Innocent Mutabazi - Academia.edu (original) (raw)

Papers by Innocent Mutabazi

Journal of Fluid Mechanics, Dec 15, 2020

Abstract The dynamics of flow of a dielectric fluid in a vertical cylindrical annulus with a fixe... more Abstract The dynamics of flow of a dielectric fluid in a vertical cylindrical annulus with a fixed temperature difference and an increasing alternating electric tension has been investigated using a direct numerical simulation (DNS). The temperature difference imposed on the cylindrical surfaces induces a radial temperature gradient perpendicular to the ground gravity which generates a baroclinic flow ascending near the hot surface and descending near the cold one. The electric field coupled with the permittivity gradient generates a dielectrophoretic buoyancy force which is a source of vorticity. Above a critical value of the electric tension, the flow bifurcates to a pattern of stationary columnar vortices. These columnar vortices which characterize the thermoelectric convection are not axially invariant, in contrast with classical Taylor columns. They bifurcate to regular wave patterns and then to spatio-temporal chaotic patterns when the electric field intensity is increased. The flow and temperature fields, the kinetic energy and the enstrophy of thermoelectric convective regimes are computed for different values of the electric tension.

SPIE Proceedings, Feb 15, 2006

Spatio-temporal dynamics of waves propagating in resonators in opposite directions is investigate... more Spatio-temporal dynamics of waves propagating in resonators in opposite directions is investigated for media with anomalous dispersion. Numerical experiments demonstrated that stationary sources may exist during interaction of the counterpropagating waves in media, where group and phase velocities have opposite signs. We have found regimes when additional spatial periods referred to as "phase slipping" are formed periodically in time in the counterpropagating waves against the background of source.

한국전산유체공학회지, Sep 1, 2009

Numerical simulation has been carried out to investigate the influence of radial temperature grad... more Numerical simulation has been carried out to investigate the influence of radial temperature gradient on the Circular-Couette flow. Varying the Grashof number, we study the detailed flow and temperature fields. The current numerical results show good agreement with the analytical and experimental results currently available. It turns out that spiral vortices are generated by increasing temperature gradient. We classify the flow patterns for various Grashof number based on the characteristics of flow fields and spiral vortices. The correlation between Richardson number with wave number shows that the spiral angle and size of spiral vortices increase with increasing Richardson number.

대한기계학회 논문집 B권, Jun 1, 2006

Comptes Rendus Mecanique, 2017

The stability of the flow of a dielectric fluid confined in a cylindrical annulus submitted to a ... more The stability of the flow of a dielectric fluid confined in a cylindrical annulus submitted to a radial temperature gradient and a radial electric field is investigated theoretically and experimentally. The radial temperature gradient induces a vertical Archimedean buoyancy and a radial dielectrophoretic buoyancy. These two forces intervene simultaneously in the destabilization of the flow, leading to the occurrence of four types of modes depending on the relative intensity of these two buoyancies and on the fluid's properties: hydrodynamic and thermal modes that are axisymmetric and oscillatory, stationary columnar modes and electric modes which are stationary and non-axisymmetric modes. Experiments performed in a parabolic flight show the existence of non-axisymmetric modes that should be either columnar or helicoidal vortices.

Journal of Fluid Mechanics, Mar 29, 2017

We perform a linearized local stability analysis for short-wavelength perturbations of a circular... more We perform a linearized local stability analysis for short-wavelength perturbations of a circular Couette flow with the radial temperature gradient. Axisymmetric and nonaxisymmetric perturbations are considered and both the thermal diffusivity and the kinematic viscosity of the fluid are taken into account. The effect of the asymmetry of the heating both on the centrifugally unstable flows and on the onset of the instabilities of the centrifugally stable flows, including the flow with the Keplerian shear profile, is thoroughly investigated. It is found that the inward temperature gradient destabilizes the Rayleigh stable flow either via Hopf bifurcation if the liquid is a very good heat conductor or via steady state bifurcation if viscosity prevails over the thermal conductance.

