanding their development and mechanics is important to the design and performance improvement of these applications. Therefore, rectangular jets have been studied extensively over the past decades. Previous investigations have extensively studied the effects of various initial and boundary conditions such as nozzle type, nozzle aspect ratio, nozzle exit turbulence intensity, jet exit Reynolds number. Nozzle type (e.g. smooth contraction nozzle, channel, radially contoured nozzle) has been found to affect the development of these jets. While varying Reynolds number affects the mixing of the jet with its ambient either in the near field or in the far field. Nozzle aspect ratio is also an important boundary condition. It has been experimentally shown that aspect ratio influences the dimensionality of flow field, and hence entrainment between the jet and its ambient. Some of these investigations have used sidewalls (two parallel plates attached to the nozzle short sides) to improve the two-dimensionality of the flow fields, and/or endplate (a wall flush at the nozzle exit) to prevent mixing upstream of the nozzle. Despite this fact very few investigators have specifically considered the effect of endplate or sidewalls on jet development. In the present investigation, the effects of endplates and/or sidewalls on turbulent jets issuing from a rectangular of aspect ratio, AR= 15 have been studied. The mean streamwise and lateral velocity and turbulent characteristics of four different rectangular jets, namely, 1. jet with no endplate and no sidewalls, NENS, 2. jet with endplate and no endplate, WENS, 3. jet without endplate and with sidewalls, NEWS and 4. jet with endplate and with sidewalls, WEWS, have been measured, with x-sensor hot wire anemometry, up to an axial distance of 35 D under identical inlet conditions. Centreline measurements for the four configurations have been collected for three Reynolds number, ReD=10,000, 20,000 and 30,000. For ReD=20,000 measurements in the transverse direction were collected at 13 different downstream locations in the range of x= (0, 1, 2, 2.5, 3, 4, 5, 10, 15, 20, 25, 30 and 35) nozzle widths. The jet with no endplate and no sidewalls (NENS) and the jet with endplate and no sidewalls (WENS) produce nearly similar mean and turbulent velocity profiles indicating insignificant effect of the endplates on their development in the absence of the sidewalls. At Re=20,000, larger mean streamwise velocity values were observed at the edges of the jets (NEWS or WEWS) at distances from nozzle in the range of x/D=3-30 whereas the presence of the endplate has an insignificant effect. The presence or absence of sidewalls is also key factor determining the distributions of the lateral mean velocity component. The presence of sidewalls is associated with lower outward velocities within the edges of the jets and higher inward ones outside the edges. The absence of sidewalls makes the presence of the endplate insignificant and the lateral velocity attains outside the edges low negative values of almost the same level in both cases (NENS, WENS) The presence of an endplate has again some significance only when the sidewalls are present alleviating their effect. Absence of the endplate in jet with sidewalls, leads to lowest spread rate compared to the case with endplates (comparing jet with no endplate and with sidewalls, NEWS and jet with endplate and with sidewalls, WEWS). The presence of an endplate in the absence of sidewalls has again insignificant effect on the jet’s spread rate (comparing jet with no endplate and no sidewalls, NENS and jet with endplate and no sidewalls, WENS). The effects of endplates and/or sidewalls on the decay rates have been investigated for ReD=10,000, 20,000 and 30,000. The presence of the endplate in jets with no sidewalls has insignificant effect on decay rate as was observed for all Reynolds numbers. The presence of the endplate in jet with sidewalls, leads to higher decay rates for all Re tested compared to all cases. The decay rates of the jets with no sidewalls in the presence and absence of the endplate (NENS, WENS) seem to reach their asymptotic values at around ReD=20,000. But the jets with sidewalls have not reached