The Experts below are selected from a list of 45 Experts worldwide ranked by ideXlab platform
Toan T. Nguyen - One of the best experts on this subject based on the ideXlab platform.
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Green Function of Orr--Sommerfeld Equations Away from Critical Layers
Siam Journal on Mathematical Analysis, 2019Co-Authors: Emmanuel Grenier, Toan T. NguyenAbstract:The classical Orr--Sommerfeld Equations are the resolvent Equations of the linearized Navier--Stokes Equations around a stationary shear layer profile in the half plane. In this paper, we derive po...
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Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers
arXiv: Analysis of PDEs, 2017Co-Authors: Emmanuel Grenier, Toan T. NguyenAbstract:This is a continuation and completion of the program (initiated in \cite{GrN1,GrN2}) to derive pointwise estimates on the Green function and sharp bounds on the semigroup of linearized Navier-Stokes around a generic stationary boundary layer profile. This is done via a spectral analysis approach and a careful study of the Orr-Sommerfeld Equations, or equivalently the Navier-Stokes resolvent operator $(\lambda - L)^{-1}$. The earlier work (\cite{GrN1,GrN2}) treats the Orr-Sommerfeld Equations away from critical layers: this is the case when the phase velocity is away from the range of the background profile or when $\lambda$ is away from the Euler continuous spectrum. In this paper, we study the critical case: the Orr-Sommerfeld Equations near critical layers, providing pointwise estimates on the Green function as well as carefully studying the Dunford's contour integral near the critical layers. As an application, we obtain pointwise estimates on the Green function and sharp bounds on the semigroup of the linearized Navier-Stokes problem near monotonic boundary layers that are spectrally stable to the Euler Equations, complementing \cite{GrN1,GrN2} where unstable profiles are considered.
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Green function of Orr Sommerfeld Equations away from critical layers
arXiv: Analysis of PDEs, 2017Co-Authors: Emmanuel Grenier, Toan T. NguyenAbstract:The classical Orr-Sommerfeld Equations are the resolvent Equations of the linearized Navier Stokes Equations around a stationary shear layer profile in the half plane. In this paper, we derive pointwise bounds on the Green function of the Orr Sommerfeld problem away from its critical layers.
Emmanuel Grenier - One of the best experts on this subject based on the ideXlab platform.
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Green Function of Orr--Sommerfeld Equations Away from Critical Layers
Siam Journal on Mathematical Analysis, 2019Co-Authors: Emmanuel Grenier, Toan T. NguyenAbstract:The classical Orr--Sommerfeld Equations are the resolvent Equations of the linearized Navier--Stokes Equations around a stationary shear layer profile in the half plane. In this paper, we derive po...
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Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers
arXiv: Analysis of PDEs, 2017Co-Authors: Emmanuel Grenier, Toan T. NguyenAbstract:This is a continuation and completion of the program (initiated in \cite{GrN1,GrN2}) to derive pointwise estimates on the Green function and sharp bounds on the semigroup of linearized Navier-Stokes around a generic stationary boundary layer profile. This is done via a spectral analysis approach and a careful study of the Orr-Sommerfeld Equations, or equivalently the Navier-Stokes resolvent operator $(\lambda - L)^{-1}$. The earlier work (\cite{GrN1,GrN2}) treats the Orr-Sommerfeld Equations away from critical layers: this is the case when the phase velocity is away from the range of the background profile or when $\lambda$ is away from the Euler continuous spectrum. In this paper, we study the critical case: the Orr-Sommerfeld Equations near critical layers, providing pointwise estimates on the Green function as well as carefully studying the Dunford's contour integral near the critical layers. As an application, we obtain pointwise estimates on the Green function and sharp bounds on the semigroup of the linearized Navier-Stokes problem near monotonic boundary layers that are spectrally stable to the Euler Equations, complementing \cite{GrN1,GrN2} where unstable profiles are considered.
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Green function of Orr Sommerfeld Equations away from critical layers
arXiv: Analysis of PDEs, 2017Co-Authors: Emmanuel Grenier, Toan T. NguyenAbstract:The classical Orr-Sommerfeld Equations are the resolvent Equations of the linearized Navier Stokes Equations around a stationary shear layer profile in the half plane. In this paper, we derive pointwise bounds on the Green function of the Orr Sommerfeld problem away from its critical layers.
Richard R. Simons - One of the best experts on this subject based on the ideXlab platform.