It is shown that surface waves propagating against the external current, slowly varying in the ho... more It is shown that surface waves propagating against the external current, slowly varying in the horizontal direction in deep water, are governed by the equation which is tantamount to the Gross-Pitaevskii equation modelling the mean-field dynamics of Bose-Einstein condensate. The repulsive or attractive sign of the cubic term in the Gross-Pitaevskii equation is controlled by the choice of the carrier wavelength of the surface waves, while the spatial variation of the current plays the role of the external potential in that equation. The current profile can be easily controlled in the experiments by small variation of the bottom profile, so that the corresponding effective potential in the Gross-Pitaevskii equation can be made in the form of a well or hump. It is shown that the phenomenon of the Bose-Einstein condensation can be effectively emulated in relatively simple laboratory setups for water waves. Generating perturbations with an appropriate carrier wavelength, one can create patterns in the form of trapped waves which correspond to pinned states of Gross-Pitaevskii equation with local potentials. The estimates demonstrate that the parameters of bottom profile, background current, and surface waves are quite accessible to laboratory experiments.

International Journal of Thermal Sciences, Feb 1, 2016

Abstract The stability of buoyancy-driven convection in a vertical infinite fluid layer between t... more Abstract The stability of buoyancy-driven convection in a vertical infinite fluid layer between two rigid walls with different thermal conductivities and thicknesses is presented. Analytical solutions are derived for parallel base flow, for which linear stability analysis predicts the growth of two-dimensional disturbance. The resulting eigenvalue problem was solved using finite-elements method. Neutral stability curves and associated critical Grashof numbers and wavenumbers are supplied for different characteristic parameters of the flow. It is shown that thermal conductivity and thickness of the walls has a weak influence on hydrodynamic modes but a strong influence on thermal modes which become critical for lower values of Prandtl number than in the case of perfect conducting walls.

River Publishers eBooks, Sep 1, 2022

Physical review fluids, Mar 22, 2021

The stability of the circular Couette flow with two differentially heated cylinders is studied in... more The stability of the circular Couette flow with two differentially heated cylinders is studied in the special cases of hydrodynamically stable rotation regimes. A one-dimensional model is developed to derive the condition of flow stability. This condition combines the curvature of the cylinders, the applied temperature difference between the two cylinders, and the diffusion properties of the fluid. The three-dimensional analysis is performed for two different rotation regimes: the Keplerian regime and the regime where the inner cylinder is stationary. The main results of this analysis is that, for a given radius ratio of the two cylinders, a single parameter combining the Prandtl number and the thermal expansion parameter can describe the critical state of the system. The description is in good agreement with the result of the one-dimensional model. An energy analysis shows a subtle role played by the shear stress in these two rotation regimes.

APS Division of Fluid Dynamics Meeting Abstracts, 2020

We investigate the parametric excitation of newtonian fluid in Couette-Taylor system. The outer c... more We investigate the parametric excitation of newtonian fluid in Couette-Taylor system. The outer cylinder is stationary whereas the rotation of inner cylinder is modulated sinusoidally as Ω(t) = Ω 0 [1 + ε cos (2π f t)]. It is observed that the destabilisation varies inversely as the amplitude of the modulation, eventually attaining insensitivity towards the modulation frequency. An increase in the vortex size can be achieved by increasing either the Taylor number or the modulation frequency.

Geophysical and Astrophysical Fluid Dynamics, Feb 3, 2021

Instability modes of viscoelastic Taylor–Couette flow in the Keplerian regime are investigated us... more Instability modes of viscoelastic Taylor–Couette flow in the Keplerian regime are investigated using both linear stability analysis and experimental detection of critical states. A generalised Rayleigh criterion has been derived and it allows to separate the zone of potential purely elastic instability modes and the zone of stability. The analogy between the instability of viscoelastic Taylor–Couette flow in the Keplerian regime and the magnetorotational instability (MRI) of conducting magnetic fluids is established. Viscoelastic stress tensor can be represented by a tensor product of magnetic-like vectors. This allows to use the Velikhov-Chandrasekhar criterion of the MRI to predict the elasto-rotational instability (ERI). ERI modes obtained in linear stability and in the experiments are assumed to represent the MRI analogue modes as they are observed in the stable zone according to generalised Rayleigh discriminant.