an asymptotic behaviour even at the highest Re tested. The implementation of sidewalls has been found to lead to a decrease of the streamwise turbulent velocity, u′, at the exit shear layer. Current results indicate that the presence of an endplate has an insignificant effect and the estimates for the root mean square of the streamwise velocity fluctuation u′, at the exit shear layer can be grouped according to the absence or presence of sidewalls (3.8% of the mean centreline velocity for NENS and WENS, and 3.1% for NEWS and WEWS). For all turbulent terms, the presence of the endplate has an effect in the presence of sidewalls and the nondimensional streamwise turbulent velocity attains always higher values in its presence (comparing WEWS with NEWS). The profiles of the streamwise turbulent velocity, u′ profiles for the jet with no endplate and no sidewalls, (NENS) and the jet with endplate and no sidewalls, (WENS) are almost indistinguishable in the range x/D=15-35 but the profiles of the jet with no endplate and with sidewalls, (NESWS) and jet with endplate and with sidewalls, (WEWS) indicate a monotonic increase of the values in the central area of the jets. This indicates that the observed trends are mainly due to the presence of the sidewalls and presence or absence endplate has insignificant effect. / Οι επίπεδες τυρβώδεις δέσμες εκροής ανήκουν στην κατηγορία των απλών ροών που παρουσιάζουν μεγάλο ενδιαφέρον για τη ρευστομηχανική και για το λόγο αυτό αποτέλεσαν θέμα μελέτης και έρευνας εδώ και πολλά χρόνια με θεωρητικά, πειραματικά και υπολογιστικά εργαλεία. Οι αρχικές διερευνήσεις επικεντρώθηκαν στη μελέτη του μέσου και τυρβώδους πεδίου της ταχύτητας ή κάποιου παθητικού ρυπαντή προσπαθώντας να αναδείξουν κυρίως τα κοινά χαρακτηριστικά αυτοομοιότητας που αναπτύσσουν οι δέσμες εκροής κυρίως στο απομακρυσμένο πεδίο. Κατά τις τελευταίες δεκαετίες και με δεδομένη τη σημασία που έχουν οι τυρβώδεις ορθογωνικές δέσμες εκροής σε πολλές πρακτικές εφαρμογές (συστήματα καύσης, ψύξη επιφανειών, έλεγχος άντωσης, έλεγχος θορύβου κλπ) η έρευνα προσανατολίστηκε στην επίδραση των αρχικών και συνοριακών συνθηκών (γεωμετρικά χαρακτηριστικά και διαμόρφωση του ακροφυσίου εκροής, αριθμό Reynolds, ένταση τύρβης στην έξοδο) στη διαμόρφωση του εγγύς και του μέσου πεδίου. Σε αρκετές από τις προηγούμενες διερευνήσεις έχουν χρησιμοποιηθεί πλευρικά τοιχώματα (sidewalls) που επεκτείνουν τις στενές πλευρές του ακροφυσίου στη διεύθυνση της ροής ή/και τοίχωμα εκροής (endplate) με στόχο την επίτευξη διδιάστατης ροής. Η σημασία της παρουσίας αυτών των τοιχωμάτων, η οποία έχει μελετηθεί ελάχιστα στο παρελθόν, αποτελεί το στόχο διερεύνησης της παρούσας διατριβής. Η επίδραση των πλευρικών τοιχωμάτων και του τοιχώματος εκροής μελετήθηκαν πειραματικά με τη χρήση ενός ακροφυσίου ομαλής σύγκλισης με λόγο πλευρών 15 με τη χρήση διατάξεων που υλοποιούσαν τέσσερεις τύπους συνοριακών συνθηκών και συγκεκριμένα: 1. Ελεύθερη δέσμη εκροής χωρίς τοίχωμα εκροής - χωρίς πλευρικά τοιχώματα (No endplate - no sidewalls, NENS), 2. Δέσμη εκροής με τοίχωμα εκροής - χωρίς πλευρικά τοιχώματα (With endplate - no sidewalls, WENS), 3. Δέσμη εκροής χωρίς τοίχωμα εκροής - με πλευρικά τοιχώματα (No endplate - with sidewalls, NEWS), 4. Δέσμη εκροής με τοίχωμα εκροής - με πλευρικά τοιχώματα (With endplate - with sidewalls, WEWS). Η πειραματική διερεύνηση έγινε με την χρήση ανεμομετρίας θερμού σύρματος (Hot wire anemometry, HWA) με αισθητήρα τύπου Χ για τη μέτρηση της διαμήκους και της εγκάρσιας συνιστώσας της ταχύτητας. Πραγματοποιήθηκαν μετρήσεις και για τις τέσσερεις διατάξεις επάνω στον άξονα εκροής για τρείς διαφορετικούς αριθμούς Reynolds, ReD = 10,000, 20,000 και 30,000 σε αποστάσεις μέχρι 35 πλάτη ακροφυσίου, D, από το σημείο εκροής. Για ReD = 20000 καταγράφηκαν επίσης οι εγκάρσιες κατανομές των δύο συνιστωσών της ταχύτητας σε δεκατρείς σταθμούς σε αποστάσεις από την έξοδο x/D = 0, 1, 2, 2.5, 3, 4, 5, 10, 15, 20, 25, 30 και 35. Τα αποτελέσματα του μέσου όσο και του τυρβώδους πεδίου καταδεικνύουν ότι η παρουσία των πλευρικών τοιχωμάτων έχει σημαντική επίδραση στην ανάπτυξη του ροϊκού πεδίου. Αντίθετα η παρουσία του τοιχώματος εκροής διαφοροποιεί τα αποτελέσματα μόνο στην περίπτωση που υπάρχουν ήδη τα πλευρικά τοιχώματα.
174