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Measurement of the Initiation and Growth of Surface Water Waves under the Action of a Laminar Air Flow
Coastal Engineering, 2001Co-Authors: Anthony J. Grass, Yuan S. Tsai, Richard R. SimonsAbstract:Miles (1997) recently presented a short review of the progress in theoretical modelling of wave generation by wind during the period since his own pioneering work and that of Benjamin in the late fifties. With minor analytical elaborations and the major advances in computational capabilities, the original Miles-Benjamin model is still widely applied in linear instability analysis of this important practical phenomenon with very useful results. It appears likely, however, that further significant advances in predictive modelling will require improved understanding of the highly complex physics of the interaction process between the turbulent wind flow at the interface and the deforming water surface. At present, this knowledge can only come from direct numerical simulation and advanced physical experimentation, paralleling similar studies of solid wall layer turbulence. On the other hand, a laminar flow is a simple and fixed model. The classic experiment of Schubauer and Skramstad and the later numerical calculation of Kaplan have proved that, on a solid plate, the initial growth rate of some selected frequencies of artificial two-dimensional air waves inside the laminar boundary layer can be explained by linear instability theory. It is, therefore, interesting to know, for the coupled flow at an air-water interface, if the physical processes of the initial formation of water waves under the action of laminar air flow will be dominated by linear instability theory. Following this reasoning, the present wind tunnel study has been designed to provide information on the basic mechanics and physics of initial formation and growth of waves on a flat water surface under the action of laminar air flow. Primary objectives of the study therefore include measurement of the wave growth rate and phase velocity as a function of wave frequency and space under the fundamentally driving laminar flow conditions. A numerical calculation to solve the coupled Orr-Sommerfeld Equations in the space-amplified growth rate was also developed for comparison with observed results.
M. A. Badri - One of the best experts on this subject based on the ideXlab platform.
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A computational study on robust prediction of transition point over NACA0012 aerofoil surfaces from laminar to turbulent flows
Theoretical and Applied Mechanics Letters, 2020Co-Authors: Mojtaba Ahmadi-baloutaki, Ahmad Sedaghat, Mohsen Saghafian, M. A. BadriAbstract:Flow transition from laminar to turbulent is prerequisite to decide whereabouts to apply surface ow control techniques. This appears missing in a number of works in which the control eects were merely investigated without getting insight into alteration of transition position. The aim of this study is to capture the correct position of transition over NACA0012 aerofoil at dierent angles of attack. Firstly, an implicit, time marching, high resolution total variation diminishing (TVD) scheme was developed to solve the governing Navier{Stokes Equations for compressible uid ows around aerofoil sections to obtain velocity proles around the aerofoil surfaces. Secondly, the linear instability solver based on the Orr{Sommerfeld Equations and the e N methods were developed to calculate the onset of transition over the aerofoil surfaces. For the low subsonic Mach number of 0.16, the accuracy of the compressible solutions was assessed by some available experimental results of low speed incompressible ows. In all cases, transition positions were accurately predicted which shows applicability and superiority of the present work to be extended for higher Mach number compressible ows. Here, transition prediction methodology is described and the results of this analysis without active ow control or separation are presented. c
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Control of Transition over Aerofoil Surfaces using Active Suction
International Journal of Flow Control, 2013Co-Authors: Mojtaba Ahmadi-baloutaki, Ahmad Sedaghat, Mohsen Saghafian, M. A. BadriAbstract:The linear stability based on Orr-Sommerfeld Equations and the eN method was employed to determine the onset and control of transition over VFW-VF-2 and NACA653-018 aerofoil sections. For the VFW-VF-2 aerofoil, the effects of active suction on shock-boundary layer interaction were investigated. An enhanced lift to drag ratio was obtained for incidence angles below 6 degrees using suction coefficient as tiny as 0.0006. A parametric study were conducted to show the effects of the suction slot location, suction inclination angle and the extent of sucked flow through slots for flows around the NACA653-018 aerofoil. It was observed that transition was delayed regardless of suction positions. However, maximum delay in transition occurred when the sucked region was located between a critical point and the transition point. For all the cases studied here, lift to drag ratio was increased using active surface suction.
RR Simons - One of the best experts on this subject based on the ideXlab platform.
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On the spatial linear growth of gravity-capillary water waves sheared by a laminar air flow
PHYS FLUIDS, 2005Co-Authors: RR SimonsAbstract:The initial growth of mechanically generated small amplitude water waves below a laminar air stream was examined numerically and experimentally in order to explore the primary growth mechanism, that is, the interfacial instability of coupled laminar air and water flows. Measurements of the laminar velocity profile in the air over the water surface were found to be consistent with Lock's [Q. J. Mech. Appl. Math. 4, 42 (1951)] theory. This profile was then used to calculate the spatial growth rates by solving the Orr-Sommerfeld Equations. The simulation shows that the growth of the boundary layer affects the exponential growth of water waves along the fetch. The sensitivity of the growth rate is observed to vary by a factor of 2 for changes in the laminar velocity profile as small as 2% at the water surface. This indicates that the interfacial instability is strongly influenced by the wind-induced surface current. A laminar airflow was produced in the wind tunnel over mechanically generated monochromatic gravity-capillary water waves with the ka value in the order of 10(-3). The novel experiment was designed to measure the minute changes in the wave slope and phase velocity simultaneously using a highly sensitive reflected twin laser beam technique. Agreement between linear theory and experiments for the spatial development of wave height and phase velocity suggests that the linear instability mechanism determines the initial stages of development of small-scale water waves. (c) 2005 American Institute of Physics.