HAL (Le Centre pour la Communication Scientifique Directe), Nov 24, 2013

International audienc

Experiments in Fluids, Jul 1, 2017

An experimental method was developed to measure the growth rate of the capillary instability for ... more An experimental method was developed to measure the growth rate of the capillary instability for free liquid jets. The method uses a standard shadow-graph imaging technique to visualize a jet, produced by extruding a liquid through a circular orifice, and a statistical analysis of the entire jet. The analysis relies on the computation of the standard deviation of a set of jet profiles, obtained in the same experimental conditions. The principle and robustness of the method are illustrated with a set of emulated jet profiles. The method is also applied to free falling jet experiments conducted for various Weber numbers and two low-viscosity solutions: a Newtonian and a viscoelastic one. Growth rate measurements are found in good agreement with linear stability theory in the Rayleigh’s regime, as expected from previous studies. In addition, the standard deviation curve is used to obtain an indirect measurement of the initial perturbation amplitude and to identify beads on a string structure on the jet. This last result serves to demonstrate the capability of the present technique to explore in the future the dynamics of viscoelastic liquid jets.

HAL (Le Centre pour la Communication Scientifique Directe), Mar 26, 2019

l'écoulement de Taylor-Couette, l'écoulement entre deux cylindres coaxiaux en rotation. A partir ... more l'écoulement de Taylor-Couette, l'écoulement entre deux cylindres coaxiaux en rotation. A partir d'uń ecoulement initialement laminaire, les cylindres sont soumis à un arrêt brutal qui génère l'apparition de turbulence transitoire. Deux approches expérimentales complémentaires, les visualisations et les mesures de vitesse par stéréo-PIV, ont été utilisées pour mieux comprendre le phénomène présenté pour plusieurs vitesses initiales de rotation correspondant toujours à un écoulement laminaire. Trois configurations différentes peuvent être distinguées : rotation du cylindre extérieur seulement, co-rotation et contra-rotation. Lorsque seul le cylindre extérieur est en rotation, le seuil d'apparition de la turbulence correspond à un nombre de Reynolds extérieur initial Reo = 606. En co-ou contra-rotation, ce seuil diminue jusqu'à une valeur minimale de Reo = 433. Dans tous les cas, le retour à l'écoulement laminaire est plus lent qu'en stoppant le système à partir d'un écoulement turbulent. Contrairement à l'étude de Verschoof et al. [12], une décroissance auto-similaire de la turbulence n'a pas été observée.

HAL (Le Centre pour la Communication Scientifique Directe), Aug 28, 2017

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

APS Division of Fluid Dynamics Meeting Abstracts, 2020

Journal of Fluid Mechanics, Dec 15, 2020

Abstract The dynamics of flow of a dielectric fluid in a vertical cylindrical annulus with a fixe... more Abstract The dynamics of flow of a dielectric fluid in a vertical cylindrical annulus with a fixed temperature difference and an increasing alternating electric tension has been investigated using a direct numerical simulation (DNS). The temperature difference imposed on the cylindrical surfaces induces a radial temperature gradient perpendicular to the ground gravity which generates a baroclinic flow ascending near the hot surface and descending near the cold one. The electric field coupled with the permittivity gradient generates a dielectrophoretic buoyancy force which is a source of vorticity. Above a critical value of the electric tension, the flow bifurcates to a pattern of stationary columnar vortices. These columnar vortices which characterize the thermoelectric convection are not axially invariant, in contrast with classical Taylor columns. They bifurcate to regular wave patterns and then to spatio-temporal chaotic patterns when the electric field intensity is increased. The flow and temperature fields, the kinetic energy and the enstrophy of thermoelectric convective regimes are computed for different values of the electric tension.

SPIE Proceedings, Feb 15, 2006

Spatio-temporal dynamics of waves propagating in resonators in opposite directions is investigate... more Spatio-temporal dynamics of waves propagating in resonators in opposite directions is investigated for media with anomalous dispersion. Numerical experiments demonstrated that stationary sources may exist during interaction of the counterpropagating waves in media, where group and phase velocities have opposite signs. We have found regimes when additional spatial periods referred to as "phase slipping" are formed periodically in time in the counterpropagating waves against the background of source.

한국전산유체공학회지, Sep 1, 2009

Numerical simulation has been carried out to investigate the influence of radial temperature grad... more Numerical simulation has been carried out to investigate the influence of radial temperature gradient on the Circular-Couette flow. Varying the Grashof number, we study the detailed flow and temperature fields. The current numerical results show good agreement with the analytical and experimental results currently available. It turns out that spiral vortices are generated by increasing temperature gradient. We classify the flow patterns for various Grashof number based on the characteristics of flow fields and spiral vortices. The correlation between Richardson number with wave number shows that the spiral angle and size of spiral vortices increase with increasing Richardson number.