Análise do software CFD++ com vistas a simulação da geração de som em um eslate / The CFD++ analysis aiming the simulation of the slat generated noise

Vinicius Malatesta 11 March 2010 (has links)
A poluição sonora é um problema central de uma grande diversidade de aplicações industriais. Na engenharia, podemos citar diversos casos que geram ruído, como exemplos os trens, automóveis, rotores de helicópteros e o ruído aerodinâmico das aeronaves, o qual se divide em ruído gerado pelos motores a jato e a estruturas da aeronave. No presente momento o ruído dos motores aeronáuticos, principalmente os jatos, atingiu níveis de ruídos semelhantes às estruturas da aeronave, como por exemplo, eslates, flaps e trens de pouso. Desta forma, as autoridades de transporte aéreo estão exigindo também redução no ruído das estruturas. O presente trabalho apresenta a verificação das potencialidades e limitações do software CFD++, programa este adquirido pela EMBRAER e inserido como parte do projeto Aeronave Silenciosa, para assim poder compreender de uma melhor maneira o fenômeno da aeroacústica, e deste modo, poder contribuir para a redução do ruído externo das aeronaves. Para verificar as potencialidades e limitações do CFD++, foi proposto investigar o mecanismo de som do eslate. Tal fenômeno é devido ao deslocamento da camada limite no intradorso do eslate a partir de onde se desenvolve a camada de mistura, foco do presente trabalho. / Noise pollution is a central problem of a wide variety of industrial applications. In engineering, cite several cases that generate noise, as examples trains, automobiles, rotors of helicopters and the noise generated by aircraft, which is divided into noise generated by jet engines and airframe. At present the noise of aircraft engines, largely the jets reached noise levels similar structures, such as slat, flaps and landing gear. Thus, the air transport authorities are also demanding a reduction in noise of the structures of airframe. This report presents the verification of potentialities and limitations of CFD++, a program acquired by EMBRAER and inserted as part of the Silent Aircraft, so they can understand better how the phenomenon of aeroacoustics, and thus able to reduce contribute external noise from aircraft. To check the potentialities and limitations of CFD++, was proposed to investigate the mechanism of sound generated by the slat. This phenomenon is due to the displacement of the boundary layer on the lower surface of the slat from which the mixed layer develops. The mixing layer is the focus of this work.
175

Parametric analysis of turbulent shearing flow over stationary solid waves – a RANS study

Sherikar, Akshay January 2021 (has links)
No description available.
176

Numerical simulation of shear instability in shallow shear flows

Pinilla, Camilo Ernesto. January 2008 (has links)
No description available.
177

Simulating hemodynamics in in vitro culture models: Implications on Nano-biointeractions

Sharma, Monita January 2013 (has links)
No description available.
178

The effect of ultrafine particles on the interfacial and hydrodynamic properties of multiphase systems

Eftekhari, Milad 11 January 2024 (has links)
Ultrafine particles are relevant to many practical applications, including froth flotation, emulsion and foam formation, printing, and drug delivery. Such particles have tremendous effect on the interfacial and hydrodynamic properties of the multiphase systems both in static and dynamic conditions. Combining experimental and theoretical approaches, this research scrutinizes a multidisciplinary subject focusing on hydrodynamic and physicochemical characteristics of the ultrafine particles at fluidic interfaces. In particular, the effect of ultrafine particles on the (i) surface activity of the surfactants of different charges, (ii) mobility of the interfaces, and (iii) kinetics of particles attachment are investigated. In the first part of this thesis the effect of negatively charged silica nanoparticles, as model particles for ultrafine particles, on the interfacial behavior of the cationic surfactant (CTAB) is investigated using Profile Analysis Tensiometry (PAT). The results indicate that neither surfactant concentration nor NPs alone can determine the surface tension of the system, and that the ratio of surfactants to nanoparticles is the decisive factor. Below a critical ratio, the surface tension values remain relatively constant as the free surfactant molecules are completely depleted from the solution due to the formation of nanoparticle-surfactant complexes. Above this critical ratio, the number of free surfactant molecules increases as the surfactant concentration increases, causing the surface tension to decrease. In this regime, free surfactant molecules and nanoparticle-surfactant complexes coexist and can co-adsorb at the interface. This is demonstrated by combining high amplitude compression and dynamic surface tension measurements. Furthermore, the effect of negatively charged nanoparticles on the surface activity of anionic surfactant (SDBS) in an aqueous phase is studied. Although recent studies indicate that nanoparticles increase the surface activity of surfactants through electrostatic repulsive forces, it is observed that the surface activity of surfactants is mainly affected by the change in ionic strength of the system due to the presence of nanoparticles. Several characteristic parameters including the equivalent concentration of the surfactant and the critical micelle concentration (CMC) are theoretically calculated and further employed to validate experimental observations. Based on the obtained results, a criterion to estimate the possible influence of the electrostatic repulsive forces for nanoparticles of different sizes and mass fractions is introduced. In the next step, the effect of ultrafine particles on the mobility of interfaces is investigated. The shear stress of the axisymmetric flow field triggers a nonuniform distribution of the surfactants at the surface of a rising bubble, known as stagnant cap, which gives rise to Marangoni stress that can reduce the mobility of the interface. The conditions in technological processes; however, usually deviate from the linear rise of a single bubble in a quiescent unbounded liquid. Asymmetric shear can act on the bubble surface due to the vorticity in the surrounding flow, or due to the bubble-bubble interactions, which can significantly change the surfactant distribution at the interface. To better understand this effect, Particle Image Velocimetry (PIV) is applied in an experimental setup that is specifically designed to study the hydrodynamics of bubbles and droplets and their interfacial mobility under asymmetric shear flow. Series of PIV experiments are performed with a buoyant bubble/pendant drop at the tip of a capillary placed in a defined shear flow in the presence of surfactants and nanoparticles. A direct experimental observation of the circulating flow at the interface under asymmetric shear, which prevents the formation of the typical stagnant cap is observed. The results show that the interface remains mobile under these conditions regardless of the surfactant concentration. The response of the interface to the surrounding asymmetric flow under successive reduction of the surface area revealed that in the presence of nanoparticles, a contiguous network of particles forms at the interface through densification of surface structures that can drastically change the interfacial mobility of the bubbles and drops. The immobilization is characterized by a dimensionless number, defined as the ratio of the interfacial elasticity to bulk shear forces, which provides an estimate of the interfacial forces required to impose interfacial immobility at a defined flow field. In the last part of this thesis, the kinetics of particles attachment to a buoyant bubble is investigated. The results showed that the technique can be used to investigate the floatability of different particles as a function of various parameters such as hydrophobicity, particle size, and number density. Furthermore, a specific setup was developed to collect the attached particles and measure their mass and size distribution after collection. For a monomodal particle system, the results indicated almost identical size distribution before and after collection with a slight shift to smaller sizes after collection. For a bimodal particle system, on the other hand, results showed that the majority of the collected particles belong to smaller fractions. Next, the effects of ultrafine particles on the kinetics of particle attachment and the distribution and mobility of particles on the bubble surface is studied. It is shown that the ultrafine particles can increase the attachment rate of fine particles and at the same time decrease their packing density. The presence of ultrafine particles at the interface strongly influenced the distribution of the fine particles on bubble surface. The effect is more pronounced for pre-compressed bubbles, where the dense layer of ultrafine particles on the bubble surface completely prevents the attachment of the fine particles. It is also observed that the mobility of the fine particles at the interface changes significantly when ultrafine particles are adsorbed on the bubble surface.
179

Shear-flow instabilities in closed flow / Instabilités dans les écoulements de cisaillement dans un milieu confiné