대한기계학회 논문집 B권, Jun 1, 2006

Comptes Rendus Mecanique, 2017

The stability of the flow of a dielectric fluid confined in a cylindrical annulus submitted to a ... more The stability of the flow of a dielectric fluid confined in a cylindrical annulus submitted to a radial temperature gradient and a radial electric field is investigated theoretically and experimentally. The radial temperature gradient induces a vertical Archimedean buoyancy and a radial dielectrophoretic buoyancy. These two forces intervene simultaneously in the destabilization of the flow, leading to the occurrence of four types of modes depending on the relative intensity of these two buoyancies and on the fluid's properties: hydrodynamic and thermal modes that are axisymmetric and oscillatory, stationary columnar modes and electric modes which are stationary and non-axisymmetric modes. Experiments performed in a parabolic flight show the existence of non-axisymmetric modes that should be either columnar or helicoidal vortices.

Journal of Fluid Mechanics, Mar 29, 2017

We perform a linearized local stability analysis for short-wavelength perturbations of a circular... more We perform a linearized local stability analysis for short-wavelength perturbations of a circular Couette flow with the radial temperature gradient. Axisymmetric and nonaxisymmetric perturbations are considered and both the thermal diffusivity and the kinematic viscosity of the fluid are taken into account. The effect of the asymmetry of the heating both on the centrifugally unstable flows and on the onset of the instabilities of the centrifugally stable flows, including the flow with the Keplerian shear profile, is thoroughly investigated. It is found that the inward temperature gradient destabilizes the Rayleigh stable flow either via Hopf bifurcation if the liquid is a very good heat conductor or via steady state bifurcation if viscosity prevails over the thermal conductance.

It is shown that surface waves propagating against the external current, slowly varying in the ho... more It is shown that surface waves propagating against the external current, slowly varying in the horizontal direction in deep water, are governed by the equation which is tantamount to the Gross-Pitaevskii equation modelling the mean-field dynamics of Bose-Einstein condensate. The repulsive or attractive sign of the cubic term in the Gross-Pitaevskii equation is controlled by the choice of the carrier wavelength of the surface waves, while the spatial variation of the current plays the role of the external potential in that equation. The current profile can be easily controlled in the experiments by small variation of the bottom profile, so that the corresponding effective potential in the Gross-Pitaevskii equation can be made in the form of a well or hump. It is shown that the phenomenon of the Bose-Einstein condensation can be effectively emulated in relatively simple laboratory setups for water waves. Generating perturbations with an appropriate carrier wavelength, one can create patterns in the form of trapped waves which correspond to pinned states of Gross-Pitaevskii equation with local potentials. The estimates demonstrate that the parameters of bottom profile, background current, and surface waves are quite accessible to laboratory experiments.

International Journal of Thermal Sciences, Feb 1, 2016

Abstract The stability of buoyancy-driven convection in a vertical infinite fluid layer between t... more Abstract The stability of buoyancy-driven convection in a vertical infinite fluid layer between two rigid walls with different thermal conductivities and thicknesses is presented. Analytical solutions are derived for parallel base flow, for which linear stability analysis predicts the growth of two-dimensional disturbance. The resulting eigenvalue problem was solved using finite-elements method. Neutral stability curves and associated critical Grashof numbers and wavenumbers are supplied for different characteristic parameters of the flow. It is shown that thermal conductivity and thickness of the walls has a weak influence on hydrodynamic modes but a strong influence on thermal modes which become critical for lower values of Prandtl number than in the case of perfect conducting walls.

River Publishers eBooks, Sep 1, 2022

Physical review fluids, Mar 22, 2021

The stability of the circular Couette flow with two differentially heated cylinders is studied in... more The stability of the circular Couette flow with two differentially heated cylinders is studied in the special cases of hydrodynamically stable rotation regimes. A one-dimensional model is developed to derive the condition of flow stability. This condition combines the curvature of the cylinders, the applied temperature difference between the two cylinders, and the diffusion properties of the fluid. The three-dimensional analysis is performed for two different rotation regimes: the Keplerian regime and the regime where the inner cylinder is stationary. The main results of this analysis is that, for a given radius ratio of the two cylinders, a single parameter combining the Prandtl number and the thermal expansion parameter can describe the critical state of the system. The description is in good agreement with the result of the one-dimensional model. An energy analysis shows a subtle role played by the shear stress in these two rotation regimes.

APS Division of Fluid Dynamics Meeting Abstracts, 2020

We investigate the parametric excitation of newtonian fluid in Couette-Taylor system. The outer c... more We investigate the parametric excitation of newtonian fluid in Couette-Taylor system. The outer cylinder is stationary whereas the rotation of inner cylinder is modulated sinusoidally as Ω(t) = Ω 0 [1 + ε cos (2π f t)]. It is observed that the destabilisation varies inversely as the amplitude of the modulation, eventually attaining insensitivity towards the modulation frequency. An increase in the vortex size can be achieved by increasing either the Taylor number or the modulation frequency.

Geophysical and Astrophysical Fluid Dynamics, Feb 3, 2021

Instability modes of viscoelastic Taylor–Couette flow in the Keplerian regime are investigated us... more Instability modes of viscoelastic Taylor–Couette flow in the Keplerian regime are investigated using both linear stability analysis and experimental detection of critical states. A generalised Rayleigh criterion has been derived and it allows to separate the zone of potential purely elastic instability modes and the zone of stability. The analogy between the instability of viscoelastic Taylor–Couette flow in the Keplerian regime and the magnetorotational instability (MRI) of conducting magnetic fluids is established. Viscoelastic stress tensor can be represented by a tensor product of magnetic-like vectors. This allows to use the Velikhov-Chandrasekhar criterion of the MRI to predict the elasto-rotational instability (ERI). ERI modes obtained in linear stability and in the experiments are assumed to represent the MRI analogue modes as they are observed in the stable zone according to generalised Rayleigh discriminant.

HAL (Le Centre pour la Communication Scientifique Directe), Nov 24, 2013

International audienc

Experiments in Fluids, Jul 1, 2017

An experimental method was developed to measure the growth rate of the capillary instability for ... more An experimental method was developed to measure the growth rate of the capillary instability for free liquid jets. The method uses a standard shadow-graph imaging technique to visualize a jet, produced by extruding a liquid through a circular orifice, and a statistical analysis of the entire jet. The analysis relies on the computation of the standard deviation of a set of jet profiles, obtained in the same experimental conditions. The principle and robustness of the method are illustrated with a set of emulated jet profiles. The method is also applied to free falling jet experiments conducted for various Weber numbers and two low-viscosity solutions: a Newtonian and a viscoelastic one. Growth rate measurements are found in good agreement with linear stability theory in the Rayleigh’s regime, as expected from previous studies. In addition, the standard deviation curve is used to obtain an indirect measurement of the initial perturbation amplitude and to identify beads on a string structure on the jet. This last result serves to demonstrate the capability of the present technique to explore in the future the dynamics of viscoelastic liquid jets.

HAL (Le Centre pour la Communication Scientifique Directe), Mar 26, 2019

l'écoulement de Taylor-Couette, l'écoulement entre deux cylindres coaxiaux en rotation. A partir ... more l'écoulement de Taylor-Couette, l'écoulement entre deux cylindres coaxiaux en rotation. A partir d'uń ecoulement initialement laminaire, les cylindres sont soumis à un arrêt brutal qui génère l'apparition de turbulence transitoire. Deux approches expérimentales complémentaires, les visualisations et les mesures de vitesse par stéréo-PIV, ont été utilisées pour mieux comprendre le phénomène présenté pour plusieurs vitesses initiales de rotation correspondant toujours à un écoulement laminaire. Trois configurations différentes peuvent être distinguées : rotation du cylindre extérieur seulement, co-rotation et contra-rotation. Lorsque seul le cylindre extérieur est en rotation, le seuil d'apparition de la turbulence correspond à un nombre de Reynolds extérieur initial Reo = 606. En co-ou contra-rotation, ce seuil diminue jusqu'à une valeur minimale de Reo = 433. Dans tous les cas, le retour à l'écoulement laminaire est plus lent qu'en stoppant le système à partir d'un écoulement turbulent. Contrairement à l'étude de Verschoof et al. [12], une décroissance auto-similaire de la turbulence n'a pas été observée.

HAL (Le Centre pour la Communication Scientifique Directe), Aug 28, 2017

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

APS Division of Fluid Dynamics Meeting Abstracts, 2020