Lemée, Thomas 12 March 2013 (has links)
Cette étude se concentre sur la compréhension de la physique des instabilités dans différents écoulements de cisaillement, particulièrement la cavité entraînée et la cavité thermocapillaire, où l'écoulement d'un fluide incompressible est assuré soit par le mouvement d’une ou plusieurs parois, soit par des contraintes d’origine thermique.Un code spectral a été validé sur le cas très étudié de la cavité entrainée par une paroi mobile. Il est démontré dans ce cas que l'écoulement transit d'un régime stationnaire à un instationnaire au-delà d'une valeur critique du nombre de Reynolds. Ce travail est le premier à donner une interprétation physique de l'évolution non monotonique du nombre de Reynolds critique en fonction du facteur d'aspect. Lorsque le fluide est entraîné par deux parois mobiles, la cavité entraînée possède un plan de symétrie particulièrement sensible. Des solutions asymétriques peuvent être observés en plus de la solution symétrique au-dessus d'une certaine valeur du nombre de Reynolds. La transition oscillatoire entre la solution symétrique et les solutions asymétriques est expliquée physiquement par les forces en compétition. Dans le cas asymétrique, l'évolution de la topologie permet à l'écoulement de rester stationnaire avec l'augmentation du nombre de Reynolds. Lorsque l'équilibre est perdu une instabilité se manifeste par l'apparition d'un régime oscillatoire dans l'écoulement asymétrique.Dans une cavité thermocapillaire rectangulaire avec une surface libre, Smith et Davis prévoient deux types d'instabilités convectives thermiques: des rouleaux longitudinaux stationnaires et des ondes hydrothermales instationnaires. L'apparition de ses instabilités a été mis en évidence à plusieurs reprises expérimentalement et numériquement. Alors que les applications impliquent souvent plus d'une surface libre, il semble qu'il y ait peu de connaissances sur l'écoulement thermocapillaire entraînée avec deux surfaces libres. Un film liquide libre soumis à des contraintes thermocapillaires possède un plan de symétrie particulier comme dans le cas de la cavité entrainée par deux parois mobiles. Une étude de stabilité linéaire avec deux profils de vitesse pour le film liquide libre est présentée avec différents nombres de Prandtl. Au-delà d'un nombre de Marangoni critique, il est découvert que ces états de base sont sensibles à quatre types d'instabilités convectives thermiques qui peuvent conserver ou briser la symétrie du système. Les mécanismes qui permettent de prédire ces instabilités sont également découverts et interpréter en fonction de la valeur du nombre de Prandtl du fluide. La comparaison avec les travaux de Smith et Davis est faite. Une simulation numérique directe permet de valider les résultats obtenus avec l'étude de stabilité de linéaire. / This study focuses on the understanding of the physics of different instabilities in driven cavities, specifically the lid-driven cavity and the thermocapillarity driven cavity where flow in an incompressible fluid is driven either due to one or many moving walls or due to surface stresses that appear from surface tension gradients caused by thermal gradients. A spectral code is benchmarked on the well-studied case of the lid-cavity driven by one moving wall. In this case, It is shown that the flow transit form a steady regime to unsteady regime beyond a critical value of the Reynolds number. This work is the first to give a physical interpretation of the non-monotonic evolution of the critical Reynolds number versus the size of the cavity. When the fluid is driven by two facing walls moving in the same direction, the cavity possesses a plane of symmetry particularly sensitive. Thus, asymmetrical solutions can be observed in addition to the symmetrical solution above a certain value of the Reynolds number. The oscillatory transition between the symmetric solution and asymmetric solutions is explained physically by the forces in competition. In the asymmetric case, the change of the topology allows the flow to remain steady with increasing the Reynolds number. When the equilibrium is lost, an instability manifests by the appearance of an oscillatory regime in the asymmetric flow. In a rectangular cavity thermocapillary with a free surface, Smith and Davis found two types of thermal convective instabilities: steady longitudinal rolls and unsteady hydrothermal waves. The appearance of its instability has been highlighted repeatedly experimentally and numerically. While applications often involve more than a free surface, it seems that there is little knowledge about the thermocapillary driven flow with two free surfaces. A free liquid film possesses a particular plane of symmetry as in the case of the two-sided lid-driven cavity. A linear stability analysis for the free liquid film with two velocity profiles is presented with various Prandtl numbers. Beyond a critical Marangoni number, it is observed that these basic states are sensitive to four types of thermal convective instabilities, which can keep or break the symmetry of the system. Mechanisms that predict these instabilities are discovered and interpreted according to the value of the Prandtl number of the fluid. Comparison with the work of Smith and Davis is made. A direct numerical simulation is done to validate the results obtained with the linear stability analysis.
180

Mathematical modelling of nonlinear ring waves in a stratified fluid

Zhang, Xizheng January 2015 (has links)
Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this thesis, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition, which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a 2+1-dimensional cylindrical Korteweg-de Vries (cKdV)-type equation for the amplitudes of the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise-constant shear flow, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first order differential equation, constituting generalisation of the dispersion relation in this curvilinear geometry. There exists a striking difference in the shape of the wavefronts: the wavefront of the surface wave is elongated in the shear flow direction while the wavefront of the interfacial wave is squeezed in this direction. We solve the derived 2+1-dimensional cKdV-type equation numerically using a finite-difference scheme. The effects of nonlinearity and dispersion are studied by considering numerical results for surface and interfacial ring waves generated from a localised source with and without shear flow and the 2D dam break problem. In these examples, the linear and nonlinear surface waves are faster than interfacial waves, the wave height decreases faster at the surface, the shear flow leads to the wave height decreasing slower downstream and faster upstream, and the effect becomes more prominent as the shear flow strengthens.

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